%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU659^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n189.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 13:32:44 EDT 2014

% Result   : Timeout 300.07s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU659^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n189.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:04:31 CDT 2014
% % CPUTime  : 300.07 
% 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 0x205b3b0>, <kernel.DependentProduct object at 0x205bb48>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x20b8758>, <kernel.DependentProduct object at 0x205bb48>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x205b248>, <kernel.DependentProduct object at 0x205ba70>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x205b8c0>, <kernel.Sort object at 0x1b43368>) of role type named cartprodmempair1_type
% Using role type
% Declaring cartprodmempair1:Prop
% FOF formula (((eq Prop) cartprodmempair1) (forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))) of role definition named cartprodmempair1
% A new definition: (((eq Prop) cartprodmempair1) (forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))))
% Defined: cartprodmempair1:=(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy))))))))))
% FOF formula (<kernel.Constant object at 0x205b5a8>, <kernel.Sort object at 0x1b43368>) of role type named setukpairinjL_type
% Using role type
% Declaring setukpairinjL:Prop
% FOF formula (((eq Prop) setukpairinjL) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((kpair Xx) Xy)) ((kpair Xz) Xu))->(((eq fofType) Xx) Xz)))) of role definition named setukpairinjL
% A new definition: (((eq Prop) setukpairinjL) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((kpair Xx) Xy)) ((kpair Xz) Xu))->(((eq fofType) Xx) Xz))))
% Defined: setukpairinjL:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((kpair Xx) Xy)) ((kpair Xz) Xu))->(((eq fofType) Xx) Xz)))
% FOF formula (cartprodmempair1->(setukpairinjL->(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A))))) of role conjecture named cartprodpairmemEL
% Conjecture to prove = (cartprodmempair1->(setukpairinjL->(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(cartprodmempair1->(setukpairinjL->(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A)))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter kpair:(fofType->(fofType->fofType)).
% Parameter cartprod:(fofType->(fofType->fofType)).
% Definition cartprodmempair1:=(forall (A:fofType) (B:fofType) (Xu:fofType), (((in Xu) ((cartprod A) B))->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) B)) (((eq fofType) Xu) ((kpair Xx) Xy)))))))))):Prop.
% Definition setukpairinjL:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((kpair Xx) Xy)) ((kpair Xz) Xu))->(((eq fofType) Xx) Xz))):Prop.
% Trying to prove (cartprodmempair1->(setukpairinjL->(forall (A:fofType) (B:fofType) (Xx:fofType) (Xy:fofType), (((in ((kpair Xx) Xy)) ((cartprod A) B))->((in Xx) A)))))
% Found eq_ref00:=(eq_ref0 ((kpair Xx0) Xy0)):(((eq fofType) ((kpair Xx0) Xy0)) ((kpair Xx0) Xy0))
% Found (eq_ref0 ((kpair Xx0) Xy0)) as proof of (((eq fofType) ((kpair Xx0) Xy0)) ((kpair A) Xu))
% Found ((eq_ref fofType) ((kpair Xx0) Xy0)) as proof of (((eq fofType) ((kpair Xx0) Xy0)) ((kpair A) Xu))
% Found ((eq_ref fofType) ((kpair Xx0) Xy0)) as proof of (((eq fofType) ((kpair Xx0) Xy0)) ((kpair A) Xu))
% Found ((eq_ref fofType) ((kpair Xx0) Xy0)) as proof of (((eq fofType) ((kpair Xx0) Xy0)) ((kpair A) Xu))
% Found ((eq_ref fofType) ((kpair Xx0) Xy0)) as proof of (((eq fofType) ((kpair Xx0) Xy0)) ((kpair A) Xu))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx0) Xu0))
% Found eq_ref00:=(eq_ref0 ((kpair Xx00) Xy00)):(((eq fofType) ((kpair Xx00) Xy00)) ((kpair Xx00) Xy00))
% Found (eq_ref0 ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found eq_ref00:=(eq_ref0 ((kpair Xx00) Xy00)):(((eq fofType) ((kpair Xx00) Xy00)) ((kpair Xx00) Xy00))
% Found (eq_ref0 ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found ((eq_ref fofType) ((kpair Xx00) Xy00)) as proof of (((eq fofType) ((kpair Xx00) Xy00)) ((kpair A) Xu0))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx01) Xy01)):(((eq fofType) ((kpair Xx01) Xy01)) ((kpair Xx01) Xy01))
% Found (eq_ref0 ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx0) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx00) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx01) Xy01)):(((eq fofType) ((kpair Xx01) Xy01)) ((kpair Xx01) Xy01))
% Found (eq_ref0 ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx01) Xy01)):(((eq fofType) ((kpair Xx01) Xy01)) ((kpair Xx01) Xy01))
% Found (eq_ref0 ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx01) Xy01)):(((eq fofType) ((kpair Xx01) Xy01)) ((kpair Xx01) Xy01))
% Found (eq_ref0 ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found ((eq_ref fofType) ((kpair Xx01) Xy01)) as proof of (((eq fofType) ((kpair Xx01) Xy01)) ((kpair A) Xu1))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx00) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx0) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx01) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx02) Xy02)):(((eq fofType) ((kpair Xx02) Xy02)) ((kpair Xx02) Xy02))
% Found (eq_ref0 ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found ((eq_ref fofType) ((kpair Xx02) Xy02)) as proof of (((eq fofType) ((kpair Xx02) Xy02)) ((kpair A) Xu2))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx4) Xy4)):(((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx4) Xy4))
% Found (eq_ref0 ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found ((eq_ref fofType) ((kpair Xx4) Xy4)) as proof of (((eq fofType) ((kpair Xx4) Xy4)) ((kpair Xx3) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx03) Xy03)):(((eq fofType) ((kpair Xx03) Xy03)) ((kpair Xx03) Xy03))
% Found (eq_ref0 ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx30) Xy30)):(((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx30) Xy30))
% Found (eq_ref0 ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx30) Xy30)) as proof of (((eq fofType) ((kpair Xx30) Xy30)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx20) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx3) Xy3)):(((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx3) Xy3))
% Found (eq_ref0 ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found ((eq_ref fofType) ((kpair Xx3) Xy3)) as proof of (((eq fofType) ((kpair Xx3) Xy3)) ((kpair Xx2) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx10) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx2) Xy2)):(((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx2) Xy2))
% Found (eq_ref0 ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found ((eq_ref fofType) ((kpair Xx2) Xy2)) as proof of (((eq fofType) ((kpair Xx2) Xy2)) ((kpair Xx11) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx11) Xy11)):(((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx11) Xy11))
% Found (eq_ref0 ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found ((eq_ref fofType) ((kpair Xx11) Xy11)) as proof of (((eq fofType) ((kpair Xx11) Xy11)) ((kpair Xx00) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx10) Xy10)):(((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx10) Xy10))
% Found (eq_ref0 ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found ((eq_ref fofType) ((kpair Xx10) Xy10)) as proof of (((eq fofType) ((kpair Xx10) Xy10)) ((kpair Xx01) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx12) Xy12)):(((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx12) Xy12))
% Found (eq_ref0 ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found ((eq_ref fofType) ((kpair Xx12) Xy12)) as proof of (((eq fofType) ((kpair Xx12) Xy12)) ((kpair Xx0) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx1) Xy1)):(((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx1) Xy1))
% Found (eq_ref0 ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found ((eq_ref fofType) ((kpair Xx1) Xy1)) as proof of (((eq fofType) ((kpair Xx1) Xy1)) ((kpair Xx02) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx03) Xy03)):(((eq fofType) ((kpair Xx03) Xy03)) ((kpair Xx03) Xy03))
% Found (eq_ref0 ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx03) Xy03)):(((eq fofType) ((kpair Xx03) Xy03)) ((kpair Xx03) Xy03))
% Found (eq_ref0 ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx03) Xy03)):(((eq fofType) ((kpair Xx03) Xy03)) ((kpair Xx03) Xy03))
% Found (eq_ref0 ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx03) Xy03)):(((eq fofType) ((kpair Xx03) Xy03)) ((kpair Xx03) Xy03))
% Found (eq_ref0 ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found ((eq_ref fofType) ((kpair Xx03) Xy03)) as proof of (((eq fofType) ((kpair Xx03) Xy03)) ((kpair A) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx21) Xy21)):(((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx21) Xy21))
% Found (eq_ref0 ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx21) Xy21)) as proof of (((eq fofType) ((kpair Xx21) Xy21)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx1) Xu3))
% Found eq_ref00:=(eq_ref0 ((kpair Xx20) Xy20)):(((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx20) Xy20))
% Found (eq_ref0 ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kpair Xx20) Xy20)) ((kpair Xx10) Xu3))
% Found ((eq_ref fofType) ((kpair Xx20) Xy20)) as proof of (((eq fofType) ((kp
% EOF
%------------------------------------------------------------------------------