%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYN036^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n109.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 13:37:44 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SYN036^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n109.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 07:43:46 CDT 2014
% % CPUTime: 300.10 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x14cab00>, <kernel.DependentProduct object at 0x1528cb0>) of role type named cQ
% Using role type
% Declaring cQ:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x14ca050>, <kernel.DependentProduct object at 0x1528b48>) of role type named cP
% Using role type
% Declaring cP:(fofType->Prop)
% FOF formula ((iff ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))))) of role conjecture named cX2129
% Conjecture to prove = ((iff ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((iff ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))))']
% Parameter fofType:Type.
% Parameter cQ:(fofType->Prop).
% Parameter cP:(fofType->Prop).
% Trying to prove ((iff ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found ((iff_sym0 (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found ((iff_sym0 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym0 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found ((iff_sym1 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found ((iff_sym1 (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym0 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found ((iff_sym1 (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found ((iff_sym1 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_sym100:=(iff_sym10 x00):((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (iff_sym10 x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((iff_sym1 (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found iff_sym100:=(iff_sym10 x00):((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (iff_sym10 x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found ((iff_sym1 (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found ((iff_sym2 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found ((iff_sym2 (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_sym200:=(iff_sym20 x00):((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (iff_sym20 x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found ((iff_sym2 (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found iff_sym200:=(iff_sym20 x00):((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (iff_sym20 x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((iff_sym2 (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym2 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym2 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym2 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym2 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_sym200:=(iff_sym20 x00):((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (iff_sym20 x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((iff_sym2 (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_sym200:=(iff_sym20 x00):((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (iff_sym20 x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found ((iff_sym2 (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_sym200:=(iff_sym20 x00):((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (iff_sym20 x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((iff_sym2 (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found iff_sym200:=(iff_sym20 x00):((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (iff_sym20 x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found ((iff_sym2 (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym2 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym2 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym2 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym2 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym0 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_sym300:=(iff_sym30 x00):((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (iff_sym30 x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((iff_sym3 (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found iff_sym300:=(iff_sym30 x00):((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (iff_sym30 x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found ((iff_sym3 (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym0 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_sym300:=(iff_sym30 x00):((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (iff_sym30 x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found ((iff_sym3 (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cQ Xy))) ((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found iff_sym300:=(iff_sym30 x00):((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (iff_sym30 x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found ((iff_sym3 (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found (((iff_sym ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy))) x00) as proof of ((iff (forall (Xy:fofType), (cP Xy))) ((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found ((iff_sym0 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found ((iff_sym0 (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x20:=(x2 x30):(forall (Xy:fofType), (cQ Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cQ Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cQ Xy))
% Found x20:=(x2 x30):(forall (Xy:fofType), (cP Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found ((iff_sym0 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found ((iff_sym0 (cP x1)) (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found ((iff_sym1 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found ((iff_sym1 (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found ((iff_sym0 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x2:(cP Xy)
% Instantiate: x1:=Xy:fofType
% Found (fun (x2:(cP Xy))=> x2) as proof of (cP x1)
% Found (fun (x2:(cP Xy))=> x2) as proof of ((cP Xy)->(cP x1))
% Found x2:(cP x1)
% Instantiate: x1:=Xy:fofType
% Found (fun (x2:(cP x1))=> x2) as proof of (cP Xy)
% Found (fun (x2:(cP x1))=> x2) as proof of ((cP x1)->(cP Xy))
% Found ((conj10 (fun (x2:(cP x1))=> x2)) (fun (x2:(cP Xy))=> x2)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (((conj1 ((cP Xy)->(cP x1))) (fun (x2:(cP x1))=> x2)) (fun (x2:(cP Xy))=> x2)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found ((((conj ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1))) (fun (x2:(cP x1))=> x2)) (fun (x2:(cP Xy))=> x2)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found ((((conj ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1))) (fun (x2:(cP x1))=> x2)) (fun (x2:(cP Xy))=> x2)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found x2:(cQ Xy)
% Instantiate: x1:=Xy:fofType
% Found (fun (x2:(cQ Xy))=> x2) as proof of (cQ x1)
% Found (fun (x2:(cQ Xy))=> x2) as proof of ((cQ Xy)->(cQ x1))
% Found x2:(cQ x1)
% Instantiate: x1:=Xy:fofType
% Found (fun (x2:(cQ x1))=> x2) as proof of (cQ Xy)
% Found (fun (x2:(cQ x1))=> x2) as proof of ((cQ x1)->(cQ Xy))
% Found ((conj10 (fun (x2:(cQ x1))=> x2)) (fun (x2:(cQ Xy))=> x2)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (((conj1 ((cQ Xy)->(cQ x1))) (fun (x2:(cQ x1))=> x2)) (fun (x2:(cQ Xy))=> x2)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found ((((conj ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1))) (fun (x2:(cQ x1))=> x2)) (fun (x2:(cQ Xy))=> x2)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found ((((conj ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1))) (fun (x2:(cQ x1))=> x2)) (fun (x2:(cQ Xy))=> x2)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym1 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (iff_refl (cP x1)) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (iff_refl (cQ x1)) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym2 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym2 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x3:(cQ x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cQ x2))=> x3) as proof of (cQ Xy)
% Found (fun (x3:(cQ x2))=> x3) as proof of ((cQ x2)->(cQ Xy))
% Found x3:(cQ Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cQ Xy))=> x3) as proof of (cQ x2)
% Found (fun (x3:(cQ Xy))=> x3) as proof of ((cQ Xy)->(cQ x2))
% Found ((conj10 (fun (x3:(cQ x2))=> x3)) (fun (x3:(cQ Xy))=> x3)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (((conj1 ((cQ Xy)->(cQ x2))) (fun (x3:(cQ x2))=> x3)) (fun (x3:(cQ Xy))=> x3)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found ((((conj ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2))) (fun (x3:(cQ x2))=> x3)) (fun (x3:(cQ Xy))=> x3)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found ((((conj ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2))) (fun (x3:(cQ x2))=> x3)) (fun (x3:(cQ Xy))=> x3)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found ((iff_sym1 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x1)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found ((iff_sym1 (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((iff (cP x1)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (iff_refl (cQ x2)) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x1))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found ((iff_sym1 (cP x1)) (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found (((iff_sym (cP Xy)) (cP x1)) (iff_refl (cP Xy))) as proof of ((and ((cP x1)->(cP Xy))) ((cP Xy)->(cP x1)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x1))
% Found (iff_sym10 (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found ((iff_sym1 (cQ x1)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found (((iff_sym (cQ Xy)) (cQ x1)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x1)->(cQ Xy))) ((cQ Xy)->(cQ x1)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2))) as proof of (((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2))) as proof of ((((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))->(((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->((iff (cP x2)) (cP Xy))))
% Found (and_rect10 (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((and_rect1 ((iff (cP x2)) (cP Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Type) (x3:((((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) P) x3) x00)) ((iff (cP x2)) (cP Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Type) (x3:((((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) P) x3) (x0 x10))) ((iff (cP x2)) (cP Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Type) (x3:((((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) P) x3) (x0 x10))) ((iff (cP x2)) (cP Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x4:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (fun (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))) (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2))) as proof of (((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cQ x2)) (cQ Xy)))
% Found (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))) (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2))) as proof of ((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))->(((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cQ x2)) (cQ Xy))))
% Found (and_rect10 (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))) (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2)))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((and_rect1 ((iff (cQ x2)) (cQ Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))) (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2)))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((fun (P:Type) (x3:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cQ Xy)))->(((forall (Xy:fofType), (cQ Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cQ Xy)))) ((forall (Xy:fofType), (cQ Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x3) x00)) ((iff (cQ x2)) (cQ Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))) (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2)))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((fun (P:Type) (x3:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cQ Xy)))->(((forall (Xy:fofType), (cQ Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cQ Xy)))) ((forall (Xy:fofType), (cQ Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x3) (x0 x10))) ((iff (cQ x2)) (cQ Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))) (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2)))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((fun (P:Type) (x3:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cQ Xy)))->(((forall (Xy:fofType), (cQ Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cQ Xy)))) ((forall (Xy:fofType), (cQ Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x3) (x0 x10))) ((iff (cQ x2)) (cQ Xy))) (fun (x3:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cQ Xy0)))) (x4:((forall (Xy0:fofType), (cQ Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cQ x2)))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x20:=(x2 x30):(forall (Xy:fofType), (cQ Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cQ Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cQ Xy))
% Found x20:=(x2 x30):(forall (Xy:fofType), (cP Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x2 x30) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x1)):((iff (cP x1)) (cP x1))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found (iff_refl (cP x1)) as proof of ((iff (cP x1)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ x1)):((iff (cQ x1)) (cQ x1))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found (iff_refl (cQ x1)) as proof of ((iff (cQ x1)) (cQ Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym00 (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found ((iff_sym0 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((and ((cQ x2)->(cQ Xy))) ((cQ Xy)->(cQ x2)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found iff_refl0:=(iff_refl (cQ x2)):((iff (cQ x2)) (cQ x2))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (iff_refl (cQ x2)) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym2 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym2 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cQ Xx)) (cQ Xy)))))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00 as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x11):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x11) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym20 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym2 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cQ Xy)):((iff (cQ Xy)) (cQ Xy))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_refl (cQ Xy)) as proof of ((iff (cQ Xy)) (cQ x2))
% Found (iff_sym20 (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found ((iff_sym2 (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found (((iff_sym (cQ Xy)) (cQ x2)) (iff_refl (cQ Xy))) as proof of ((iff (cQ x2)) (cQ Xy))
% Found x00:=(x0 x12):((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found (x0 x12) as proof of ((iff ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))) (forall (Xy:fofType), (cP Xy)))
% Found x00:=(x0 x10):((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cQ Xy)))
% Found (x0 x10) as proof of ((iff ((ex fofType) (fun (Xx:
% EOF
%------------------------------------------------------------------------------