%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SET614^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.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 13:30:51 EDT 2014

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

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET614^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.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 10:21:21 CDT 2014
% % CPUTime  : 300.04 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0xb483f8>, <kernel.Type object at 0xb48ea8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))) of role conjecture named cBOOL_PROP_88_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (x:a)=> ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (eq_ref0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x01:(P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P0 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found x01:(P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P0 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x01:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found x01:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P0 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P0 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Instantiate: b:=(fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))):(a->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found x:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Instantiate: f:=(fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))):(a->Prop)
% Found x as proof of (P0 f)
% Found x:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Instantiate: f:=(fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))):(a->Prop)
% Found x as proof of (P0 f)
% Found x:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Instantiate: b:=(fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))):(a->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (x:a)=> ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found x:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Instantiate: f:=(fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))):(a->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:a), (((eq Prop) (f x)) ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found x:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Instantiate: f:=(fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))):(a->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (X x0)) (not ((or (Y x0)) (Z x0)))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:a), (((eq Prop) (f x)) ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) (fun (x:a)=> ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found x:(P0 b)
% Instantiate: b:=(fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))):(a->Prop)
% Found (fun (x:(P0 b))=> x) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (P0:((a->Prop)->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))
% Found (fun (P0:((a->Prop)->Prop)) (x:(P0 b))=> x) as proof of (P b)
% Found x3:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x3) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x3) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (x:a)=> ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found x:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Instantiate: b:=(fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))):(a->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (x:a)=> ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (x:a)=> ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b0)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b0)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found x:(P0 b)
% Instantiate: b:=(fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))):(a->Prop)
% Found (fun (x:(P0 b))=> x) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (P0:((a->Prop)->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))
% Found (fun (P0:((a->Prop)->Prop)) (x:(P0 b))=> x) as proof of (P b)
% Found x3:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x3) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x3) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) (fun (x:a)=> ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Instantiate: b:=(fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))):(a->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) (fun (x:a)=> ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found x:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Instantiate: f:=(fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))):(a->Prop)
% Found x as proof of (P0 f)
% Found x:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Instantiate: f:=(fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))):(a->Prop)
% Found x as proof of (P0 f)
% Found x0:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Instantiate: b:=((and ((and (X x)) ((Y x)->False))) ((Z x)->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found x0:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Instantiate: b:=((and ((and (X x)) ((Y x)->False))) ((Z x)->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) (fun (x:a)=> ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b0)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b0)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b0)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b0)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found ((eta_expansion0 Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found x:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Instantiate: f:=(fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))):(a->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:a), (((eq Prop) (f x)) ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found x:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Instantiate: f:=(fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))):(a->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and ((and (X x0)) (not (Y x0)))) (not (Z x0))))
% Found (fun (x0:a)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:a), (((eq Prop) (f x)) ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found x0:(P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Instantiate: b:=((and ((and (X x)) (not (Y x)))) (not (Z x))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found x0:(P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Instantiate: b:=((and ((and (X x)) (not (Y x)))) (not (Z x))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x3:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x3) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x3) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P2 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P2 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P2 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P1 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P2 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b0)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b0)
% Found x02:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x02:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x02) as proof of (P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x02:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x02) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x02:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x02:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x02) as proof of (P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x02:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x02) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and ((and (X x)) ((Y x)->False))) ((Z x)->False)):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and ((and (X x)) ((Y x)->False))) ((Z x)->False)):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P1 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P2 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x3:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x3) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x3:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x3) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) b0)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found x0:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Instantiate: b:=((and (X x)) (((or (Y x)) (Z x))->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found x0:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Instantiate: b:=((and (X x)) (((or (Y x)) (Z x))->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P2 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P2 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P2 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P1 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x01:(P1 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x01) as proof of (P2 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (((or (Y x)) (Z x))->False))
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) (fun (x:a)=> ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))) b)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eta_expansion0 Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x02:(P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x02:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x02) as proof of (P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x02:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x02) as proof of (P0 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x02:(P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x02:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x02) as proof of (P ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (x02:(P ((and ((and (X x)) (not (Y x)))) (not (Z x)))))=> x02) as proof of (P0 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x0:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Instantiate: b:=((and (X x)) (((or (Y x)) (Z x))->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found x0:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Instantiate: b:=((and (X x)) (((or (Y x)) (Z x))->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and ((and (X x)) (not (Y x)))) (not (Z x))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and ((and (X x)) (not (Y x)))) (not (Z x))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (eq_ref0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq (a->Prop)) b0) b)
% Found ((eta_expansion0 Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found (((eta_expansion a) Prop) b0) as proof of (((eq (a->Prop)) b0) b)
% Found x0:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Instantiate: b:=((and (X x)) (not ((or (Y x)) (Z x)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found x0:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Instantiate: b:=((and (X x)) (not ((or (Y x)) (Z x)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (eq_ref0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found ((eq_ref (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found x0:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Instantiate: b:=((and (X x)) (not ((or (Y x)) (Z x)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found x0:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Instantiate: b:=((and (X x)) (not ((or (Y x)) (Z x)))):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))):(((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found (eq_ref0 ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) as proof of (((eq Prop) ((and ((and (X x)) (not (Y x)))) (not (Z x)))) b)
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (fun (x01:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))))=> x01) as proof of (P0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (not ((or (Y x)) (Z x))))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P1 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x01:(P1 ((and (X x)) (((or (Y x)) (Z x))->False))))=> x01) as proof of (P2 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 b0):(((eq (a->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found ((eq_ref (a->Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x02:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found x02:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (a->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found ((eq_ref (a->Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) ((Y Xx)->False))) ((Z Xx)->False))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) (fun (x:a)=> ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))) b)
% Found x02:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x02:(P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (x02:(P ((and (X x)) (((or (Y x)) (Z x))->False))))=> x02) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and (X x)) (((or (Y x)) (Z x))->False)):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found x0:(P0 b)
% Instantiate: b:=((and (X x)) (((or (Y x)) (Z x))->False)):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((and (X x)) (((or (Y x)) (Z x))->False))))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x0:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Instantiate: b:=((and ((and (X x)) ((Y x)->False))) ((Z x)->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P1 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x01:(P1 ((and (X x)) (not ((or (Y x)) (Z x))))))=> x01) as proof of (P2 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found x0:(P ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Instantiate: b:=((and ((and (X x)) ((Y x)->False))) ((Z x)->False)):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b)
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eq_ref00:=(eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))):(((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found (eq_ref0 ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found ((eq_ref Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) as proof of (((eq Prop) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (a->Prop)) b0) (fun (x:a)=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b0) as proof of (((eq (a->Prop)) b0) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx))))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion a) Prop) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))):(((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) (fun (x:a)=> ((and (X x)) (not ((or (Y x)) (Z x))))))
% Found (eta_expansion_dep00 (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found ((eta_expansion_dep0 (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found (((eta_expansion_dep a) (fun (x1:a)=> Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) as proof of (((eq (a->Prop)) (fun (Xx:a)=> ((and (X Xx)) (not ((or (Y Xx)) (Z Xx)))))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (a->Prop)) b) (fun (x:a)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found (((eta_expansion a) Prop) b) as proof of (((eq (a->Prop)) b) (fun (Xx:a)=> ((and ((and (X Xx)) (not (Y Xx)))) (not (Z Xx)))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))):(((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) ((and (X x)) (((or (Y x)) (Z x))->False)))
% Found (eq_ref0 ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found ((eq_ref Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) as proof of (((eq Prop) ((and (X x)) (((or (Y x)) (Z x))->False))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((and ((and (X x)) ((Y x)->False))) ((Z x)->False)))
% Found x02:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x02:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x02) as proof of (P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x02:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x02) as proof of (P0 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found x02:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x02:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x02) as proof of (P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x02:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x02) as proof of (P0 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (X x)) (not (Y x)))) (not (Z x))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found (fun (x2:(P (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False)))))=> x2) as proof of (P0 (fun (Xx:a)=> ((and (X Xx)) (((or (Y Xx)) (Z Xx))->False))))
% Found x02:(P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x02:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x02) as proof of (P ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (fun (x02:(P ((and (X x)) (not ((or (Y x)) (Z x))))))=> x02) as proof of (P0 ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found eq_ref00:=(eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))):(((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) ((and (X x)) (not ((or (Y x)) (Z x)))))
% Found (eq_ref0 ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as proof of (((eq Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) b)
% Found ((eq_ref Prop) ((and (X x)) (not ((or (Y x)) (Z x))))) as 
% EOF
%------------------------------------------------------------------------------