TSTP Solution File: SEV061^5 by cocATP---0.2.0

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV061^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n096.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:41 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV061^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n096.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 07:50:41 CDT 2014
% % CPUTime  : 300.02 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x100dea8>, <kernel.Type object at 0x100da70>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x13e5488>, <kernel.Type object at 0x100d950>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), ((forall (Xx_2:b) (Xy_47:a), (((Xk Xx_2) Xy_47)->((or ((Xs Xx_2) Xy_47)) ((and (((eq b) Xx_2) Xx)) (((eq a) Xy_47) Xy)))))->(forall (Xx_3:b) (Xy_48:a), (((and ((Xk Xx_3) Xy_48)) (((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))->False))->((Xs Xx_3) Xy_48))))) of role conjecture named cTHM176_pme
% Conjecture to prove = (forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), ((forall (Xx_2:b) (Xy_47:a), (((Xk Xx_2) Xy_47)->((or ((Xs Xx_2) Xy_47)) ((and (((eq b) Xx_2) Xx)) (((eq a) Xy_47) Xy)))))->(forall (Xx_3:b) (Xy_48:a), (((and ((Xk Xx_3) Xy_48)) (((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))->False))->((Xs Xx_3) Xy_48))))):Prop
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), ((forall (Xx_2:b) (Xy_47:a), (((Xk Xx_2) Xy_47)->((or ((Xs Xx_2) Xy_47)) ((and (((eq b) Xx_2) Xx)) (((eq a) Xy_47) Xy)))))->(forall (Xx_3:b) (Xy_48:a), (((and ((Xk Xx_3) Xy_48)) (((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))->False))->((Xs Xx_3) Xy_48)))))']
% Parameter b:Type.
% Parameter a:Type.
% Trying to prove (forall (Xx:b) (Xy:a) (Xs:(b->(a->Prop))) (Xk:(b->(a->Prop))), ((forall (Xx_2:b) (Xy_47:a), (((Xk Xx_2) Xy_47)->((or ((Xs Xx_2) Xy_47)) ((and (((eq b) Xx_2) Xx)) (((eq a) Xy_47) Xy)))))->(forall (Xx_3:b) (Xy_48:a), (((and ((Xk Xx_3) Xy_48)) (((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))->False))->((Xs Xx_3) Xy_48)))))
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 (((eq a) Xy_48) Xy)):(((eq Prop) (((eq a) Xy_48) Xy)) (((eq a) Xy_48) Xy))
% Found (eq_ref0 (((eq a) Xy_48) Xy)) as proof of (((eq Prop) (((eq a) Xy_48) Xy)) b0)
% Found ((eq_ref Prop) (((eq a) Xy_48) Xy)) as proof of (((eq Prop) (((eq a) Xy_48) Xy)) b0)
% Found ((eq_ref Prop) (((eq a) Xy_48) Xy)) as proof of (((eq Prop) (((eq a) Xy_48) Xy)) b0)
% Found ((eq_ref Prop) (((eq a) Xy_48) Xy)) as proof of (((eq Prop) (((eq a) Xy_48) Xy)) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xx_3)->(P Xx_3))
% Found (eq_ref00 P) as proof of (P0 Xx_3)
% Found ((eq_ref0 Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found eq_ref000:=(eq_ref00 P):((P Xy_48)->(P Xy_48))
% Found (eq_ref00 P) as proof of (P0 Xy_48)
% Found ((eq_ref0 Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found False_rect00:=(False_rect0 (((eq b) Xx_3) Xx)):(((eq b) Xx_3) Xx)
% Found (False_rect0 (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P:Type)=> ((False_rect P) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P:Type)=> ((False_rect P) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found False_rect00:=(False_rect0 (((eq a) Xy_48) Xy)):(((eq a) Xy_48) Xy)
% Found (False_rect0 (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P:Type)=> ((False_rect P) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P:Type)=> ((False_rect P) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((conj00 ((fun (P:Type)=> ((False_rect P) x20)) (((eq b) Xx_3) Xx))) ((fun (P:Type)=> ((False_rect P) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found (((conj0 (((eq a) Xy_48) Xy)) ((fun (P:Type)=> ((False_rect P) x20)) (((eq b) Xx_3) Xx))) ((fun (P:Type)=> ((False_rect P) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P:Type)=> ((False_rect P) x20)) (((eq b) Xx_3) Xx))) ((fun (P:Type)=> ((False_rect P) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P:Type)=> ((False_rect P) x20)) (((eq b) Xx_3) Xx))) ((fun (P:Type)=> ((False_rect P) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found False_rect00:=(False_rect0 (P b0)):(P b0)
% Found (False_rect0 (P b0)) as proof of (P b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0)) as proof of (P b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0)) as proof of (P b0)
% Found ((eq_sym0000 ((eq_ref a) Xy_48)) ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0))) as proof of ((Xs Xx_3) Xy_48)
% Found ((eq_sym0000 ((eq_ref a) Xy_48)) ((fun (P0:Type)=> ((False_rect P0) x20)) (P b0))) as proof of ((Xs Xx_3) Xy_48)
% Found (((fun (x3:(((eq a) Xy_48) b0))=> ((eq_sym000 x3) (Xs Xx_3))) ((eq_ref a) Xy_48)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0))) as proof of ((Xs Xx_3) Xy_48)
% Found (((fun (x3:(((eq a) Xy_48) Xy_48))=> (((eq_sym00 Xy_48) x3) (Xs Xx_3))) ((eq_ref a) Xy_48)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) Xy_48))) as proof of ((Xs Xx_3) Xy_48)
% Found (((fun (x3:(((eq a) Xy_48) Xy_48))=> ((((eq_sym0 Xy_48) Xy_48) x3) (Xs Xx_3))) ((eq_ref a) Xy_48)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) Xy_48))) as proof of ((Xs Xx_3) Xy_48)
% Found (((fun (x3:(((eq a) Xy_48) Xy_48))=> (((((eq_sym a) Xy_48) Xy_48) x3) (Xs Xx_3))) ((eq_ref a) Xy_48)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) Xy_48))) as proof of ((Xs Xx_3) Xy_48)
% Found (((fun (x3:(((eq a) Xy_48) Xy_48))=> (((((eq_sym a) Xy_48) Xy_48) x3) (Xs Xx_3))) ((eq_ref a) Xy_48)) ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) Xy_48))) as proof of ((Xs Xx_3) Xy_48)
% 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: b0:=(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 b0
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found x3:(P Xy_48)
% Instantiate: b0:=Xy_48:a
% Found x3 as proof of (P0 b0)
% Found x3:(P Xx_3)
% Instantiate: b0:=Xx_3:b
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% 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) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% 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_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xx_3)->(P Xx_3))
% Found (eq_ref00 P) as proof of (P0 Xx_3)
% Found ((eq_ref0 Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xy_48)->(P Xy_48))
% Found (eq_ref00 P) as proof of (P0 Xy_48)
% Found ((eq_ref0 Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref b) b0) as proof of (P b0)
% Found ((eq_ref b) b0) as proof of (P b0)
% Found ((eq_ref b) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% 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) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% 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_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P0 b0)
% Found x3:(P Xx)
% Instantiate: b0:=Xx:b
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xx_3)->(P Xx_3))
% Found (eq_ref00 P) as proof of (P0 Xx_3)
% Found ((eq_ref0 Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found eq_ref000:=(eq_ref00 P):((P Xy_48)->(P Xy_48))
% Found (eq_ref00 P) as proof of (P0 Xy_48)
% Found ((eq_ref0 Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% 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: b0:=(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 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) (((eq a) Xy_48) Xy))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) Xy_48) Xy))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) Xy_48) Xy))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq a) Xy_48) Xy))
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: a0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of a0
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) b0)):((Xs Xx_3) b0)
% Found (False_rect0 ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of (P b0)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) b0)):((Xs Xx_3) b0)
% Found (False_rect0 ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) b0)):((Xs Xx_3) b0)
% Found (False_rect0 ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) b0)):((Xs Xx_3) b0)
% Found (False_rect0 ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of ((Xs Xx_3) b0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) b0)) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found x3:(P Xy_48)
% Instantiate: b0:=Xy_48:a
% Found x3 as proof of (P0 b0)
% Found x3:(P Xx_3)
% Instantiate: b0:=Xx_3:b
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref a) b0) as proof of (P0 b0)
% Found ((eq_ref a) b0) as proof of (P0 b0)
% Found ((eq_ref a) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xx_3)->(P Xx_3))
% Found (eq_ref00 P) as proof of (P0 Xx_3)
% Found ((eq_ref0 Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found (((eq_ref b) Xx_3) P) as proof of (P0 Xx_3)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xy_48)->(P Xy_48))
% Found (eq_ref00 P) as proof of (P0 Xy_48)
% Found ((eq_ref0 Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found (((eq_ref a) Xy_48) P) as proof of (P0 Xy_48)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found x3:(P Xx_3)
% Instantiate: a0:=Xx_3:b
% Found x3 as proof of (P0 a0)
% Found x3:(P Xy_48)
% Instantiate: a0:=Xy_48:a
% Found x3 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref b) b0) as proof of (P b0)
% Found ((eq_ref b) b0) as proof of (P b0)
% Found ((eq_ref b) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy_48)->(P0 Xy_48))
% Found (eq_ref00 P0) as proof of (P1 Xy_48)
% Found ((eq_ref0 Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref a) b0) as proof of (P0 b0)
% Found ((eq_ref a) b0) as proof of (P0 b0)
% Found ((eq_ref a) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy_48)->(P0 Xy_48))
% Found (eq_ref00 P0) as proof of (P1 Xy_48)
% Found ((eq_ref0 Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% 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 b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy_48)->(P0 Xy_48))
% Found (eq_ref00 P0) as proof of (P1 Xy_48)
% Found ((eq_ref0 Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy_48)->(P0 Xy_48))
% Found (eq_ref00 P0) as proof of (P1 Xy_48)
% Found ((eq_ref0 Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy_48)->(P0 Xy_48))
% Found (eq_ref00 P0) as proof of (P1 Xy_48)
% Found ((eq_ref0 Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found (((eq_ref a) Xy_48) P0) as proof of (P1 Xy_48)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P0 b0)
% Found x3:(P Xx)
% Instantiate: b0:=Xx:b
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref b) b0) as proof of (P1 b0)
% Found ((eq_ref b) b0) as proof of (P1 b0)
% Found ((eq_ref b) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref a) b0) as proof of (P1 b0)
% Found ((eq_ref a) b0) as proof of (P1 b0)
% Found ((eq_ref a) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref b) b0) as proof of (P1 b0)
% Found ((eq_ref b) b0) as proof of (P1 b0)
% Found ((eq_ref b) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref a) b0) as proof of (P1 b0)
% Found ((eq_ref a) b0) as proof of (P1 b0)
% Found ((eq_ref a) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P0 b0)
% Found ((eq_ref a) Xy) as proof of (P0 b0)
% Found ((eq_ref a) Xy) as proof of (P0 b0)
% Found ((eq_ref a) Xy) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found x3:(P0 Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P1 b0)
% Found x3:(P1 Xx)
% Instantiate: b0:=Xx:b
% Found x3 as proof of (P2 b0)
% Found x3:(P1 Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P2 b0)
% Found x3:(P1 Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P2 b0)
% Found x3:(P1 Xx)
% Instantiate: b0:=Xx:b
% Found x3 as proof of (P2 b0)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P0 b0)
% Found x3:(P Xx)
% Instantiate: b0:=Xx:b
% Found x3 as proof of (P0 b0)
% Found x3:(P b0)
% Found x3 as proof of (P0 Xx_3)
% Found x3:(P b0)
% Found x3 as proof of (P0 Xy_48)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xx)->(P1 Xx))
% Found (eq_ref00 P1) as proof of (P2 Xx)
% Found ((eq_ref0 Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P0 b0)
% Found ((eq_ref a) Xy) as proof of (P0 b0)
% Found ((eq_ref a) Xy) as proof of (P0 b0)
% Found ((eq_ref a) Xy) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found x3:(P b0)
% Instantiate: b00:=b0:b
% Found x3 as proof of (P0 b00)
% Found x3:(P b0)
% Instantiate: b1:=b0:a
% Found x3 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found x3:(P0 Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P1 b0)
% Found x3:(P Xx)
% Instantiate: a0:=Xx:b
% Found x3 as proof of (P0 a0)
% Found x3:(P Xy)
% Instantiate: a0:=Xy:a
% Found x3 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% 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 b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found ((eq_ref b) a0) as proof of (((eq b) a0) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b01)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b01)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b01)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq a) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq a) b01) Xy)
% Found ((eq_ref a) b01) as proof of (((eq a) b01) Xy)
% Found ((eq_ref a) b01) as proof of (((eq a) b01) Xy)
% Found ((eq_ref a) b01) as proof of (((eq a) b01) Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b01)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b01)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b01)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq b) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq b) b01) Xx)
% Found ((eq_ref b) b01) as proof of (((eq b) b01) Xx)
% Found ((eq_ref b) b01) as proof of (((eq b) b01) Xx)
% Found ((eq_ref b) b01) as proof of (((eq b) b01) Xx)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% Instantiate: a0:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% Found proj1 as proof of a0
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy)->(P0 Xy))
% Found (eq_ref00 P0) as proof of (P1 Xy)
% Found ((eq_ref0 Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx)->(P0 Xx))
% Found (eq_ref00 P0) as proof of (P1 Xx)
% Found ((eq_ref0 Xx) P0) as proof of (P1 Xx)
% Found (((eq_ref b) Xx) P0) as proof of (P1 Xx)
% Found (((eq_ref b) Xx) P0) as proof of (P1 Xx)
% 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 proj1 as proof of a0
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref a) b0) P1) as proof of (P2 b0)
% Found (((eq_ref a) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref b) b0) P1) as proof of (P2 b0)
% Found (((eq_ref b) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref b) b0) P1) as proof of (P2 b0)
% Found (((eq_ref b) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref a) b0) P1) as proof of (P2 b0)
% Found (((eq_ref a) b0) P1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xx)->(P1 Xx))
% Found (eq_ref00 P1) as proof of (P2 Xx)
% Found ((eq_ref0 Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xx)->(P1 Xx))
% Found (eq_ref00 P1) as proof of (P2 Xx)
% Found ((eq_ref0 Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found (((eq_ref b) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref b) b00) P) as proof of (P0 b00)
% Found (((eq_ref b) b00) P) as proof of (P0 b00)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref a) b00) P) as proof of (P0 b00)
% Found (((eq_ref a) b00) P) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (P Xy_48)
% Found ((eq_ref a) Xy_48) as proof of (P Xy_48)
% Found ((eq_ref a) Xy_48) as proof of (P Xy_48)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b00)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (P Xx_3)
% Found ((eq_ref b) Xx_3) as proof of (P Xx_3)
% Found ((eq_ref b) Xx_3) as proof of (P Xx_3)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found x3:(P Xy)
% Instantiate: b1:=Xy:a
% Found x3 as proof of (P0 b1)
% Found x3:(P Xx)
% Instantiate: b00:=Xx:b
% Found x3 as proof of (P0 b00)
% Found x3:(P Xx)
% Instantiate: b00:=Xx:b
% Found x3 as proof of (P0 b00)
% Found x3:(P Xy)
% Instantiate: b1:=Xy:a
% Found x3 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) a0)):((Xs Xx_3) a0)
% Found (False_rect0 ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% 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 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) a0)):((Xs Xx_3) a0)
% Found (False_rect0 ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of (P a0)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) a0)):((Xs Xx_3) a0)
% Found (False_rect0 ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b0)
% Found x3:(P Xy)
% Found x3 as proof of (P0 Xy)
% Found x3:(P Xx)
% Found x3 as proof of (P0 Xx)
% Found False_rect00:=(False_rect0 (((eq a) Xy_48) Xy)):(((eq a) Xy_48) Xy)
% Found (False_rect0 (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found False_rect00:=(False_rect0 (((eq b) Xx_3) Xx)):(((eq b) Xx_3) Xx)
% Found (False_rect0 (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((conj00 ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found (((conj0 (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found False_rect00:=(False_rect0 (((eq b) Xx_3) Xx)):(((eq b) Xx_3) Xx)
% Found (False_rect0 (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found False_rect00:=(False_rect0 (((eq a) Xy_48) Xy)):(((eq a) Xy_48) Xy)
% Found (False_rect0 (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((conj00 ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found (((conj0 (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) a0)):((Xs Xx_3) a0)
% Found (False_rect0 ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy_48)
% 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_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) a0)):((Xs Xx_3) a0)
% Found (False_rect0 ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of (P a0)
% Found False_rect00:=(False_rect0 ((Xs Xx_3) a0)):((Xs Xx_3) a0)
% Found (False_rect0 ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of ((Xs Xx_3) a0)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) ((Xs Xx_3) a0)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found False_rect00:=(False_rect0 (((eq b) Xx_3) Xx)):(((eq b) Xx_3) Xx)
% Found (False_rect0 (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found False_rect00:=(False_rect0 (((eq a) Xy_48) Xy)):(((eq a) Xy_48) Xy)
% Found (False_rect0 (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((conj00 ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found (((conj0 (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found eq_ref000:=(eq_ref00 P0):((P0 Xx_3)->(P0 Xx_3))
% Found (eq_ref00 P0) as proof of (P1 Xx_3)
% Found ((eq_ref0 Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found (((eq_ref b) Xx_3) P0) as proof of (P1 Xx_3)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found False_rect00:=(False_rect0 (((eq b) Xx_3) Xx)):(((eq b) Xx_3) Xx)
% Found (False_rect0 (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found False_rect00:=(False_rect0 (((eq a) Xy_48) Xy)):(((eq a) Xy_48) Xy)
% Found (False_rect0 (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((conj00 ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found (((conj0 (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found False_rect00:=(False_rect0 (((eq a) Xy_48) Xy)):(((eq a) Xy_48) Xy)
% Found (False_rect0 (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found False_rect00:=(False_rect0 (((eq b) Xx_3) Xx)):(((eq b) Xx_3) Xx)
% Found (False_rect0 (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((conj00 ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found (((conj0 (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found False_rect00:=(False_rect0 (((eq a) Xy_48) Xy)):(((eq a) Xy_48) Xy)
% Found (False_rect0 (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy)) as proof of (((eq a) Xy_48) Xy)
% Found False_rect00:=(False_rect0 (((eq b) Xx_3) Xx)):(((eq b) Xx_3) Xx)
% Found (False_rect0 (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx)) as proof of (((eq b) Xx_3) Xx)
% Found ((conj00 ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found (((conj0 (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found ((((conj (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy)) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq b) Xx_3) Xx))) ((fun (P0:Type)=> ((False_rect P0) x20)) (((eq a) Xy_48) Xy))) as proof of ((and (((eq b) Xx_3) Xx)) (((eq a) Xy_48) Xy))
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy_48):(((eq a) Xy_48) Xy_48)
% Found (eq_ref0 Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found ((eq_ref a) Xy_48) as proof of (((eq a) Xy_48) b1)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b01):(((eq a) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq a) b01) Xy_48)
% Found ((eq_ref a) b01) as proof of (((eq a) b01) Xy_48)
% Found ((eq_ref a) b01) as proof of (((eq a) b01) Xy_48)
% Found ((eq_ref a) b01) as proof of (((eq a) b01) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b01)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b01)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b01)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq b) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq b) b01) Xx_3)
% Found ((eq_ref b) b01) as proof of (((eq b) b01) Xx_3)
% Found ((eq_ref b) b01) as proof of (((eq b) b01) Xx_3)
% Found ((eq_ref b) b01) as proof of (((eq b) b01) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b01)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b01)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b01)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b01)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref b) b0) P1) as proof of (P2 b0)
% Found (((eq_ref b) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xx)->(P1 Xx))
% Found (eq_ref00 P1) as proof of (P2 Xx)
% Found ((eq_ref0 Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xx)->(P1 Xx))
% Found (eq_ref00 P1) as proof of (P2 Xx)
% Found ((eq_ref0 Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xx)->(P1 Xx))
% Found (eq_ref00 P1) as proof of (P2 Xx)
% Found ((eq_ref0 Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found (((eq_ref b) Xx) P1) as proof of (P2 Xx)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) Xy_48)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx_3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 Xx_3):(((eq b) Xx_3) Xx_3)
% Found (eq_ref0 Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found ((eq_ref b) Xx_3) as proof of (((eq b) Xx_3) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref b) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq b) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found ((eq_ref b) Xx) as proof of (((eq b) Xx) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found ((eq_ref a) b1) as proof of (P b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found ((eq_ref b) b00) as proof of (P b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found ((eq_ref b) b0) as proof of (((eq b) b0) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq b) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found ((eq_ref b) b00) as proof of (((eq b) b00) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq b) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq b) b0) b00)
% Found (
% EOF
%------------------------------------------------------------------------------