TSTP Solution File: SYO246^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO246^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n029.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 293.47s 293.76s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO246^5 : TPTP v7.5.0. Released v4.0.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n029.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 21:31:30 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
% 6.15/6.34 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 6.15/6.34 FOF formula (<kernel.Constant object at 0x22280e0>, <kernel.Type object at 0x2228e60>) of role type named a_type
% 6.15/6.34 Using role type
% 6.15/6.34 Declaring a:Type
% 6.15/6.34 FOF formula ((forall (Xs:(((a->Prop)->Prop)->Prop)), ((forall (X:((a->Prop)->Prop)), ((Xs X)->((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))))->((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), ((Xs X)->(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 cTHM535
% 6.15/6.34 Conjecture to prove = ((forall (Xs:(((a->Prop)->Prop)->Prop)), ((forall (X:((a->Prop)->Prop)), ((Xs X)->((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))))->((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), ((Xs X)->(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
% 6.15/6.34 Parameter a_DUMMY:a.
% 6.15/6.34 We need to prove ['((forall (Xs:(((a->Prop)->Prop)->Prop)), ((forall (X:((a->Prop)->Prop)), ((Xs X)->((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))))->((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), ((Xs X)->(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)))))))))))']
% 6.15/6.34 Parameter a:Type.
% 6.15/6.34 Trying to prove ((forall (Xs:(((a->Prop)->Prop)->Prop)), ((forall (X:((a->Prop)->Prop)), ((Xs X)->((ex (a->Prop)) (fun (Xt:(a->Prop))=> (X Xt)))))->((ex (((a->Prop)->Prop)->(a->Prop))) (fun (Xf:(((a->Prop)->Prop)->(a->Prop)))=> (forall (X:((a->Prop)->Prop)), ((Xs X)->(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)))))))))))
% 6.15/6.34 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))))))))
% 6.15/6.34 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)
% 8.84/9.00 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)
% 8.84/9.00 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)
% 8.84/9.00 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)
% 8.84/9.00 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 8.84/9.00 Found (eta_expansion_dep00 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))))))))
% 8.84/9.00 Found ((eta_expansion_dep0 (fun (x2: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))))))))
% 8.84/9.00 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 8.84/9.00 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 8.84/9.00 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 8.84/9.00 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))))))))
% 8.84/9.00 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))))))))
% 8.84/9.00 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))))))))
% 8.84/9.00 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))))))))
% 8.84/9.00 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))))))))
% 8.84/9.00 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))))))))
% 8.84/9.00 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))))))))
% 8.84/9.00 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))))))))
% 18.85/19.00 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))))))))
% 18.85/19.00 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))))))))
% 18.85/19.00 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)
% 18.85/19.00 Found ((eta_expansion_dep0 (fun (x4: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)
% 18.85/19.00 Found (((eta_expansion_dep a) (fun (x4: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)
% 18.85/19.00 Found (((eta_expansion_dep a) (fun (x4: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)
% 18.85/19.00 Found (((eta_expansion_dep a) (fun (x4: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)
% 18.85/19.00 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 18.85/19.00 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))))))))
% 18.85/19.00 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))))))))
% 18.85/19.00 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))))))))
% 18.85/19.00 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))))))))
% 18.85/19.00 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))))))))
% 18.85/19.00 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))))))))
% 18.85/19.00 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))))))))
% 23.85/24.01 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))))))))
% 23.85/24.01 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)
% 23.85/24.01 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)
% 23.85/24.01 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)
% 23.85/24.01 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)
% 23.85/24.01 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)
% 23.85/24.01 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 23.85/24.01 Found (eta_expansion_dep00 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))))))))
% 23.85/24.01 Found ((eta_expansion_dep0 (fun (x2: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))))))))
% 23.85/24.01 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 23.85/24.01 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 23.85/24.01 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 23.85/24.01 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))))))))
% 23.85/24.01 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))))))))
% 28.98/29.19 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))))))))
% 28.98/29.19 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))))))))
% 28.98/29.19 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))))))))
% 28.98/29.19 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))))))))
% 28.98/29.19 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)))))))
% 28.98/29.19 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)
% 28.98/29.19 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)
% 28.98/29.19 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)
% 28.98/29.19 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)
% 28.98/29.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 28.98/29.19 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)))))))
% 28.98/29.19 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)))))))
% 28.98/29.19 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)))))))
% 28.98/29.19 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)))))))
% 28.98/29.19 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)))))))
% 28.98/29.19 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)
% 34.46/34.66 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)
% 34.46/34.66 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)
% 34.46/34.66 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)
% 34.46/34.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.46/34.66 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)))))))
% 34.46/34.66 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)))))))
% 34.46/34.66 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)))))))
% 34.46/34.66 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)))))))
% 34.46/34.66 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))))))))
% 34.46/34.66 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))))))))
% 34.46/34.66 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))))))))
% 34.46/34.66 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))))))))
% 34.46/34.66 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))))))))
% 34.46/34.66 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))))))))
% 34.46/34.66 Found x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 34.46/34.66 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)))))))
% 34.46/34.66 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)))))))
% 49.35/49.55 Found x20:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 49.35/49.55 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)))))))
% 49.35/49.55 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)))))))
% 49.35/49.55 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))))))))
% 49.35/49.55 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)
% 49.35/49.55 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)
% 49.35/49.55 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)
% 49.35/49.55 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)
% 49.35/49.55 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)
% 49.35/49.55 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 49.35/49.55 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))))))))
% 49.35/49.55 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))))))))
% 49.35/49.55 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))))))))
% 49.35/49.55 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))))))))
% 49.35/49.55 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 49.35/49.55 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))))))))
% 60.85/61.05 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))))))))
% 60.85/61.05 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))))))))
% 60.85/61.05 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))))))))
% 60.85/61.05 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))))))))
% 60.85/61.05 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)
% 60.85/61.05 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)
% 60.85/61.05 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)
% 60.85/61.05 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)
% 60.85/61.05 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)
% 60.85/61.05 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))))))))
% 60.85/61.05 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))))))))
% 60.85/61.05 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))))))))
% 60.85/61.05 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))))))))
% 60.85/61.05 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))))))))
% 65.24/65.41 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))))))))
% 65.24/65.41 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))))))))
% 65.24/65.41 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))))))))
% 65.24/65.41 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))))))))
% 65.24/65.41 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)))))))
% 65.24/65.41 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)
% 65.24/65.41 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)
% 65.24/65.41 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)
% 65.24/65.41 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)
% 65.24/65.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 65.24/65.41 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)))))))
% 65.24/65.41 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)))))))
% 65.24/65.41 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)))))))
% 65.24/65.41 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)))))))
% 65.24/65.41 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)))))))
% 65.24/65.41 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)
% 66.34/66.57 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)
% 66.34/66.57 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)
% 66.34/66.57 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)
% 66.34/66.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 66.34/66.57 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)))))))
% 66.34/66.57 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)))))))
% 66.34/66.57 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)))))))
% 66.34/66.57 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)))))))
% 66.34/66.57 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 66.34/66.57 Found (eta_expansion_dep00 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))))))))
% 66.34/66.57 Found ((eta_expansion_dep0 (fun (x4: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))))))))
% 66.34/66.57 Found (((eta_expansion_dep a) (fun (x4: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))))))))
% 66.34/66.57 Found (((eta_expansion_dep a) (fun (x4: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))))))))
% 66.34/66.57 Found (((eta_expansion_dep a) (fun (x4: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))))))))
% 66.34/66.57 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))))))))
% 66.34/66.57 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)
% 66.34/66.57 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)
% 82.92/83.10 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)
% 82.92/83.10 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)
% 82.92/83.10 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)
% 82.92/83.10 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))))))))
% 82.92/83.10 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))))))))
% 82.92/83.10 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))))))))
% 82.92/83.10 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))))))))
% 82.92/83.10 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))))))))
% 82.92/83.10 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))))))))
% 82.92/83.10 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)))))))
% 82.92/83.10 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)
% 83.51/83.74 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)
% 83.51/83.74 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)
% 83.51/83.74 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)
% 83.51/83.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 83.51/83.74 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)))))))
% 83.51/83.74 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)))))))
% 83.51/83.74 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)))))))
% 83.51/83.74 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)))))))
% 83.51/83.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 83.51/83.74 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)))))))
% 83.51/83.74 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)))))))
% 83.51/83.74 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)))))))
% 83.51/83.74 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)))))))
% 83.51/83.74 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)))))))
% 83.51/83.74 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)
% 83.51/83.74 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)
% 83.51/83.74 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)
% 84.71/84.90 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)
% 84.71/84.90 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 84.71/84.90 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)))))))
% 84.71/84.90 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)))))))
% 84.71/84.90 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 84.71/84.90 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)))))))
% 84.71/84.90 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)))))))
% 84.71/84.90 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)))))))
% 84.71/84.90 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)
% 84.71/84.90 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)
% 84.71/84.90 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)
% 84.71/84.90 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)
% 84.71/84.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 84.71/84.90 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)))))))
% 84.71/84.90 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)))))))
% 84.71/84.90 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)))))))
% 91.43/91.68 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)))))))
% 91.43/91.68 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)))))))
% 91.43/91.68 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)
% 91.43/91.68 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)
% 91.43/91.68 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)
% 91.43/91.68 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)
% 91.43/91.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.43/91.68 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)))))))
% 91.43/91.68 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)))))))
% 91.43/91.68 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)))))))
% 91.43/91.68 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)))))))
% 91.43/91.68 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)))))))
% 91.43/91.68 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)
% 91.43/91.68 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)
% 91.43/91.68 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)
% 95.73/95.97 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)
% 95.73/95.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 95.73/95.97 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)))))))
% 95.73/95.97 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)))))))
% 95.73/95.97 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)))))))
% 95.73/95.97 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)))))))
% 95.73/95.97 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)))))))
% 95.73/95.97 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)
% 95.73/95.97 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)
% 95.73/95.97 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)
% 95.73/95.97 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)
% 95.73/95.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 95.73/95.97 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)))))))
% 95.73/95.97 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)))))))
% 95.73/95.97 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)))))))
% 95.73/95.97 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)))))))
% 95.73/95.97 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))))))))
% 95.73/95.97 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))))))))
% 95.73/95.97 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))))))))
% 109.32/109.52 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))))))))
% 109.32/109.52 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))))))))
% 109.32/109.52 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))))))))
% 109.32/109.52 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)))))))
% 109.32/109.52 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)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 109.32/109.52 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 (P0 ((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)))))))
% 109.32/109.52 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)))))))
% 109.32/109.52 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)->Prop)), ((A Xa)->((and (Xa (Xf Xa))) ((Xf Xa) x1)))))))
% 109.32/109.52 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 (P0 ((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)))))))
% 109.32/109.52 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 109.32/109.52 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x40) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 109.32/109.52 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x40) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 109.32/109.52 Found x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 109.32/109.52 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x40) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 138.77/138.99 Found (fun (x40:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x40) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 138.77/138.99 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))))))))
% 138.77/138.99 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)
% 138.77/138.99 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)
% 138.77/138.99 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)
% 138.77/138.99 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)
% 138.77/138.99 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)
% 138.77/138.99 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 138.77/138.99 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))))))))
% 138.77/138.99 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))))))))
% 138.77/138.99 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))))))))
% 138.77/138.99 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))))))))
% 138.77/138.99 Found x1:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 138.77/138.99 Instantiate: b:=(fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))):(a->Prop)
% 138.77/138.99 Found x1 as proof of (P0 b)
% 138.77/138.99 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))))))))
% 139.59/139.86 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)
% 139.59/139.86 Found ((eta_expansion_dep0 (fun (x3: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)
% 139.59/139.86 Found (((eta_expansion_dep a) (fun (x3: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)
% 139.59/139.86 Found (((eta_expansion_dep a) (fun (x3: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)
% 139.59/139.86 Found (((eta_expansion_dep a) (fun (x3: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)
% 139.59/139.86 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 139.59/139.86 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))))))))
% 139.59/139.86 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))))))))
% 139.59/139.86 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))))))))
% 139.59/139.86 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))))))))
% 139.59/139.86 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))))))))
% 139.59/139.86 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))))))))
% 140.99/141.21 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)
% 140.99/141.21 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)
% 140.99/141.21 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)
% 140.99/141.21 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)
% 140.99/141.21 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))))))))
% 140.99/141.21 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)
% 140.99/141.21 Found ((eta_expansion_dep0 (fun (x6: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)
% 140.99/141.21 Found (((eta_expansion_dep a) (fun (x6: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)
% 140.99/141.21 Found (((eta_expansion_dep a) (fun (x6: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)
% 140.99/141.21 Found (((eta_expansion_dep a) (fun (x6: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)
% 144.52/144.75 Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% 144.52/144.75 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))))))))
% 144.52/144.75 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))))))))
% 144.52/144.75 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))))))))
% 144.52/144.75 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))))))))
% 144.52/144.75 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 144.52/144.75 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 144.52/144.75 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 144.52/144.75 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 144.52/144.75 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 144.52/144.75 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 144.52/144.75 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) x5)))))))
% 144.52/144.75 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) x5)))))))
% 144.52/144.75 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) x5)))))))
% 144.52/144.75 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) x5)))))))
% 144.52/144.75 Found eq_ref00:=(eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))):(((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 144.52/144.75 Found (eq_ref0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 144.52/144.75 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 152.30/152.51 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 152.30/152.51 Found ((eq_ref Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) as proof of (((eq Prop) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))) b)
% 152.30/152.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 152.30/152.51 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) x5)))))))
% 152.30/152.51 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) x5)))))))
% 152.30/152.51 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) x5)))))))
% 152.30/152.51 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) x5)))))))
% 152.30/152.51 Found x1:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 152.30/152.51 Instantiate: f:=(fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))):(a->Prop)
% 152.30/152.51 Found x1 as proof of (P0 f)
% 152.30/152.51 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 152.30/152.51 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 152.30/152.51 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 152.30/152.51 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 152.30/152.51 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 152.30/152.51 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((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))))))))
% 152.30/152.51 Found x1:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 152.30/152.51 Instantiate: f:=(fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))):(a->Prop)
% 152.30/152.51 Found x1 as proof of (P0 f)
% 152.30/152.51 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 152.30/152.51 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 152.30/152.51 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 152.30/152.51 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 165.56/165.78 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((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) x2)))))))
% 165.56/165.78 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) ((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))))))))
% 165.56/165.78 Found x50:(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))))))))
% 165.56/165.78 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 165.56/165.78 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 165.56/165.78 Found x50:(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))))))))
% 165.56/165.78 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 165.56/165.78 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 165.56/165.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.56/165.78 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 x3)))))))
% 165.56/165.78 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 x3)))))))
% 165.56/165.78 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 x3)))))))
% 165.56/165.78 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 x3)))))))
% 165.56/165.78 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) x3))))))):(((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) x3))))))) ((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)))))))
% 165.56/165.78 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 166.60/166.86 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 x3)))))))
% 166.60/166.86 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 x3)))))))
% 166.60/166.86 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 x3)))))))
% 166.60/166.86 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 x3)))))))
% 166.60/166.86 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) x3))))))):(((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) x3))))))) ((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)))))))
% 166.60/166.86 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 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) x3))))))) 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) x3))))))) b)
% 166.60/166.86 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) x3))))))):(((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) x3))))))) ((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)))))))
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 166.99/167.22 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 166.99/167.22 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 x3)))))))
% 166.99/167.22 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 x3)))))))
% 166.99/167.22 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 x3)))))))
% 166.99/167.22 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 x3)))))))
% 166.99/167.22 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) x3))))))):(((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) x3))))))) ((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)))))))
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 166.99/167.22 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) x3))))))) 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) x3))))))) b)
% 178.39/178.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.39/178.64 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 x3)))))))
% 178.39/178.64 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 x3)))))))
% 178.39/178.64 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 x3)))))))
% 178.39/178.64 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 x3)))))))
% 178.39/178.64 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))))))))
% 178.39/178.64 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)
% 178.39/178.64 Found ((eta_expansion_dep0 (fun (x2: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)
% 178.39/178.64 Found (((eta_expansion_dep a) (fun (x2: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)
% 178.39/178.64 Found (((eta_expansion_dep a) (fun (x2: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)
% 178.39/178.64 Found (((eta_expansion_dep a) (fun (x2: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)
% 178.39/178.64 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 178.39/178.64 Found (eta_expansion_dep00 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))))))))
% 178.39/178.64 Found ((eta_expansion_dep0 (fun (x2: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))))))))
% 178.39/178.64 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 178.39/178.64 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 178.39/178.64 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 185.67/185.95 Found x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 185.67/185.95 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))))=> x60) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 185.67/185.95 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))))=> x60) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 185.67/185.95 Found x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 185.67/185.95 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))))=> x60) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 185.67/185.95 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5))))))))=> x60) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x5)))))))
% 185.67/185.95 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)))))))
% 185.67/185.95 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)
% 185.67/185.95 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)
% 185.67/185.95 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)
% 185.67/185.95 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)
% 185.67/185.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 185.67/185.95 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)))))))
% 185.67/185.95 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)))))))
% 185.67/185.95 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)))))))
% 185.67/185.95 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)))))))
% 185.67/185.95 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)))))))
% 186.26/186.48 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)
% 186.26/186.48 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)
% 186.26/186.48 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)
% 186.26/186.48 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)
% 186.26/186.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.26/186.48 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)))))))
% 186.26/186.48 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)))))))
% 186.26/186.48 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)))))))
% 186.26/186.48 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)))))))
% 186.26/186.48 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)))))))
% 186.26/186.48 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)
% 186.26/186.48 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)
% 186.26/186.48 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)
% 186.26/186.48 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)
% 186.26/186.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.26/186.48 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)))))))
% 186.26/186.48 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)))))))
% 186.26/186.48 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)))))))
% 186.26/186.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 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)
% 195.18/195.48 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)
% 195.18/195.48 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)
% 195.18/195.48 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)
% 195.18/195.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.18/195.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.18/195.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 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)))))))
% 195.18/195.48 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)
% 195.18/195.48 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)
% 197.06/197.36 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)
% 197.06/197.36 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)
% 197.06/197.36 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)))))))
% 197.06/197.36 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)
% 197.06/197.36 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)
% 197.06/197.36 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)
% 197.06/197.36 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)
% 197.06/197.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 197.06/197.36 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)))))))
% 197.06/197.36 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)))))))
% 197.06/197.36 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)))))))
% 197.06/197.36 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)))))))
% 197.06/197.36 Found x50:(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))))))))
% 197.06/197.36 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 197.06/197.36 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 197.06/197.36 Found x50:(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))))))))
% 202.47/202.70 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 202.47/202.70 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 202.47/202.70 Found x50:(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))))))))
% 202.47/202.70 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 202.47/202.70 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 202.47/202.70 Found x50:(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))))))))
% 202.47/202.70 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 202.47/202.70 Found (fun (x50:(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)))))))))=> x50) 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))))))))
% 202.47/202.70 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) x3))))))):(((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) x3))))))) ((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)))))))
% 202.47/202.70 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) x3))))))) 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) x3))))))) b)
% 202.47/202.70 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) x3))))))) 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) x3))))))) b)
% 202.47/202.70 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) x3))))))) 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) x3))))))) b)
% 206.96/207.27 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) x3))))))) 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) x3))))))) b)
% 206.96/207.27 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 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) x3))))))):(((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) x3))))))) ((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)))))))
% 206.96/207.27 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) x3))))))) 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) x3))))))) b)
% 206.96/207.27 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) x3))))))) 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) x3))))))) b)
% 206.96/207.27 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) x3))))))) 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) x3))))))) b)
% 206.96/207.27 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) x3))))))) 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) x3))))))) b)
% 206.96/207.27 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 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 x3)))))))
% 206.96/207.27 Found x40:(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) x3)))))))
% 208.87/209.18 Found (fun (x40:(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) x3))))))))=> x40) as proof of (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) x3)))))))
% 208.87/209.18 Found (fun (x40:(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) x3))))))))=> x40) as proof of (P0 ((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)))))))
% 208.87/209.18 Found x40:(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) x3)))))))
% 208.87/209.18 Found (fun (x40:(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) x3))))))))=> x40) as proof of (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) x3)))))))
% 208.87/209.18 Found (fun (x40:(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) x3))))))))=> x40) as proof of (P0 ((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)))))))
% 208.87/209.18 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 208.87/209.18 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)))))))
% 208.87/209.18 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)))))))
% 208.87/209.18 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)))))))
% 208.87/209.18 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)))))))
% 208.87/209.18 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)))))))
% 208.87/209.18 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)
% 208.87/209.18 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)
% 208.87/209.18 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)
% 208.87/209.18 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)
% 218.67/218.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.67/218.91 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)))))))
% 218.67/218.91 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)))))))
% 218.67/218.91 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)))))))
% 218.67/218.91 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)))))))
% 218.67/218.91 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)))))))
% 218.67/218.91 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)
% 218.67/218.91 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)
% 218.67/218.91 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)
% 218.67/218.91 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)
% 218.67/218.91 Found x3:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 218.67/218.91 Instantiate: b:=(fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))):(a->Prop)
% 218.67/218.91 Found x3 as proof of (P0 b)
% 218.67/218.91 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))))))))
% 218.67/218.91 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)
% 230.27/230.51 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)
% 230.27/230.51 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)
% 230.27/230.51 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)
% 230.27/230.51 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)
% 230.27/230.51 Found x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x60) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x60) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 230.27/230.51 Found x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x60) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1))))))))=> x60) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 230.27/230.51 Found x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x60) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x60) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 230.27/230.51 Found x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x60) as proof of (P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 230.27/230.51 Found (fun (x60:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3))))))))=> x60) as proof of (P0 (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x3)))))))
% 236.91/237.19 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))))))))
% 236.91/237.19 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)
% 236.91/237.19 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)
% 236.91/237.19 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)
% 236.91/237.19 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)
% 236.91/237.19 Found x1:(P0 b)
% 236.91/237.19 Instantiate: b:=(fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))):(a->Prop)
% 236.91/237.19 Found (fun (x1:(P0 b))=> x1) 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))))))))
% 236.91/237.19 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx)))))))))
% 236.91/237.19 Found (fun (P0:((a->Prop)->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% 236.91/237.19 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))))))))
% 236.91/237.19 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))))))))
% 236.91/237.19 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))))))))
% 236.91/237.19 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))))))))
% 240.65/240.89 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)
% 240.65/240.89 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)
% 240.65/240.89 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)
% 240.65/240.89 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)
% 240.65/240.89 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 240.65/240.89 Found (eta_expansion_dep00 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))))))))
% 240.65/240.89 Found ((eta_expansion_dep0 (fun (x2: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))))))))
% 240.65/240.89 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 240.65/240.89 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 240.65/240.89 Found (((eta_expansion_dep a) (fun (x2: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))))))))
% 240.65/240.89 Found x1:(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))))))))
% 240.65/240.89 Instantiate: 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))))))):(a->Prop)
% 240.65/240.89 Found x1 as proof of (P0 b)
% 240.65/240.89 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))))))))
% 240.65/240.89 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)
% 240.65/240.89 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)
% 240.65/240.89 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)
% 244.57/244.86 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)
% 244.57/244.86 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)
% 244.57/244.86 Found x40:(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) x3)))))))
% 244.57/244.86 Found (fun (x40:(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) x3))))))))=> x40) as proof of (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) x3)))))))
% 244.57/244.86 Found (fun (x40:(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) x3))))))))=> x40) as proof of (P0 ((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)))))))
% 244.57/244.86 Found x40:(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) x3)))))))
% 244.57/244.86 Found (fun (x40:(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) x3))))))))=> x40) as proof of (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) x3)))))))
% 244.57/244.86 Found (fun (x40:(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) x3))))))))=> x40) as proof of (P0 ((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)))))))
% 244.57/244.86 Found x3:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 244.57/244.86 Instantiate: f:=(fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))):(a->Prop)
% 244.57/244.86 Found x3 as proof of (P0 f)
% 244.57/244.86 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 244.57/244.86 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 244.57/244.86 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 244.57/244.86 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 244.57/244.86 Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 244.57/244.86 Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:a), (((eq Prop) (f x)) ((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))))))))
% 246.95/247.20 Found x3:(P (fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))))
% 246.95/247.20 Instantiate: f:=(fun (Xx:a)=> (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb Xx))))))):(a->Prop)
% 246.95/247.20 Found x3 as proof of (P0 f)
% 246.95/247.20 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 246.95/247.20 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 246.95/247.20 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 246.95/247.20 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 246.95/247.20 Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((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) x4)))))))
% 246.95/247.20 Found (fun (x4:a)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:a), (((eq Prop) (f x)) ((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))))))))
% 246.95/247.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.95/247.20 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)))))))
% 246.95/247.20 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)))))))
% 246.95/247.20 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)))))))
% 246.95/247.20 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)))))))
% 246.95/247.20 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)))))))
% 246.95/247.20 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)
% 246.95/247.20 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)
% 246.95/247.20 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)
% 246.95/247.20 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)
% 248.62/248.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 248.62/248.88 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)))))))
% 248.62/248.88 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)))))))
% 248.62/248.88 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)))))))
% 248.62/248.88 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)))))))
% 248.62/248.88 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)))))))
% 248.62/248.88 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)
% 248.62/248.88 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)
% 248.62/248.88 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)
% 248.62/248.88 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)
% 248.62/248.88 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)))))))
% 248.62/248.88 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)
% 248.62/248.88 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)
% 259.53/259.79 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)
% 259.53/259.79 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)
% 259.53/259.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 259.53/259.79 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)))))))
% 259.53/259.79 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)))))))
% 259.53/259.79 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)))))))
% 259.53/259.79 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)))))))
% 259.53/259.79 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)))))))
% 259.53/259.79 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)
% 259.53/259.79 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)
% 259.53/259.79 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)
% 259.53/259.79 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)
% 259.53/259.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 259.53/259.79 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)))))))
% 259.53/259.79 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)))))))
% 259.53/259.79 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)))))))
% 259.53/259.79 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)))))))
% 259.53/259.79 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))))))))
% 275.79/276.04 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)))))))) b0)
% 275.79/276.04 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)))))))) b0)
% 275.79/276.04 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)))))))) b0)
% 275.79/276.04 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)))))))) b0)
% 275.79/276.04 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)))))))) b0)
% 275.79/276.04 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% 275.79/276.04 Found (eta_expansion_dep00 b0) as proof of (((eq (a->Prop)) b0) (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))))))))
% 275.79/276.04 Found ((eta_expansion_dep0 (fun (x2:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (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))))))))
% 275.79/276.04 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (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))))))))
% 275.79/276.04 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (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))))))))
% 275.79/276.04 Found (((eta_expansion_dep a) (fun (x2:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (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))))))))
% 275.79/276.04 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))))))))
% 275.79/276.04 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)
% 275.79/276.04 Found ((eta_expansion_dep0 (fun (x4: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)
% 284.18/284.44 Found (((eta_expansion_dep a) (fun (x4: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)
% 284.18/284.44 Found (((eta_expansion_dep a) (fun (x4: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)
% 284.18/284.44 Found (((eta_expansion_dep a) (fun (x4: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)
% 284.18/284.44 Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% 284.18/284.44 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))))))))
% 284.18/284.44 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))))))))
% 284.18/284.44 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))))))))
% 284.18/284.44 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))))))))
% 284.18/284.44 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))))))))
% 284.18/284.44 Found x1:(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))))))))
% 284.18/284.44 Instantiate: f:=(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))))))):(a->Prop)
% 284.18/284.44 Found x1 as proof of (P0 f)
% 284.18/284.44 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 284.18/284.44 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 284.18/284.44 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 284.18/284.44 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 284.18/284.44 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 284.18/284.44 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x))))))))
% 284.18/284.44 Found x1:(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))))))))
% 293.47/293.76 Instantiate: f:=(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))))))):(a->Prop)
% 293.47/293.76 Found x1 as proof of (P0 f)
% 293.47/293.76 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 293.47/293.76 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 293.47/293.76 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 293.47/293.76 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 293.47/293.76 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x2)))))))
% 293.47/293.76 Found (fun (x2:a)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:a), (((eq Prop) (f x)) (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x))))))))
% 293.47/293.76 Found x40:(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)))))))
% 293.47/293.76 Found (fun (x40:(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))))))))=> x40) as proof of (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)))))))
% 293.47/293.76 Found (fun (x40:(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))))))))=> x40) as proof of (P0 ((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)))))))
% 293.47/293.76 Found x40:(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)))))))
% 293.47/293.76 Found (fun (x40:(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))))))))=> x40) as proof of (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)))))))
% 293.47/293.76 Found (fun (x40:(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))))))))=> x40) as proof of (P0 ((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)))))))
% 293.47/293.76 Found x2:(P (forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))))
% 293.47/293.76 Instantiate: b:=(forall (Xa:((a->Prop)->Prop)), ((A Xa)->((ex (a->Prop)) (fun (Xb:(a->Prop))=> ((and (Xa Xb)) (Xb x1)))))):Prop
% 293.47/293.76 Found x2 as proof of (P0 b)
% 293.47/293.76 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)))))))
% 293.47/293.76 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 X
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