%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU866^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n097.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 13:33:18 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU866^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n097.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 11:37:56 CDT 2014
% % CPUTime  : 300.01 
% 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 0x1291290>, <kernel.Type object at 0x12916c8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xp:(a->Prop)), ((forall (Xw:((a->Prop)->Prop)), (((and (Xw (fun (Xx:a)=> False))) (forall (Xr:(a->Prop)) (Xx:a), ((Xw Xr)->(Xw (fun (Xt:a)=> ((or (Xr Xt)) (((eq a) Xt) Xx)))))))->(Xw Xp)))->(((ex (a->Prop)) (fun (Xq:(a->Prop))=> ((and ((and (forall (Xx:a), ((Xq Xx)->(Xp Xx)))) ((ex a) (fun (Xx:a)=> ((and ((Xq Xx)->False)) (Xp Xx)))))) ((ex (a->a)) (fun (Xf:(a->a))=> (forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (Xq Xx)) (((eq a) Xy) (Xf Xx))))))))))))->False))) of role conjecture named cTHM161_pme
% Conjecture to prove = (forall (Xp:(a->Prop)), ((forall (Xw:((a->Prop)->Prop)), (((and (Xw (fun (Xx:a)=> False))) (forall (Xr:(a->Prop)) (Xx:a), ((Xw Xr)->(Xw (fun (Xt:a)=> ((or (Xr Xt)) (((eq a) Xt) Xx)))))))->(Xw Xp)))->(((ex (a->Prop)) (fun (Xq:(a->Prop))=> ((and ((and (forall (Xx:a), ((Xq Xx)->(Xp Xx)))) ((ex a) (fun (Xx:a)=> ((and ((Xq Xx)->False)) (Xp Xx)))))) ((ex (a->a)) (fun (Xf:(a->a))=> (forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (Xq Xx)) (((eq a) Xy) (Xf Xx))))))))))))->False))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xp:(a->Prop)), ((forall (Xw:((a->Prop)->Prop)), (((and (Xw (fun (Xx:a)=> False))) (forall (Xr:(a->Prop)) (Xx:a), ((Xw Xr)->(Xw (fun (Xt:a)=> ((or (Xr Xt)) (((eq a) Xt) Xx)))))))->(Xw Xp)))->(((ex (a->Prop)) (fun (Xq:(a->Prop))=> ((and ((and (forall (Xx:a), ((Xq Xx)->(Xp Xx)))) ((ex a) (fun (Xx:a)=> ((and ((Xq Xx)->False)) (Xp Xx)))))) ((ex (a->a)) (fun (Xf:(a->a))=> (forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (Xq Xx)) (((eq a) Xy) (Xf Xx))))))))))))->False)))']
% Parameter a:Type.
% Trying to prove (forall (Xp:(a->Prop)), ((forall (Xw:((a->Prop)->Prop)), (((and (Xw (fun (Xx:a)=> False))) (forall (Xr:(a->Prop)) (Xx:a), ((Xw Xr)->(Xw (fun (Xt:a)=> ((or (Xr Xt)) (((eq a) Xt) Xx)))))))->(Xw Xp)))->(((ex (a->Prop)) (fun (Xq:(a->Prop))=> ((and ((and (forall (Xx:a), ((Xq Xx)->(Xp Xx)))) ((ex a) (fun (Xx:a)=> ((and ((Xq Xx)->False)) (Xp Xx)))))) ((ex (a->a)) (fun (Xf:(a->a))=> (forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (Xq Xx)) (((eq a) Xy) (Xf Xx))))))))))))->False)))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x90:False
% Found (fun (x10:(Xp x7))=> x90) as proof of False
% Found (fun (x10:(Xp x7))=> x90) as proof of ((Xp x7)->False)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x90:False
% Found (fun (x10:(Xp x7))=> x90) as proof of False
% Found (fun (x10:(Xp x7))=> x90) as proof of ((Xp x7)->False)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x110:False
% Found (fun (x12:(Xp x9))=> x110) as proof of False
% Found (fun (x12:(Xp x9))=> x110) as proof of ((Xp x9)->False)
% Found x110:False
% Found (fun (x12:(Xp x9))=> x110) as proof of False
% Found (fun (x12:(Xp x9))=> x110) as proof of ((Xp x9)->False)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x110:False
% Found (fun (x12:(Xp x7))=> x110) as proof of False
% Found (fun (x12:(Xp x7))=> x110) as proof of ((Xp x7)->False)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x90:False
% Found (fun (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of False
% Found (fun (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of ((forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx)))))))->False)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x90:False
% Found (fun (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of False
% Found (fun (x11:(a->a)) (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of ((forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx)))))))->False)
% Found (fun (x11:(a->a)) (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of (forall (x:(a->a)), ((forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x Xx)))))))->False))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x110:False
% Found (fun (x12:(Xp x9))=> x110) as proof of False
% Found (fun (x12:(Xp x9))=> x110) as proof of ((Xp x9)->False)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x110:False
% Found (fun (x12:(Xp x9))=> x110) as proof of False
% Found (fun (x12:(Xp x9))=> x110) as proof of ((Xp x9)->False)
% Found x110:False
% Found (fun (x12:(Xp x7))=> x110) as proof of False
% Found (fun (x12:(Xp x7))=> x110) as proof of ((Xp x7)->False)
% Found x90:False
% Found (fun (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of False
% Found (fun (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of ((forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx)))))))->False)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 x7):(((eq a) x7) x7)
% Found (eq_ref0 x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found x90:False
% Found (fun (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of False
% Found (fun (x11:(a->a)) (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of ((forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx)))))))->False)
% Found (fun (x11:(a->a)) (x12:(forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x11 Xx))))))))=> x90) as proof of (forall (x:(a->a)), ((forall (Xy:a), ((Xp Xy)->((ex a) (fun (Xx:a)=> ((and (x1 Xx)) (((eq a) Xy) (x Xx)))))))->False))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x90)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x90)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x90)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->((x1 x7)->(x1 x7))))):(((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) ((a->Prop)->(a->((x1 x7)->(x1 x7)))))
% Found (eq_ref0 ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x7))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x7))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x7)->((and False) ((a->Prop)->(a->(False->False)))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 x7):(((eq a) x7) x7)
% Found (eq_ref0 x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x90)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x90)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x90)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 x9):(((eq a) x9) x9)
% Found (eq_ref0 x9) as proof of (((eq a) x9) b)
% Found ((eq_ref a) x9) as proof of (((eq a) x9) b)
% Found ((eq_ref a) x9) as proof of (((eq a) x9) b)
% Found ((eq_ref a) x9) as proof of (((eq a) x9) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->((x1 x7)->(x1 x7))))):(((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) ((a->Prop)->(a->((x1 x7)->(x1 x7)))))
% Found (eq_ref0 ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) as proof of (((eq Prop) ((a->Prop)->(a->((x1 x7)->(x1 x7))))) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((a->Prop)->(a->(False->False))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x7))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x7))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x7)->((and False) ((a->Prop)->(a->(False->False)))))
% Found eq_ref00:=(eq_ref0 x7):(((eq a) x7) x7)
% Found (eq_ref0 x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found ((eq_ref a) x7) as proof of (((eq a) x7) b)
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found x12:False
% Found (fun (x12:False)=> x12) as proof of False
% Found (fun (Xx:a) (x12:False)=> x12) as proof of (False->False)
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of (a->(False->False))
% Found (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12) as proof of ((a->Prop)->(a->(False->False)))
% Found (conj000 (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found ((conj00 ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> ((conj0 B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12)) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((and False) ((a->Prop)->(a->(False->False))))
% Found (fun (x11:(Xp x8))=> (((fun (B:Prop)=> (((conj False) B) x100)) ((a->Prop)->(a->(False->False)))) (fun (Xr:(a->Prop)) (Xx:a) (x12:False)=> x12))) as proof of ((Xp x8)->((and False) ((a->Prop)->(a->(False->False)))))
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 x9):(((eq a) x9) x9)
% Found (eq_ref0 x9) as proof of (((eq a) x9) b)
% Found ((eq_ref a) x9) as proof of (((eq a) x9) b)
% Found ((eq_ref a) x9) as proof of (((eq a) x9) b)
% Found ((eq_ref a) x9) as proof of (((eq a) x9) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found eq_ref00:=(eq_ref0 ((a->Prop)->(a->(False->False)))):(((eq Prop) ((a->Prop)->(a->(False->False)))) ((a->Prop)->(a->(False->False))))
% Found (eq_ref0 ((a->Prop)->(a->(False->False)))) as proof of (((eq Prop) ((a->Prop)->(a->(False->False)))) b)
% Found ((eq_ref Prop) ((a->Prop)->(a->(Fa
% EOF
%------------------------------------------------------------------------------