%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV394^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n105.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 13:34:08 EDT 2014

% Result   : Timeout 300.08s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV394^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n105.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 09:05:21 CDT 2014
% % CPUTime  : 300.08 
% 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 0xfe4050>, <kernel.Type object at 0xd8c2d8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xw:(a->Prop)) (Xy:(a->Prop)) (Xz:(a->Prop)), (((and (forall (Xx:a), (((and (Xw Xx)) ((Xz Xx)->False))->(Xy Xx)))) (((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False)))) (fun (Xx:a)=> False)))->(forall (Xx:a), ((Xw Xx)->(Xy Xx))))) of role conjecture named cTHM269_pme
% Conjecture to prove = (forall (Xw:(a->Prop)) (Xy:(a->Prop)) (Xz:(a->Prop)), (((and (forall (Xx:a), (((and (Xw Xx)) ((Xz Xx)->False))->(Xy Xx)))) (((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False)))) (fun (Xx:a)=> False)))->(forall (Xx:a), ((Xw Xx)->(Xy Xx))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xw:(a->Prop)) (Xy:(a->Prop)) (Xz:(a->Prop)), (((and (forall (Xx:a), (((and (Xw Xx)) ((Xz Xx)->False))->(Xy Xx)))) (((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False)))) (fun (Xx:a)=> False)))->(forall (Xx:a), ((Xw Xx)->(Xy Xx)))))']
% Parameter a:Type.
% Trying to prove (forall (Xw:(a->Prop)) (Xy:(a->Prop)) (Xz:(a->Prop)), (((and (forall (Xx:a), (((and (Xw Xx)) ((Xz Xx)->False))->(Xy Xx)))) (((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False)))) (fun (Xx:a)=> False)))->(forall (Xx:a), ((Xw Xx)->(Xy Xx)))))
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b)
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of b
% Found (conj000 or_ind) as proof of (P b)
% Found ((conj00 b) or_ind) as proof of (P b)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b) or_ind) as proof of (P b)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b) or_ind) as proof of (P b)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b) or_ind) as proof of (P b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of b
% Found (conj000 or_ind) as proof of (P b)
% Found ((conj00 b) or_ind) as proof of (P b)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b) or_ind) as proof of (P b)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b) or_ind) as proof of (P b)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b) or_ind) as proof of (P b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((Xz Xx)->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((Xz Xx)->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((Xz Xx)->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((Xz Xx)->False))
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: a0:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of a0
% Found (conj000 classical_choice) as proof of (P a0)
% Found ((conj00 a0) classical_choice) as proof of (P a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) classical_choice) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) classical_choice) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) classical_choice) as proof of (P a0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of a0
% Found (conj000 x2) as proof of (P a0)
% Found ((conj00 a0) x2) as proof of (P a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) x2) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) x2) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) x2) as proof of (P a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (not (Xz Xx)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (Xz Xx)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (Xz Xx)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not (Xz Xx)))
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))))=> ((((((or_ind ((ex B) (fun (z:B)=> ((R x) z)))) (not ((ex B) (fun (z:B)=> ((R x) z))))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) ((((ex_ind B) (fun (z:B)=> ((R x) z))) ((ex B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y))))) (fun (y:B) (H:((R x) y))=> ((((ex_intro B) (fun (y0:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y0)))) y) (fun (_:((ex B) (fun (z:B)=> ((R x) z))))=> H))))) (fun (N:(not ((ex B) (fun (z:B)=> ((R x) z)))))=> ((((ex_intro B) (fun (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))) b) (fun (H:((ex B) (fun (z:B)=> ((R x) z))))=> ((False_rect ((R x) b)) (N H)))))) C0)) (classic ((ex B) (fun (z:B)=> ((R x) z)))))))) (((choice A) B) (fun (x:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x) z)))->((R x) y)))))):(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x))))))))
% Instantiate: a0:=(forall (A:Type) (B:Type) (R:(A->(B->Prop))), (B->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((ex B) (fun (y:B)=> ((R x) y)))->((R x) (f x)))))))):Prop
% Found classical_choice as proof of a0
% Found (conj000 classical_choice) as proof of (P a0)
% Found ((conj00 a0) classical_choice) as proof of (P a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) classical_choice) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) classical_choice) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) classical_choice) as proof of (P a0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of a0
% Found (conj000 x2) as proof of (P a0)
% Found ((conj00 a0) x2) as proof of (P a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) x2) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) x2) as proof of (P a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) x2) as proof of (P a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of b0
% Found (conj000 proj1) as proof of (P0 b0)
% Found ((conj00 b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of b0
% Found (conj000 proj1) as proof of (P0 b0)
% Found ((conj00 b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found eq_ref00:=(eq_ref0 ((Xz b)->False)):(((eq Prop) ((Xz b)->False)) ((Xz b)->False))
% Found (eq_ref0 ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found ((eq_ref Prop) ((Xz b)->False)) as proof of (((eq Prop) ((Xz b)->False)) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 (not (Xz b))):(((eq Prop) (not (Xz b))) (not (Xz b)))
% Found (eq_ref0 (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found ((eq_ref Prop) (not (Xz b))) as proof of (((eq Prop) (not (Xz b))) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b0
% Found ((conj00 x0) or_comm_i) as proof of (P0 b0)
% Found (((conj0 b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found ((((conj (Xw b)) b0) x0) or_comm_i) as proof of (P0 b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->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 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: a0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of a0
% Found ((conj00 x0) choice_operator) as proof of (P0 a0)
% Found (((conj0 a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 (not (Xz a0))):(((eq Prop) (not (Xz a0))) (not (Xz a0)))
% Found (eq_ref0 (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of a0
% Found ((conj00 x0) x2) as proof of (P0 a0)
% Found (((conj0 a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 (not (Xz a0))):(((eq Prop) (not (Xz a0))) (not (Xz a0)))
% Found (eq_ref0 (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz a0))):(((eq Prop) (not (Xz a0))) (not (Xz a0)))
% Found (eq_ref0 (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of b0
% Found (conj000 proj1) as proof of (P0 b0)
% Found ((conj00 b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw 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 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False)))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) ((Xy Xx0)->False))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of a0
% Found (conj000 x2) as proof of (P0 a0)
% Found ((conj00 a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: a0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of a0
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found ((conj00 x0) choice_operator) as proof of (P0 a0)
% Found (((conj0 a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: a0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of a0
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found ((conj00 x0) choice_operator) as proof of (P0 a0)
% Found (((conj0 a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz a0))):(((eq Prop) (not (Xz a0))) (not (Xz a0)))
% Found (eq_ref0 (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x2:(((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False)))) (fun (Xx:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False))))->(P (fun (Xx:a)=> False)))):Prop
% Found x2 as proof of a0
% Found ((conj00 x0) x2) as proof of (P0 a0)
% Found (((conj0 a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of a0
% Found ((conj00 x0) x2) as proof of (P0 a0)
% Found (((conj0 a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (not (Xz b)))
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: b0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of b0
% Found (conj000 proj1) as proof of (P0 b0)
% Found ((conj00 b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) b0) proj1) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x2:(((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False)))) (fun (Xx:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx:a)=> ((and (Xz Xx)) ((Xy Xx)->False))))->(P (fun (Xx:a)=> False)))):Prop
% Found x2 as proof of a0
% Found (conj000 x2) as proof of (P0 a0)
% Found ((conj00 a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 (not (Xz a0))):(((eq Prop) (not (Xz a0))) (not (Xz a0)))
% Found (eq_ref0 (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (not (Xz a0))):(((eq Prop) (not (Xz a0))) (not (Xz a0)))
% Found (eq_ref0 (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found ((eq_ref Prop) (not (Xz a0))) as proof of (((eq Prop) (not (Xz a0))) b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw Xx)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x2:(((eq (a->Prop)) (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0))))) (fun (Xx0:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx0:a)=> ((and (Xz Xx0)) (not (Xy Xx0)))))->(P (fun (Xx0:a)=> False)))):Prop
% Found x2 as proof of a0
% Found (conj000 x2) as proof of (P0 a0)
% Found ((conj00 a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw Xx)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: a0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of a0
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found ((conj00 x0) choice_operator) as proof of (P0 a0)
% Found (((conj0 a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) choice_operator) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: a0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of a0
% Found (conj000 iff_trans) as proof of (P0 a0)
% Found ((conj00 a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) iff_trans) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b:=Xx:a
% Found x0 as proof of (Xw b)
% Found x2:(((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) (not (Xy Xx))))) (fun (Xx:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx:a)=> ((and (Xz Xx)) (not (Xy Xx)))))->(P (fun (Xx:a)=> False)))):Prop
% Found x2 as proof of a0
% Found ((conj00 x0) x2) as proof of (P0 a0)
% Found (((conj0 a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found ((((conj (Xw b)) a0) x0) x2) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x2:(((eq (a->Prop)) (fun (Xx:a)=> ((and (Xz Xx)) (not (Xy Xx))))) (fun (Xx:a)=> False))
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xx:a)=> ((and (Xz Xx)) (not (Xy Xx)))))->(P (fun (Xx:a)=> False)))):Prop
% Found x2 as proof of a0
% Found (conj000 x2) as proof of (P0 a0)
% Found ((conj00 a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found (((fun (B:Prop)=> (((conj (Xw b)) B) x0)) a0) x2) as proof of (P0 a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found iff_trans:=(fun (A:Prop) (B:Prop) (C:Prop) (AB:((iff A) B)) (BC:((iff B) C))=> ((((conj (A->C)) (C->A)) (fun (x:A)=> ((((proj1 (B->C)) (C->B)) BC) ((((proj1 (A->B)) (B->A)) AB) x)))) (fun (x:C)=> ((((proj2 (A->B)) (B->A)) AB) ((((proj2 (B->C)) (C->B)) BC) x))))):(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (C:Prop), (((iff A) B)->(((iff B) C)->((iff A) C)))):Prop
% Found iff_trans as proof of b0
% Found (conj000 iff_trans) as proof of (P0 b0)
% Found ((conj00 b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> ((conj0 B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found (((fun (B:Prop)=> (((conj (Xw a0)) B) x0)) b0) iff_trans) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b0:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b0
% Found ((conj00 x0) choice_operator) as proof of (P0 b0)
% Found (((conj0 b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found ((((conj (Xw a0)) b0) x0) choice_operator) as proof of (P0 b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x20:=(x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))):((P1 ((Xz Xx)->False))->(P1 ((Xz Xx)->False)))
% Found (x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))) as proof of (P2 ((Xz Xx)->False))
% Found (x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))) as proof of (P2 ((Xz Xx)->False))
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: a0:=Xx:a
% Found x0 as proof of (Xw a0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x20:=(x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))):((P1 (not (Xz Xx)))->(P1 (not (Xz Xx))))
% Found (x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))) as proof of (P2 (not (Xz Xx)))
% Found (x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))) as proof of (P2 (not (Xz Xx)))
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x20:=(x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))):((P1 ((Xz Xx)->False))->(P1 ((Xz Xx)->False)))
% Found (x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))) as proof of (P2 ((Xz Xx)->False))
% Found (x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))) as proof of (P2 ((Xz Xx)->False))
% Found x20:=(x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))):((P1 ((Xz Xx)->False))->(P1 ((Xz Xx)->False)))
% Found (x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))) as proof of (P2 ((Xz Xx)->False))
% Found (x2 (fun (x3:(a->Prop))=> (P1 ((Xz Xx)->False)))) as proof of (P2 ((Xz Xx)->False))
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 ((Xz Xx)->False)):(((eq Prop) ((Xz Xx)->False)) ((Xz Xx)->False))
% Found (eq_ref0 ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found ((eq_ref Prop) ((Xz Xx)->False)) as proof of (((eq Prop) ((Xz Xx)->False)) b1)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x20:=(x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))):((P1 (not (Xz Xx)))->(P1 (not (Xz Xx))))
% Found (x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))) as proof of (P2 (not (Xz Xx)))
% Found (x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))) as proof of (P2 (not (Xz Xx)))
% Found x20:=(x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))):((P1 (not (Xz Xx)))->(P1 (not (Xz Xx))))
% Found (x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))) as proof of (P2 (not (Xz Xx)))
% Found (x2 (fun (x3:(a->Prop))=> (P1 (not (Xz Xx))))) as proof of (P2 (not (Xz Xx)))
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% Found eq_ref00:=(eq_ref0 (not (Xz Xx))):(((eq Prop) (not (Xz Xx))) (not (Xz Xx)))
% Found (eq_ref0 (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found ((eq_ref Prop) (not (Xz Xx))) as proof of (((eq Prop) (not (Xz Xx))) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found x0:(Xw Xx)
% Instantiate: b0:=Xx:a
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found x0:(Xw Xx)
% Found x0 as proof of (Xw b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) ((Xz Xx)->False))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (not (Xz Xx)))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 ((Xz a0)->False)):(((eq Prop) ((Xz a0)->False)) ((Xz a0)->False))
% Found (eq_ref0 ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found ((eq_ref Prop) ((Xz a0)->False)) as proof of (((eq Prop) ((Xz a0)->False)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((Xz b)->False))
% 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 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of
% EOF
%------------------------------------------------------------------------------