%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SET017^1 : TPTP v6.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n098.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 13:29:56 EDT 2014

% Result   : Timeout 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET017^1 : TPTP v6.1.0. Released v3.6.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 07:46:21 CDT 2014
% % CPUTime  : 300.03 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET008^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x1ed93f8>, <kernel.DependentProduct object at 0x1ed9fc8>) of role type named in_decl
% Using role type
% Declaring in:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named in
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) in) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% Defined: in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% FOF formula (<kernel.Constant object at 0x1ed93f8>, <kernel.DependentProduct object at 0x1ed9f38>) of role type named is_a_decl
% Using role type
% Declaring is_a:(fofType->((fofType->Prop)->Prop))
% FOF formula (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X))) of role definition named is_a
% A new definition: (((eq (fofType->((fofType->Prop)->Prop))) is_a) (fun (X:fofType) (M:(fofType->Prop))=> (M X)))
% Defined: is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X))
% FOF formula (<kernel.Constant object at 0x1ed9f38>, <kernel.DependentProduct object at 0x1ed9ea8>) of role type named emptyset_decl
% Using role type
% Declaring emptyset:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False)) of role definition named emptyset
% A new definition: (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False))
% Defined: emptyset:=(fun (X:fofType)=> False)
% FOF formula (<kernel.Constant object at 0x1ed93f8>, <kernel.DependentProduct object at 0x1ed93b0>) of role type named unord_pair_decl
% Using role type
% Declaring unord_pair:(fofType->(fofType->(fofType->Prop)))
% FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))) of role definition named unord_pair
% A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) unord_pair) (fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))))
% Defined: unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y)))
% FOF formula (<kernel.Constant object at 0x1ed9440>, <kernel.DependentProduct object at 0x1ed9f38>) of role type named singleton_decl
% Using role type
% Declaring singleton:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))) of role definition named singleton
% A new definition: (((eq (fofType->(fofType->Prop))) singleton) (fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)))
% Defined: singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X))
% FOF formula (<kernel.Constant object at 0x1ed93f8>, <kernel.DependentProduct object at 0x1ed9dd0>) of role type named union_decl
% Using role type
% Declaring union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))) of role definition named union
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))))
% Defined: union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x1ed93b0>, <kernel.DependentProduct object at 0x1cf7e18>) of role type named excl_union_decl
% Using role type
% Declaring excl_union:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))) of role definition named excl_union
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) excl_union) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))))
% Defined: excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U))))
% FOF formula (<kernel.Constant object at 0x1ed93b0>, <kernel.DependentProduct object at 0x1cf7ab8>) of role type named intersection_decl
% Using role type
% Declaring intersection:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))) of role definition named intersection
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) intersection) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))))
% Defined: intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U)))
% FOF formula (<kernel.Constant object at 0x1ed93b0>, <kernel.DependentProduct object at 0x1cf7908>) of role type named setminus_decl
% Using role type
% Declaring setminus:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))) of role definition named setminus
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) setminus) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))))
% Defined: setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False)))
% FOF formula (<kernel.Constant object at 0x1cf7908>, <kernel.DependentProduct object at 0x1cf7998>) of role type named complement_decl
% Using role type
% Declaring complement:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))) of role definition named complement
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) complement) (fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)))
% Defined: complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False))
% FOF formula (<kernel.Constant object at 0x1cf7998>, <kernel.DependentProduct object at 0x1cf7cf8>) of role type named disjoint_decl
% Using role type
% Declaring disjoint:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))) of role definition named disjoint
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) disjoint) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)))
% Defined: disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset))
% FOF formula (<kernel.Constant object at 0x1bbfa28>, <kernel.DependentProduct object at 0x1cf7f38>) of role type named subset_decl
% Using role type
% Declaring subset:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))) of role definition named subset
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))))
% Defined: subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))
% FOF formula (<kernel.Constant object at 0x1bbf9e0>, <kernel.DependentProduct object at 0x1cf7e18>) of role type named meets_decl
% Using role type
% Declaring meets:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))) of role definition named meets
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) meets) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))))
% Defined: meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U)))))
% FOF formula (<kernel.Constant object at 0x1cf7e18>, <kernel.DependentProduct object at 0x1cf7758>) of role type named misses_decl
% Using role type
% Declaring misses:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))) of role definition named misses
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) misses) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)))
% Defined: misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False))
% FOF formula (forall (X:fofType) (Y:fofType) (Z:fofType), ((((eq (fofType->Prop)) ((unord_pair X) Y)) ((unord_pair X) Z))->(((eq fofType) Y) Z))) of role conjecture named thm
% Conjecture to prove = (forall (X:fofType) (Y:fofType) (Z:fofType), ((((eq (fofType->Prop)) ((unord_pair X) Y)) ((unord_pair X) Z))->(((eq fofType) Y) Z))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (X:fofType) (Y:fofType) (Z:fofType), ((((eq (fofType->Prop)) ((unord_pair X) Y)) ((unord_pair X) Z))->(((eq fofType) Y) Z)))']
% Parameter fofType:Type.
% Definition in:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% Definition is_a:=(fun (X:fofType) (M:(fofType->Prop))=> (M X)):(fofType->((fofType->Prop)->Prop)).
% Definition emptyset:=(fun (X:fofType)=> False):(fofType->Prop).
% Definition unord_pair:=(fun (X:fofType) (Y:fofType) (U:fofType)=> ((or (((eq fofType) U) X)) (((eq fofType) U) Y))):(fofType->(fofType->(fofType->Prop))).
% Definition singleton:=(fun (X:fofType) (U:fofType)=> (((eq fofType) U) X)):(fofType->(fofType->Prop)).
% Definition union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition excl_union:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((or ((and (X U)) ((Y U)->False))) ((and ((X U)->False)) (Y U)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition intersection:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) (Y U))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition setminus:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (U:fofType)=> ((and (X U)) ((Y U)->False))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition complement:=(fun (X:(fofType->Prop)) (U:fofType)=> ((X U)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition disjoint:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((eq (fofType->Prop)) ((intersection X) Y)) emptyset)):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition subset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition meets:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition misses:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (((ex fofType) (fun (U:fofType)=> ((and (X U)) (Y U))))->False)):((fofType->Prop)->((fofType->Prop)->Prop)).
% Trying to prove (forall (X:fofType) (Y:fofType) (Z:fofType), ((((eq (fofType->Prop)) ((unord_pair X) Y)) ((unord_pair X) Z))->(((eq fofType) Y) Z)))
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x0:(P Y)
% Instantiate: b:=Y:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found x0:(P Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found x0:(P Y)
% Instantiate: b:=Y:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found x0:(P U)
% Instantiate: b:=U:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:(P Y)
% Instantiate: b:=Y:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found x0:(P Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(P Y)
% Instantiate: a:=Y:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:(P1 Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(P1 Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x1:=(x (fun (x1:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x1:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x1:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found x0:(P Y)
% Instantiate: b:=Y:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:(P Y)
% Instantiate: b:=Y:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found x0:(P Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P0 Z))):((P0 Z)->(P0 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P0 Z))) as proof of (P1 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P0 Z))) as proof of (P1 Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x0:(P Z)
% Instantiate: a:=Z:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:(P b)
% Found x0 as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:(P U)
% Instantiate: b:=U:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(P U)
% Instantiate: b:=U:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found x0:(P Z)
% Instantiate: b0:=Z:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P Z)
% Instantiate: b0:=Z:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b0))):((P b0)->(P b0))
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found x0:(P Y)
% Instantiate: a:=Y:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found x0:(P Z)
% Found x0 as proof of (P0 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:(P1 U)
% Instantiate: b:=U:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(P1 U)
% Instantiate: b:=U:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found x1:=(x (fun (x1:(fofType->Prop))=> (P1 U))):((P1 U)->(P1 U))
% Found (x (fun (x1:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found (x (fun (x1:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found x0:(P U)
% Instantiate: b:=U:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P0 U))):((P0 U)->(P0 U))
% Found (x (fun (x0:(fofType->Prop))=> (P0 U))) as proof of (P1 U)
% Found (x (fun (x0:(fofType->Prop))=> (P0 U))) as proof of (P1 U)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found x0:(P U)
% Instantiate: a:=U:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (P Z)
% Found ((eq_ref fofType) Z) as proof of (P Z)
% Found ((eq_ref fofType) Z) as proof of (P Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:(P b)
% Found x0 as proof of (P0 Y)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 U))):((P1 U)->(P1 U))
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 U))):((P1 U)->(P1 U))
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b0))):((P b0)->(P b0))
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b00)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b00)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b00)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found x0:(P U)
% Instantiate: b0:=U:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P U)
% Instantiate: b0:=U:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b0))):((P b0)->(P b0))
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 U))):((P1 U)->(P1 U))
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 U))):((P1 U)->(P1 U))
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 U))):((P1 U)->(P1 U))
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 U))):((P1 U)->(P1 U))
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found (x (fun (x0:(fofType->Prop))=> (P1 U))) as proof of (P2 U)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P U)
% Found x0 as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) Z)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Z)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Z)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P U))):((P U)->(P U))
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found (x (fun (x0:(fofType->Prop))=> (P U))) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (P U)
% Found ((eq_ref fofType) U) as proof of (P U)
% Found ((eq_ref fofType) U) as proof of (P U)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b00)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b00)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b00)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b0))):((P b0)->(P b0))
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found x0:(P Y)
% Instantiate: a:=Y:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Y)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found (x (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% Found x0:(P1 Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(P1 Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x1:=(x (fun (x1:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x1:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x1:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(P Y)
% Instantiate: b:=Y:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found x0:(P Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P0 Z))):((P0 Z)->(P0 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P0 Z))) as proof of (P1 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P0 Z))) as proof of (P1 Z)
% Found x0:(P Z)
% Instantiate: a:=Z:fofType
% Found x0 as proof of (P0 a)
% Found x0:(P Z)
% Instantiate: a:=Z:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) U)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) U)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) U)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 b))):((P1 b)->(P1 b))
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found (x (fun (x0:(fofType->Prop))=> (P1 b))) as proof of (P2 b)
% Found x0:(P b)
% Found x0 as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Z))):((P Z)->(P Z))
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found (x (fun (x0:(fofType->Prop))=> (P Z))) as proof of (P0 Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P Y))):((P Y)->(P Y))
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found (x (fun (x0:(fofType->Prop))=> (P Y))) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x0:(P U)
% Instantiate: b:=U:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(P1 Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(P1 Z)
% Instantiate: b:=Z:fofType
% Found x0 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found x1:=(x (fun (x1:(fofType->Prop))=> (P1 Z))):((P1 Z)->(P1 Z))
% Found (x (fun (x1:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found (x (fun (x1:(fofType->Prop))=> (P1 Z))) as proof of (P2 Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Z)
% Found x0:(P Z)
% Instantiate: b0:=Z:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P Z)
% Instantiate: b0:=Z:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P Z)
% Instantiate: b0:=Z:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:(P Y)
% Instantiate: a:=Y:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x0:(P Y)
% Instantiate: a:=Y:fofType
% Found x0 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b0))):((P b0)->(P b0))
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found x0:=(x (fun (x0:(fofType->Prop))=> (P b0))):((P b0)->(P b0))
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found (x (fun (x0:(fofType->Prop))=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found ((eq_ref fofType) Y) as proof of (P Y)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) U)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found x0:(P b)
% Found x0 as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fof
% EOF
%------------------------------------------------------------------------------