TSTP Solution File: SEV270^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV270^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n188.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:58 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV270^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n188.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:40:51 CDT 2014
% % CPUTime : 300.02
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x267f518>, <kernel.DependentProduct object at 0x28d6170>) of role type named cL
% Using role type
% Declaring cL:((fofType->Prop)->Prop)
% FOF formula (<kernel.Constant object at 0x26618c0>, <kernel.DependentProduct object at 0x28d6a70>) of role type named cG
% Using role type
% Declaring cG:((fofType->Prop)->Prop)
% FOF formula (((and ((and ((and (forall (C:((fofType->Prop)->Prop)), (((and (forall (Xx:(fofType->Prop)), ((C Xx)->(cG Xx)))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (C Y)) (Y Xx))))))->((ex ((fofType->Prop)->Prop)) (fun (D:((fofType->Prop)->Prop))=> ((and ((and (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw D)))) (forall (Xx:(fofType->Prop)), ((D Xx)->(C Xx))))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (D Y)) (Y Xx))))))))))) (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx)))))))) (forall (Y:(fofType->Prop)), ((cL Y)->((ex fofType) (fun (Xx:fofType)=> (Y Xx))))))) (forall (Y:(fofType->Prop)), ((cL Y)->(cG (fun (Xx:fofType)=> ((Y Xx)->False))))))->((ex fofType) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))) of role conjecture named cTHM628_pme
% Conjecture to prove = (((and ((and ((and (forall (C:((fofType->Prop)->Prop)), (((and (forall (Xx:(fofType->Prop)), ((C Xx)->(cG Xx)))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (C Y)) (Y Xx))))))->((ex ((fofType->Prop)->Prop)) (fun (D:((fofType->Prop)->Prop))=> ((and ((and (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw D)))) (forall (Xx:(fofType->Prop)), ((D Xx)->(C Xx))))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (D Y)) (Y Xx))))))))))) (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx)))))))) (forall (Y:(fofType->Prop)), ((cL Y)->((ex fofType) (fun (Xx:fofType)=> (Y Xx))))))) (forall (Y:(fofType->Prop)), ((cL Y)->(cG (fun (Xx:fofType)=> ((Y Xx)->False))))))->((ex fofType) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((and ((and ((and (forall (C:((fofType->Prop)->Prop)), (((and (forall (Xx:(fofType->Prop)), ((C Xx)->(cG Xx)))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (C Y)) (Y Xx))))))->((ex ((fofType->Prop)->Prop)) (fun (D:((fofType->Prop)->Prop))=> ((and ((and (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw D)))) (forall (Xx:(fofType->Prop)), ((D Xx)->(C Xx))))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (D Y)) (Y Xx))))))))))) (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx)))))))) (forall (Y:(fofType->Prop)), ((cL Y)->((ex fofType) (fun (Xx:fofType)=> (Y Xx))))))) (forall (Y:(fofType->Prop)), ((cL Y)->(cG (fun (Xx:fofType)=> ((Y Xx)->False))))))->((ex fofType) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))))']
% Parameter fofType:Type.
% Parameter cL:((fofType->Prop)->Prop).
% Parameter cG:((fofType->Prop)->Prop).
% Trying to prove (((and ((and ((and (forall (C:((fofType->Prop)->Prop)), (((and (forall (Xx:(fofType->Prop)), ((C Xx)->(cG Xx)))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (C Y)) (Y Xx))))))->((ex ((fofType->Prop)->Prop)) (fun (D:((fofType->Prop)->Prop))=> ((and ((and (forall (Xw:(((fofType->Prop)->Prop)->Prop)), (((and (Xw (fun (Xx:(fofType->Prop))=> False))) (forall (Xr:((fofType->Prop)->Prop)) (Xx:(fofType->Prop)), ((Xw Xr)->(Xw (fun (Xt:(fofType->Prop))=> ((or (Xr Xt)) (((eq (fofType->Prop)) Xt) Xx)))))))->(Xw D)))) (forall (Xx:(fofType->Prop)), ((D Xx)->(C Xx))))) (forall (Xx:fofType), ((ex (fofType->Prop)) (fun (Y:(fofType->Prop))=> ((and (D Y)) (Y Xx))))))))))) (forall (X:(fofType->Prop)) (Y:(fofType->Prop)), (((and (cL X)) (cL Y))->((or (forall (Xx:fofType), ((X Xx)->(Y Xx)))) (forall (Xx:fofType), ((Y Xx)->(X Xx)))))))) (forall (Y:(fofType->Prop)), ((cL Y)->((ex fofType) (fun (Xx:fofType)=> (Y Xx))))))) (forall (Y:(fofType->Prop)), ((cL Y)->(cG (fun (Xx:fofType)=> ((Y Xx)->False))))))->((ex fofType) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion0 Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion0 Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x0))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x2))))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))):(((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) (fun (x:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found (eta_expansion_dep00 (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eta_expansion000:=(eta_expansion00 (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))):(((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) (fun (x:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found (eta_expansion00 (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found ((eta_expansion0 Prop) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x4))))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))):(((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) (fun (x:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found (eta_expansion_dep00 (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) as proof of (((eq (fofType->Prop)) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa))))) b)
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eta_expansion000:=(eta_expansion00 (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))):(((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) (fun (x:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found (eta_expansion00 (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found ((eta_expansion0 Prop) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))):(((eq (fofType->Prop)) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) (fun (x:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found (eta_expansion00 (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found ((eta_expansion0 Prop) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion fofType) Prop) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y:(fofType->Prop)), ((cL Y)->(Y x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))):(((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) (fun (x:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found (eta_expansion_dep00 (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) as proof of (((eq (fofType->Prop)) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8))))) b)
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))):(((eq (fofType->Prop)) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) (fun (x:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found (eta_expansion_dep00 (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60))))) as proof of (((eq (fofType->Prop)) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))) b)
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6))))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 x2):(((eq fofType) x2) x2)
% Found (eq_ref0 x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 x2):(((eq fofType) x2) x2)
% Found (eq_ref0 x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% Found (eq_ref0 x4) as proof of (((eq fofType) x4) b)
% Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x6:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x6)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eq_ref00:=(eq_ref0 x2):(((eq fofType) x2) x2)
% Found (eq_ref0 x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% Found (eq_ref0 x4) as proof of (((eq fofType) x4) b)
% Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xa:fofType)=> (forall (Y:(fofType->Prop)), ((cL Y)->(Y Xa)))))
% Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% Found (eq_ref0 x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) b)
% Found eq_ref00:=(eq_ref0 x2):(((eq fofType) x2) x2)
% Found (eq_ref0 x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) b)
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x60:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x60)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x8:fofType)=> (forall (Y0:(fofType->Prop)), ((cL Y0)->(Y0 x8)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:f
% EOF
%------------------------------------------------------------------------------