%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV179^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n115.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 13:33:50 EDT 2014

% Result   : Timeout 300.04s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV179^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.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 08:21:51 CDT 2014
% % CPUTime  : 300.04 
% 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 0x162c1b8>, <kernel.DependentProduct object at 0x164c1b8>) of role type named cD_FOR_X5309_type
% Using role type
% Declaring cD_FOR_X5309:(((fofType->Prop)->fofType)->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->fofType)->(fofType->Prop))) cD_FOR_X5309) (fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt))))))) of role definition named cD_FOR_X5309_def
% A new definition: (((eq (((fofType->Prop)->fofType)->(fofType->Prop))) cD_FOR_X5309) (fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Defined: cD_FOR_X5309:=(fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt))))))
% FOF formula (forall (Xh:((fofType->Prop)->fofType)), ((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh)))) of role conjecture named cTHM144C_pme
% Conjecture to prove = (forall (Xh:((fofType->Prop)->fofType)), ((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xh:((fofType->Prop)->fofType)), ((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh))))']
% Parameter fofType:Type.
% Definition cD_FOR_X5309:=(fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(((fofType->Prop)->fofType)->(fofType->Prop)).
% Trying to prove (forall (Xh:((fofType->Prop)->fofType)), ((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh))))
% Found eq_ref00:=(eq_ref0 (Xh (cD_FOR_X5309 Xh))):(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_ref0 (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found x0:(x (Xh x))
% Found x0 as proof of False
% Found (fun (x0:(x (Xh x)))=> x0) as proof of False
% Found (fun (x0:(x (Xh x)))=> x0) as proof of ((x (Xh x))->False)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))):(((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) (fun (x:(fofType->Prop))=> ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eta_expansion_dep00 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b)
% Found x010:False
% Found (fun (x02:(((eq fofType) (Xh x)) (Xh x00)))=> x010) as proof of False
% Found (fun (x02:(((eq fofType) (Xh x)) (Xh x00)))=> x010) as proof of ((((eq fofType) (Xh x)) (Xh x00))->False)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt)))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt)))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt)))))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->Prop)->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):(((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found (eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found x01:(P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P1 (f x))
% Found x01:(P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P1 (f x))
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% 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) x)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_trans0000 ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((eq_trans000 (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((((eq_trans0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_sym00 (f x)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found ((conj00 (fun (x01:(x (Xh x)))=> x01)) iff_sym) as proof of ((and ((x (Xh x))->False)) b)
% Found (((conj0 b) (fun (x01:(x (Xh x)))=> x01)) iff_sym) as proof of ((and ((x (Xh x))->False)) b)
% Found ((((conj ((x (Xh x))->False)) b) (fun (x01:(x (Xh x)))=> x01)) iff_sym) as proof of ((and ((x (Xh x))->False)) b)
% Found ((((conj ((x (Xh x))->False)) b) (fun (x01:(x (Xh x)))=> x01)) iff_sym) as proof of ((and ((x (Xh x))->False)) b)
% Found ((((conj ((x (Xh x))->False)) b) (fun (x01:(x (Xh x)))=> x01)) iff_sym) as proof of (P b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found x0:(P0 (Xh (cD_FOR_X5309 Xh)))
% Instantiate: x:=(cD_FOR_X5309 Xh):(fofType->Prop)
% Found (fun (x0:(P0 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of (P0 (Xh x))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of ((P0 (Xh (cD_FOR_X5309 Xh)))->(P0 (Xh x)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of b
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found (((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found (((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans0000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found (((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found (((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found x01:(P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P1 (f x))
% Found x01:(P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P0 (f x))
% Found (fun (x01:(P0 (f x)))=> x01) as proof of (P1 (f x))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found x0:(P0 (f x))
% Instantiate: b:=(f x):Prop
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found x0:(P0 (f x))
% Instantiate: b:=(f x):Prop
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found x02:(P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P1 (f x))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x)))
% Found x02:(P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P1 (f x))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Instantiate: b:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) b))=> ((eq_sym010 x00) P0)) ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_sym01 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (fun (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0)) as proof of (P0 (f x))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0)) as proof of ((P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P0 (f x)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0)) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym000 (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_sym00 (f x)) (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b) (Xh x00))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x00))
% Found eq_ref00:=(eq_ref0 (Xh (cD_FOR_X5309 Xh))):(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_ref0 (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found x0:(x (Xh x))
% Found x0 as proof of False
% Found (fun (x0:(x (Xh x)))=> x0) as proof of False
% Found (fun (x0:(x (Xh x)))=> x0) as proof of ((x (Xh x))->False)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_trans0000 ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((eq_trans000 (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((((eq_trans0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Instantiate: a:=(forall (P:Prop), ((iff P) P)):Prop
% Found iff_refl as proof of a
% Found eq_sym0000:=(eq_sym000 x02):(((eq fofType) b) (Xh x))
% Found (eq_sym000 x02) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_sym00 b) x02) as proof of (((eq fofType) b) (Xh x))
% Found (((eq_sym0 (Xh x)) b) x02) as proof of (((eq fofType) b) (Xh x))
% Found ((((eq_sym fofType) (Xh x)) b) x02) as proof of (((eq fofType) b) (Xh x))
% Found ((((eq_sym fofType) (Xh x)) b) x02) as proof of (((eq fofType) b) (Xh x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x00))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x00))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found True:Prop
% Found True as proof of Prop
% Found (x02 True) as proof of False
% Found (x02 True) as proof of False
% Found (fun (x02:(x (Xh x)))=> (x02 True)) as proof of False
% Found (fun (x02:(x (Xh x)))=> (x02 True)) as proof of ((x (Xh x))->False)
% Found ((conj00 (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found (((conj0 a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found ((((conj ((x (Xh x))->False)) a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found ((((conj ((x (Xh x))->False)) a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found ((((conj ((x (Xh x))->False)) a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found x02:(x (Xh x))
% Found x02 as proof of False
% Found (fun (x02:(x (Xh x)))=> x02) as proof of False
% Found (fun (x02:(x (Xh x)))=> x02) as proof of ((x (Xh x))->False)
% Found x0:(P0 (Xh (cD_FOR_X5309 Xh)))
% Instantiate: x:=(cD_FOR_X5309 Xh):(fofType->Prop)
% Found (fun (x0:(P0 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of (P0 (Xh x))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of ((P0 (Xh (cD_FOR_X5309 Xh)))->(P0 (Xh x)))
% Found (fun (P0:(fofType->Prop)) (x0:(P0 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of a
% Found True:Prop
% Found True as proof of Prop
% Found (x02 True) as proof of False
% Found (x02 True) as proof of False
% Found (fun (x02:(x (Xh x)))=> (x02 True)) as proof of False
% Found (fun (x02:(x (Xh x)))=> (x02 True)) as proof of ((x (Xh x))->False)
% Found x0:(P0 (f x))
% Instantiate: b:=(f x):Prop
% Found x0 as proof of (P1 b)
% Found x0:(P0 (f x))
% Instantiate: b:=(f x):Prop
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_trans0000 ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found (((eq_trans000 (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found (((((eq_trans0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((eq_sym00 (f x)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found (((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) P0)) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found x02:(P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P1 (f x))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found x02:(P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P0 (f x))
% Found (fun (x02:(P0 (f x)))=> x02) as proof of (P1 (f x))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((eq_trans00000 ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_trans0000 x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) b)) (x00:(((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_trans000 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) b)) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((((eq_trans0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x0:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (x00:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((((eq_trans Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x0) x00) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((eq_ref Prop) (f x))) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (fun (x02:(P0 (f x)))=> x02))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found x010:False
% Found (fun (x02:(((eq fofType) (Xh x)) (Xh x00)))=> x010) as proof of False
% Found (fun (x02:(((eq fofType) (Xh x)) (Xh x00)))=> x010) as proof of ((((eq fofType) (Xh x)) (Xh x00))->False)
% Found x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Instantiate: b:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) b))=> ((eq_sym010 x00) P0)) ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_sym01 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0) as proof of (P0 (f x))
% Found (fun (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0)) as proof of (P0 (f x))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0)) as proof of ((P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P0 (f x)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0)) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym000 (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((eq_sym00 (f x)) (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found (((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found ((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) (fun (P0:(Prop->Prop)) (x0:(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P0)) ((eq_ref Prop) (f x))) x0))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% Found iff_refl as proof of b
% Found iff_refl as proof of a
% Found ((conj00 (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found (((conj0 a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found ((((conj ((x (Xh x))->False)) a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found ((((conj ((x (Xh x))->False)) a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of ((and ((x (Xh x))->False)) a)
% Found ((((conj ((x (Xh x))->False)) a) (fun (x02:(x (Xh x)))=> (x02 True))) iff_refl) as proof of (P a)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_trans0000 ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((eq_trans000 (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((((eq_trans0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_trans0000 ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((eq_trans000 (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (((((eq_trans0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_trans0000 ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found (((eq_trans000 (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found (((((eq_trans0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found eq_ref00:=(eq_ref0 (Xh (cD_FOR_X5309 Xh))):(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_ref0 (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found ((eq_ref fofType) (Xh (cD_FOR_X5309 Xh))) as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))
% Found x0:(x (Xh x))
% Found x0 as proof of False
% Found (fun (x0:(x (Xh x)))=> x0) as proof of False
% Found (fun (x0:(x (Xh x)))=> x0) as proof of ((x (Xh x))->False)
% Found x0:(P0 (f x))
% Instantiate: a:=(f x):Prop
% Found x0 as proof of (P1 a)
% Found x0:(P0 (f x))
% Instantiate: a:=(f x):Prop
% Found x0 as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))):(((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) (fun (x:(fofType->Prop))=> ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eta_expansion00 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) b) b0)
% Found x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Instantiate: b:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found x0 as proof of (P3 b)
% Found x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Instantiate: b:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found x0 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) b))=> ((eq_sym010 x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_sym01 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (fun (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of (P2 (f x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of ((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 (f x)))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym0000 (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_sym0000 (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) b))=> ((eq_sym010 x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_sym01 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (fun (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of (P2 (f x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of ((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 (f x)))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found (eq_sym0000 (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_sym0000 (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> ((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) P0)) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) b) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=x:(fofType->Prop);b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x))) as proof of (((eq Prop) b) (f x))
% Found ((eq_trans0000 ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found (((eq_trans000 (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) b) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((eq_trans00 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found (((((eq_trans0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (forall (P:(Prop->Prop)), ((P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P (f x))))
% Found ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) (((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) ((((((eq_trans Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))) ((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((eq_ref Prop) (f x))))) (fun (x01:(P0 (f x)))=> x01))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=x:(fofType->Prop);b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh a)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh a)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found x010:False
% Found (fun (x02:(((eq fofType) (Xh x)) (Xh x00)))=> x010) as proof of False
% Found (fun (x02:(((eq fofType) (Xh x)) (Xh x00)))=> x010) as proof of ((((eq fofType) (Xh x)) (Xh x00))->False)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% 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) x)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found x0:(P0 (f x))
% Instantiate: a:=(f x):Prop
% Found x0 as proof of (P1 a)
% Found x0:(P0 (f x))
% Instantiate: a:=(f x):Prop
% Found x0 as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):(((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found (eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found eta_expansion000:=(eta_expansion00 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))):(((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) (fun (x:(fofType->Prop))=> ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eta_expansion00 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) b) b0)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Instantiate: b:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found x0 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found ((eq_sym0100 ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) b))=> ((eq_sym010 x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((eq_sym01 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0) as proof of (P2 (f x))
% Found (fun (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of (P2 (f x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of ((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 (f x)))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0)) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x))
% Found ((eq_sym0000 (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found ((eq_sym0000 (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((eq_sym000 x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((eq_sym00 (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> ((((eq_sym0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> ((((eq_sym0 (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01)) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01))) as proof of ((P0 (f x))->(P0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P0:(Prop->Prop))=> (((fun (x0:(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)))=> (((((eq_sym Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) (f x)) x0) (fun (x1:Prop)=> ((P0 (f x))->(P0 x1))))) (fun (P2:(Prop->Prop)) (x0:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((fun (x00:(((eq Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))=> (((((eq_sym Prop) (f x)) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) x00) P2)) ((eq_ref Prop) (f x))) x0))) (fun (x01:(P0 (f x)))=> x01))) as proof of (forall (P:(Prop->Prop)), ((P (f x))->(P ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):(((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found (eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=x:(fofType->Prop);b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=x:(fofType->Prop);b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh a)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh a)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% 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) x)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% 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) x)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) x)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):(((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found (eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b0:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b0
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found ((conj00 (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found (((conj0 b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of (P0 b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((fofType->Prop)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((fofType->Prop)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((fofType->Prop)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found x0:(P1 (Xh (cD_FOR_X5309 Xh)))
% Instantiate: x:=(cD_FOR_X5309 Xh):(fofType->Prop)
% Found (fun (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of (P1 (Xh x))
% Found (fun (P1:(fofType->Prop)) (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of ((P1 (Xh (cD_FOR_X5309 Xh)))->(P1 (Xh x)))
% Found (fun (P1:(fofType->Prop)) (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of b0
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% 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 eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b0:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b0
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found ((conj00 (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found (((conj0 b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) eq_sym) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):(((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found (eq_ref0 (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found ((eq_ref Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) as proof of (((eq Prop) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) (Xh x)) b0)
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found x0:(P1 (Xh (cD_FOR_X5309 Xh)))
% Instantiate: x:=(cD_FOR_X5309 Xh):(fofType->Prop)
% Found (fun (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of (P1 (Xh x))
% Found (fun (P1:(fofType->Prop)) (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of ((P1 (Xh (cD_FOR_X5309 Xh)))->(P1 (Xh x)))
% Found (fun (P1:(fofType->Prop)) (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of b0
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found x1:(P3 b0)
% Instantiate: b0:=(f x):Prop
% Found (fun (x1:(P3 b0))=> x1) as proof of (P3 b)
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b0))=> x1) as proof of ((P3 b0)->(P3 b))
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b0))=> x1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found x1:(P3 b0)
% Instantiate: b0:=(f x):Prop
% Found (fun (x1:(P3 b0))=> x1) as proof of (P3 b)
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b0))=> x1) as proof of ((P3 b0)->(P3 b))
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b0))=> x1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b0)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b0)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found x00:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Instantiate: b0:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found x00 as proof of (P3 b0)
% Found x00:(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Instantiate: b0:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found x00 as proof of (P3 b0)
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b00)
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b00)
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b00)
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b00)
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b00)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType;b0:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b0) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) a)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) a)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) a)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 x):(((eq (fofType->Prop)) x) (fun (x0:fofType)=> (x x0)))
% Found (eta_expansion_dep00 x) as proof of (((eq (fofType->Prop)) x) b)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) x) as proof of (((eq (fofType->Prop)) x) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) x) as proof of (((eq (fofType->Prop)) x) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) x) as proof of (((eq (fofType->Prop)) x) b)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) x) as proof of (((eq (fofType->Prop)) x) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b0) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of b0
% Found eq_ref00:=(eq_ref0 (Xh x00)):(((eq fofType) (Xh x00)) (Xh x00))
% Found (eq_ref0 (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found ((eq_ref fofType) (Xh x00)) as proof of (((eq fofType) (Xh x00)) b0)
% Found x10:(P2 a)
% Found (fun (x10:(P2 a))=> x10) as proof of (P2 a)
% Found (fun (x10:(P2 a))=> x10) as proof of (P3 a)
% Found x10:(P2 a)
% Found (fun (x10:(P2 a))=> x10) as proof of (P2 a)
% Found (fun (x10:(P2 a))=> x10) as proof of (P3 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found ((conj00 (fun (x01:(x (Xh x)))=> x01)) or_ind) as proof of ((and ((x (Xh x))->False)) b0)
% Found (((conj0 b0) (fun (x01:(x (Xh x)))=> x01)) or_ind) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) or_ind) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) or_ind) as proof of ((and ((x (Xh x))->False)) b0)
% Found ((((conj ((x (Xh x))->False)) b0) (fun (x01:(x (Xh x)))=> x01)) or_ind) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found x1:(P3 b)
% Instantiate: b0:=b:Prop
% Found (fun (x1:(P3 b))=> x1) as proof of (P3 b0)
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b))=> x1) as proof of ((P3 b)->(P3 b0))
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b))=> x1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found x1:(P3 b)
% Instantiate: b0:=b:Prop
% Found (fun (x1:(P3 b))=> x1) as proof of (P3 b0)
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b))=> x1) as proof of ((P3 b)->(P3 b0))
% Found (fun (P3:(Prop->Prop)) (x1:(P3 b))=> x1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found x00:(P3 b0)
% Instantiate: b0:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found (fun (x00:(P3 b0))=> x00) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (fun (P3:(Prop->Prop)) (x00:(P3 b0))=> x00) as proof of ((P3 b0)->(P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P3:(Prop->Prop)) (x00:(P3 b0))=> x00) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found x00:(P3 b0)
% Instantiate: b0:=((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))):Prop
% Found (fun (x00:(P3 b0))=> x00) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (fun (P3:(Prop->Prop)) (x00:(P3 b0))=> x00) as proof of ((P3 b0)->(P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (fun (P3:(Prop->Prop)) (x00:(P3 b0))=> x00) as proof of (P2 b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found x00:(P2 b)
% Instantiate: b0:=b:Prop
% Found x00 as proof of (P3 b0)
% Found x00:(P2 b)
% Instantiate: b0:=b:Prop
% Found x00 as proof of (P3 b0)
% Found eq_ref00:=(eq_ref0 (f1 x)):(((eq Prop) (f1 x)) (f1 x))
% Found (eq_ref0 (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f1 x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f1 x)):(((eq Prop) (f1 x)) (f1 x))
% Found (eq_ref0 (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f1 x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x00):fofType;b0:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f1 x)):(((eq Prop) (f1 x)) (f1 x))
% Found (eq_ref0 (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f1 x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f1 x)):(((eq Prop) (f1 x)) (f1 x))
% Found (eq_ref0 (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found ((eq_ref Prop) (f1 x)) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (((eq Prop) (f1 x)) (f0 x))
% Found (fun (x:(fofType->Prop))=> ((eq_ref Prop) (f1 x))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f1 x)) (f0 x)))
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b0:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=(Xh x):fofType;b0:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a) b0)
% Found x01:(x (Xh x))
% Found x01 as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of False
% Found (fun (x01:(x (Xh x)))=> x01) as proof of ((x (Xh x))->False)
% Found x0:(P1 (Xh (cD_FOR_X5309 Xh)))
% Instantiate: x:=(cD_FOR_X5309 Xh):(fofType->Prop)
% Found (fun (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of (P1 (Xh x))
% Found (fun (P1:(fofType->Prop)) (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of ((P1 (Xh (cD_FOR_X5309 Xh)))->(P1 (Xh x)))
% Found (fun (P1:(fofType->Prop)) (x0:(P1 (Xh (cD_FOR_X5309 Xh))))=> x0) as proof of b0
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=x00:(fofType->Prop);b:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b) (Xh a))
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a0:=(Xh x):fofType;b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (x x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x x03))
% Found eq_ref00:=(eq_ref0 (a x03)):(((eq Prop) (a x03)) (a x03))
% Found (eq_ref0 (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found ((eq_ref Prop) (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found ((eq_ref Prop) (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found ((eq_ref Prop) (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (x x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (x x03))
% Found eq_ref00:=(eq_ref0 (a x03)):(((eq Prop) (a x03)) (a x03))
% Found (eq_ref0 (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found ((eq_ref Prop) (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found ((eq_ref Prop) (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found ((eq_ref Prop) (a x03)) as proof of (((eq Prop) (a x03)) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 x)->(P1 x))
% Found (eq_ref00 P1) as proof of (P2 x)
% Found ((eq_ref0 x) P1) as proof of (P2 x)
% Found (((eq_ref (fofType->Prop)) x) P1) as proof of (P2 x)
% Found (((eq_ref (fofType->Prop)) x) P1) as proof of (P2 x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh x))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh x))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh x))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh x))
% Found eq_ref000:=(eq_ref00 P1):((P1 x)->(P1 x))
% Found (eq_ref00 P1) as proof of (P2 x)
% Found ((eq_ref0 x) P1) as proof of (P2 x)
% Found (((eq_ref (fofType->Prop)) x) P1) as proof of (P2 x)
% Found (((eq_ref (fofType->Prop)) x) P1) as proof of (P2 x)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: b:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b) (Xh a))
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a0:=(Xh x):fofType;b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x00)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) a)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) a)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 (a x03))->(P1 (a x03)))
% Found (eq_ref00 P1) as proof of (P2 (a x03))
% Found ((eq_ref0 (a x03)) P1) as proof of (P2 (a x03))
% Found (((eq_ref Prop) (a x03)) P1) as proof of (P2 (a x03))
% Found (((eq_ref Prop) (a x03)) P1) as proof of (P2 (a x03))
% Found eq_ref000:=(eq_ref00 P1):((P1 (a x03))->(P1 (a x03)))
% Found (eq_ref00 P1) as proof of (P2 (a x03))
% Found ((eq_ref0 (a x03)) P1) as proof of (P2 (a x03))
% Found (((eq_ref Prop) (a x03)) P1) as proof of (P2 (a x03))
% Found (((eq_ref Prop) (a x03)) P1) as proof of (P2 (a x03))
% Found eq_ref000:=(eq_ref00 P2):((P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))->(P2 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))))
% Found (eq_ref00 P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) P2) as proof of (P3 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((fofType->Prop)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found eq_ref00:=(eq_ref0 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))):(((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt)))))
% Found (eq_ref0 (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh Xt))))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((fofType->Prop)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq ((fofType->Prop)->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found ((eq_ref ((fofType->Prop)->Prop)) a0) as proof of (((eq ((fofType->Prop)->Prop)) a0) b0)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a:=x00:(fofType->Prop);b:=(Xh x):fofType
% Found x02 as proof of (((eq fofType) b) (Xh a))
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a0:=(Xh x):fofType;b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a0) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a0:=(Xh x):fofType;b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a0) b)
% Found x02:(((eq fofType) (Xh x)) (Xh x00))
% Instantiate: a0:=(Xh x):fofType;b:=(Xh x00):fofType
% Found x02 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x))
% Found x10:(P2 b0)
% Found (fun (x10:(P2 b0))=> x10) as proof of (P2 b0)
% Found (fun (x10:(P2 b0))=> x10) as proof of (P3 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_sym0100:=(eq_sym010 x02):(((eq fofType) b0) (Xh x))
% Found (eq_sym010 x02) as proof of (((eq fofType) b0) (Xh x))
% Found ((eq_sym01 b0) x02) as proof of (((eq fofType) b0) (Xh x))
% Found (((eq_sym0 (Xh x)) b0) x02) as proof of (((eq fofType) b0) (Xh x))
% Found (((eq_sym0 (Xh x)) b0) x02) as proof of (((eq fofType) b0) (Xh x))
% Found x000:(P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found x000:(P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))):(((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found (eq_ref0 ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% Found ((eq_ref Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) as proof of (((eq Prop) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))) b1)
% 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) x)
% Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% 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 eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq Prop) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq Prop) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% 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 eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) x)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b0:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b0
% Found eq_sym as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x)))
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b1)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b00):(((eq Prop) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found ((eq_ref Prop) b00) as proof of (((eq Prop) b00) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) x00)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x00)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x00)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x00)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 a)->(P1 a))
% Found (eq_ref00 P1) as proof of (P2 a)
% Found ((eq_ref0 a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found (((eq_ref (fofType->Prop)) a) P1) as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_sym0000:=(eq_sym000 x02):(((eq fofType) b) (Xh a))
% Found (eq_sym000 x02) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_sym00 b) x02) as proof of (((eq fofType) b) (Xh a))
% Found (((eq_sym0 (Xh a)) b) x02) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x02) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x02) as proof of (((eq fofType) b) (Xh a))
% Found eq_sym0000:=(eq_sym000 x02):(((eq fofType) b) (Xh x))
% Found (eq_sym000 x02) as proof of (((eq fofType) b) (Xh x))
% Found ((eq_sym00 b) x02) as proof of (((eq fofType) b) (Xh x))
% Found (((eq_sym0 (Xh x)) b) x02) as proof of (((eq fofType) b) (Xh x))
% Found ((((eq_sym fofType) (Xh x)) b) x02) as proof of (((eq fofType) b) (Xh x))
% Found ((((eq_sym fofType) (Xh x)) b) x02) as proof of (((eq fofType) b) (Xh x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found eq_ref00:=(eq_ref0 (x x03)):(((eq Prop) (x x03)) (x x03))
% Found (eq_ref0 (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found eq_ref00:=(eq_ref0 (x x03)):(((eq Prop) (x x03)) (x x03))
% Found (eq_ref0 (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found eq_ref00:=(eq_ref0 (x x03)):(((eq Prop) (x x03)) (x x03))
% Found (eq_ref0 (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found eq_ref00:=(eq_ref0 (x x03)):(((eq Prop) (x x03)) (x x03))
% Found (eq_ref0 (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found ((eq_ref Prop) (x x03)) as proof of (((eq Prop) (x x03)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (a x03))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((x (Xh x))->False)) (((eq fofType) (Xh (cD_FOR_X5309 Xh)))
% EOF
%------------------------------------------------------------------------------