TSTP Solution File: SYO244^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO244^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 00:51:00 EDT 2022
% Result : Timeout 300.05s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO244^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Fri Mar 11 21:12:04 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 9.35/9.60 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 9.35/9.60 FOF formula (<kernel.Constant object at 0x24a42d8>, <kernel.Type object at 0x247db90>) of role type named a_type
% 9.35/9.60 Using role type
% 9.35/9.60 Declaring a:Type
% 9.35/9.60 FOF formula (((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), (((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))->(X (Xf X))))))->(forall (A:(((a->Prop)->Prop)->Prop)), (((and ((ex ((a->Prop)->Prop)) (fun (X:((a->Prop)->Prop))=> (A X)))) (forall (X:((a->Prop)->Prop)), ((A X)->((ex (a->Prop)) (fun (Xu:(a->Prop))=> (X Xu))))))->(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))))) of role conjecture named cTHM535B
% 9.35/9.60 Conjecture to prove = (((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), (((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))->(X (Xf X))))))->(forall (A:(((a->Prop)->Prop)->Prop)), (((and ((ex ((a->Prop)->Prop)) (fun (X:((a->Prop)->Prop))=> (A X)))) (forall (X:((a->Prop)->Prop)), ((A X)->((ex (a->Prop)) (fun (Xu:(a->Prop))=> (X Xu))))))->(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))))):Prop
% 9.35/9.60 Parameter a_DUMMY:a.
% 9.35/9.60 We need to prove ['(((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), (((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))->(X (Xf X))))))->(forall (A:(((a->Prop)->Prop)->Prop)), (((and ((ex ((a->Prop)->Prop)) (fun (X:((a->Prop)->Prop))=> (A X)))) (forall (X:((a->Prop)->Prop)), ((A X)->((ex (a->Prop)) (fun (Xu:(a->Prop))=> (X Xu))))))->(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))))']
% 9.35/9.60 Parameter a:Type.
% 9.35/9.60 Trying to prove (((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), (((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))->(X (Xf X))))))->(forall (A:(((a->Prop)->Prop)->Prop)), (((and ((ex ((a->Prop)->Prop)) (fun (X:((a->Prop)->Prop))=> (A X)))) (forall (X:((a->Prop)->Prop)), ((A X)->((ex (a->Prop)) (fun (Xu:(a->Prop))=> (X Xu))))))->(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))))
% 9.35/9.60 Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 9.35/9.60 Found (eq_ref0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 9.35/9.60 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 13.55/13.71 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 13.55/13.71 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 13.55/13.71 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 13.55/13.71 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 13.55/13.71 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 13.55/13.71 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 13.55/13.71 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 13.55/13.71 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 13.55/13.71 Found x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found (fun (x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x10) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found (fun (x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x10) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found (fun (x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x10) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found (fun (x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x10) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found (fun (x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x10) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 13.55/13.71 Found (fun (x10:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x10) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 27.93/28.10 Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (x:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x))))))))
% 27.93/28.10 Found (eta_expansion00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 27.93/28.10 Found ((eta_expansion0 Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 27.93/28.10 Found (((eta_expansion a) Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 27.93/28.10 Found (((eta_expansion a) Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 27.93/28.10 Found (((eta_expansion a) Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 27.93/28.10 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 27.93/28.10 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 27.93/28.10 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 27.93/28.10 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 27.93/28.10 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 27.93/28.10 Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (x:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x))))))))
% 27.93/28.10 Found (eta_expansion00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 27.93/28.10 Found ((eta_expansion0 Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 27.93/28.10 Found (((eta_expansion a) Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 39.06/39.25 Found (((eta_expansion a) Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 39.06/39.25 Found (((eta_expansion a) Prop) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 39.06/39.25 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 39.06/39.25 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 39.06/39.25 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 39.06/39.25 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 39.06/39.25 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 39.06/39.25 Found x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 39.06/39.25 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 39.06/39.25 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) (fun (x:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x))))))))
% 41.64/41.82 Found (eta_expansion_dep00 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 41.64/41.82 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 41.64/41.82 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 41.64/41.82 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 41.64/41.82 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 41.64/41.82 Found x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 41.64/41.82 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 41.64/41.82 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 41.64/41.82 Found x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 41.64/41.82 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 41.64/41.82 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 52.73/52.92 Found x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 52.73/52.92 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 52.73/52.92 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 52.73/52.92 Found x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 52.73/52.92 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 52.73/52.92 Found (fun (x30:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 52.73/52.92 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 52.73/52.92 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 52.73/52.92 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 52.73/52.92 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 52.73/52.92 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 52.73/52.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 52.73/52.92 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 52.73/52.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 52.73/52.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 52.73/52.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 52.73/52.92 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 52.73/52.92 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 68.10/68.34 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 68.10/68.34 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 68.10/68.34 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 68.10/68.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 68.10/68.34 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 68.10/68.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 68.10/68.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 68.10/68.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 68.10/68.34 Found x10:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 68.10/68.34 Found (fun (x10:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x10) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 68.10/68.34 Found (fun (x10:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x10) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 68.10/68.34 Found x10:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 68.10/68.34 Found (fun (x10:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x10) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 68.10/68.34 Found (fun (x10:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x10) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 68.10/68.34 Found x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 68.10/68.34 Found (fun (x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x20) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 106.18/106.47 Found (fun (x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x20) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 106.18/106.47 Found x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 106.18/106.47 Found (fun (x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x20) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 106.18/106.47 Found (fun (x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x20) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 106.18/106.47 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (x:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x))))))))
% 106.18/106.47 Found (eta_expansion_dep00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 106.18/106.47 Found ((eta_expansion_dep0 (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 106.18/106.47 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 106.18/106.47 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 106.18/106.47 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 106.18/106.47 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 106.18/106.47 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 106.18/106.47 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 106.18/106.47 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 106.18/106.47 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 106.18/106.47 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 107.18/107.39 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 107.18/107.39 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 107.18/107.39 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 107.18/107.39 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 107.18/107.39 Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) (fun (x:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x))))))))
% 107.18/107.39 Found (eta_expansion00 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 107.18/107.39 Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 107.18/107.39 Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 107.18/107.39 Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 107.18/107.39 Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 107.18/107.39 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 107.18/107.39 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 107.18/107.39 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 125.98/126.23 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 125.98/126.23 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 125.98/126.23 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 125.98/126.23 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 125.98/126.23 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 125.98/126.23 Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) (fun (x:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x))))))))
% 125.98/126.23 Found (eta_expansion00 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 125.98/126.23 Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 125.98/126.23 Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 125.98/126.23 Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 125.98/126.23 Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 125.98/126.23 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (x:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x))))))))
% 125.98/126.23 Found (eta_expansion_dep00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found ((eta_expansion_dep0 (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 128.88/129.16 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 128.88/129.16 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 128.88/129.16 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 128.88/129.16 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 128.88/129.16 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) (fun (x:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x))))))))
% 128.88/129.16 Found (eta_expansion_dep00 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found ((eta_expansion_dep0 (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 128.88/129.16 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 146.78/147.05 Found (((eta_expansion_dep a) (fun (x6:a)=> Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))) b)
% 146.78/147.05 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 146.78/147.05 Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 146.78/147.05 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 146.78/147.05 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 146.78/147.05 Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 146.78/147.05 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 146.78/147.05 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 146.78/147.05 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 146.78/147.05 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 146.78/147.05 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 146.78/147.05 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 146.78/147.05 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 146.78/147.05 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 146.78/147.05 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 146.78/147.05 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 146.78/147.05 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 149.17/149.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 149.17/149.50 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 149.17/149.50 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 149.17/149.50 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 149.17/149.50 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 149.17/149.50 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 149.17/149.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 149.17/149.50 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 149.17/149.50 Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 149.17/149.50 Found (eq_ref0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 167.06/167.30 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 167.06/167.30 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 167.06/167.30 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 167.06/167.30 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 167.06/167.30 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 167.06/167.30 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 167.06/167.30 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 167.06/167.30 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 167.06/167.30 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 167.06/167.30 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 167.06/167.30 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 167.06/167.30 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 167.06/167.30 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 167.06/167.30 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 167.06/167.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 167.06/167.30 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 167.06/167.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 168.98/169.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 168.98/169.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 168.98/169.22 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 168.98/169.22 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 168.98/169.22 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 168.98/169.22 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 168.98/169.22 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))) b)
% 168.98/169.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.98/169.22 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 168.98/169.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 168.98/169.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 168.98/169.22 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x3)))))))
% 168.98/169.22 Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))):(((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 168.98/169.22 Found (eq_ref0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 168.98/169.22 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 177.85/178.16 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 177.85/178.16 Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))) b)
% 177.85/178.16 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 177.85/178.16 Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 177.85/178.16 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 177.85/178.16 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 177.85/178.16 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 200.72/201.05 Found eq_ref00:=(eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))):(((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 200.72/201.05 Found (eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 200.72/201.05 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 201.34/201.62 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 201.34/201.62 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 201.34/201.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 201.34/201.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 201.34/201.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 201.34/201.62 Found eq_ref00:=(eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))):(((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 201.34/201.62 Found (eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 201.34/201.62 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 201.34/201.62 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 201.34/201.62 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 204.51/204.80 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 204.51/204.80 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 204.51/204.80 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 204.51/204.80 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 204.51/204.80 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 204.51/204.80 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 204.51/204.80 Found eq_ref00:=(eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))):(((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 204.51/204.80 Found (eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 204.51/204.80 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 204.51/204.80 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 204.51/204.80 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 204.51/204.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 204.51/204.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 204.51/204.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 204.51/204.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 204.51/204.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 215.55/215.83 Found eq_ref00:=(eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))):(((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 215.55/215.83 Found (eq_ref0 ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 215.55/215.83 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 215.55/215.83 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 215.55/215.83 Found ((eq_ref Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) as proof of (((eq Prop) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))) b)
% 215.55/215.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 215.55/215.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 215.55/215.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 215.55/215.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 215.55/215.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 215.55/215.83 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 215.55/215.83 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 215.55/215.83 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 215.55/215.83 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 215.55/215.83 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 215.55/215.83 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 225.13/225.47 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 225.13/225.47 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 225.13/225.47 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 225.13/225.47 Found x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 225.13/225.47 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 225.13/225.47 Found (fun (x50:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))=> x50) as proof of (P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 225.13/225.47 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 225.13/225.47 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 225.13/225.47 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 225.13/225.47 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 225.13/225.47 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 225.13/225.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 225.13/225.47 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 225.13/225.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 225.13/225.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 225.13/225.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 225.13/225.47 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 239.50/239.79 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 239.50/239.79 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 239.50/239.79 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 239.50/239.79 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 239.50/239.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.50/239.79 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 239.50/239.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 239.50/239.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 239.50/239.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 239.50/239.79 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 239.50/239.79 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 239.50/239.79 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 239.50/239.79 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 239.50/239.79 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 239.50/239.79 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x40) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 239.50/239.79 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 239.50/239.79 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 239.50/239.79 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 251.71/252.03 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 251.71/252.03 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 251.71/252.03 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 251.71/252.03 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 251.71/252.03 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 251.71/252.03 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 251.71/252.03 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 251.71/252.03 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 251.71/252.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 251.71/252.03 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 251.71/252.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 251.71/252.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 251.71/252.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 251.71/252.03 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 251.71/252.03 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 251.71/252.03 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 268.76/269.10 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 268.76/269.10 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))) b)
% 268.76/269.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 268.76/269.10 Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 268.76/269.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 268.76/269.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 268.76/269.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 268.76/269.10 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 268.76/269.10 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 268.76/269.10 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 268.76/269.10 Found x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 268.76/269.10 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 268.76/269.10 Found (fun (x30:(P (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx)))))))))=> x30) as proof of (P0 (fun (Xx:a)=> ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) Xx))))))))
% 268.76/269.10 Found x20:(P ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 268.76/269.10 Found (fun (x20:(P ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1))))))))=> x20) as proof of (P ((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (Xa:((a->Prop
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