%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU995^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n098.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:29 EDT 2014

% Result   : Timeout 300.06s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU995^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:48:56 CDT 2014
% % CPUTime  : 300.06 
% 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 0x14dad88>, <kernel.Constant object at 0x14da248>) of role type named cV
% Using role type
% Declaring cV:fofType
% FOF formula (<kernel.Constant object at 0x14db200>, <kernel.Single object at 0x14dafc8>) of role type named cU
% Using role type
% Declaring cU:fofType
% FOF formula ((not (((eq fofType) cU) cV))->((ex ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False)))) of role conjecture named cTHM24_pme
% Conjecture to prove = ((not (((eq fofType) cU) cV))->((ex ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False)))):Prop
% We need to prove ['((not (((eq fofType) cU) cV))->((ex ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))))']
% Parameter fofType:Type.
% Parameter cV:fofType.
% Parameter cU:fofType.
% Trying to prove ((not (((eq fofType) cU) cV))->((ex ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x Xx) Xy)) ((x Xy) Xx)))->False)))
% Found (eta_expansion_dep00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b)
% Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b)
% Found eta_expansion000:=(eta_expansion00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x Xx) Xy)) ((x Xy) Xx))))))
% Found (eta_expansion00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b)
% Found (((eta_expansion ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) Prop) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b)
% Found (((eta_expansion ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) Prop) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b)
% Found (((eta_expansion ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) Prop) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x Xx) Xy)) ((x Xy) Xx))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x Xx) Xy)) ((x Xy) Xx))))))
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False)))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False)))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False)))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False)))
% Found eq_ref00:=(eq_ref0 a):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) a) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found eq_ref00:=(eq_ref0 b):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx))))))
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found x1:(P cU)
% Instantiate: b:=cU:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found x2:(P cU)
% Instantiate: b:=cU:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x1:(P cV)
% Instantiate: b:=cV:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x2:(P cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found x1:(P cU)
% Instantiate: b:=cU:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x2:(P cU)
% Instantiate: b:=cU:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x2:(P cU)
% Instantiate: b:=cU:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x1:(P cV)
% Instantiate: b:=cV:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found x2:(P cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found x2:(P cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found (((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found ((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found (((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found ((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found ((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_trans0000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found (((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found ((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found (((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found ((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found ((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of (forall (P:(Prop->Prop)), ((P (f x0))->(P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))))
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x1:(P cV)
% Instantiate: b:=cV:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x2:(P cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x Xx) Xy)) ((x Xy) Xx))))))
% Found (eta_expansion_dep00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b0)
% Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b0)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b0)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b0)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (not (forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))))) b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x Xx) Xy)) ((x Xy) Xx)))->False)))
% Found (eta_expansion_dep00 (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b0)
% Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b0)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b0)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b0)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) (fun (G:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((G Xx) Xy)) ((G Xy) Xx)))->False))) b0)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 f):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found x1:(P cU)
% Instantiate: a:=cU:fofType
% Found x1 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found x2:(P cU)
% Instantiate: a:=cU:fofType
% Found x2 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x1:(P1 cV)
% Instantiate: b:=cV:fofType
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found x1:(P1 cV)
% Instantiate: b:=cV:fofType
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x2:(P1 cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found x2:(P1 cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) (fun (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found (((eta_expansion_dep ((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))) (fun (x1:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found ((eq_ref (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) as proof of (((eq (((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found x1:(P cV)
% Instantiate: a:=cV:fofType
% Found x1 as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P0):((P0 cV)->(P0 cV))
% Found (eq_ref00 P0) as proof of (P1 cV)
% Found ((eq_ref0 cV) P0) as proof of (P1 cV)
% Found (((eq_ref fofType) cV) P0) as proof of (P1 cV)
% Found (((eq_ref fofType) cV) P0) as proof of (P1 cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x1:(P b)
% Found x1 as proof of (P0 cU)
% Found x1:(P0 (f x0))
% Instantiate: b:=(f x0):Prop
% Found x1 as proof of (P1 b)
% Found x1:(P0 (f x0))
% Instantiate: b:=(f x0):Prop
% Found x1 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found x2:(P b)
% Instantiate: b0:=b:fofType
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found ((eq_trans0000 ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0)))) as proof of (forall (P:(Prop->Prop)), ((P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))->(P (f x0))))
% Found (((eq_trans000 (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0)))) as proof of (forall (P:(Prop->Prop)), ((P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))->(P (f x0))))
% Found ((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (forall (P:(Prop->Prop)), ((P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))->(P (f x0))))
% Found (((((eq_trans0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (forall (P:(Prop->Prop)), ((P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))->(P (f x0))))
% Found ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (forall (P:(Prop->Prop)), ((P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))->(P (f x0))))
% Found ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (forall (P:(Prop->Prop)), ((P ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))->(P (f x0))))
% Found ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found (eq_sym000 ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_sym00 (f x0)) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((eq_sym0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((((eq_sym Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) ((((eq_sym Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found x2:(P cV)
% Instantiate: a:=cV:fofType
% Found x2 as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref000:=(eq_ref00 P0):((P0 cV)->(P0 cV))
% Found (eq_ref00 P0) as proof of (P1 cV)
% Found ((eq_ref0 cV) P0) as proof of (P1 cV)
% Found (((eq_ref fofType) cV) P0) as proof of (P1 cV)
% Found (((eq_ref fofType) cV) P0) as proof of (P1 cV)
% Found x2:(P b)
% Found x2 as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((eq_trans0000 x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (fun (P0:(Prop->Prop))=> (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((eq_trans0000 x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (fun (P0:(Prop->Prop))=> (((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) P0)) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x2:(P cU)
% Instantiate: b:=cU:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((eq_trans0000 x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found eq_ref000:=(eq_ref00 P0):((P0 (f x0))->(P0 (f x0)))
% Found (eq_ref00 P0) as proof of (P1 (f x0))
% Found ((eq_ref0 (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found (((eq_ref Prop) (f x0)) P0) as proof of (P1 (f x0))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((eq_trans00000 ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((eq_trans0000 x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) b)) (x2:(((eq Prop) b) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_trans000 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) b)) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((((eq_trans0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (fun (P0:(Prop->Prop))=> ((((fun (x1:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (x2:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((((eq_trans Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x1) x2) (fun (x4:Prop)=> ((P0 (f x0))->(P0 x4))))) ((eq_ref Prop) (f x0))) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_ref Prop) (f x0)) P0))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found x1:(P cV)
% Instantiate: b0:=cV:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P cV)
% Instantiate: b0:=cV:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (P cU)
% Found ((eq_ref fofType) cU) as proof of (P cU)
% Found ((eq_ref fofType) cU) as proof of (P cU)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% Found (fun (x0:((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref Prop) b) as proof of (P0 b)
% Found ((eq_ref Prop) b) as proof of (P0 b)
% Found ((eq_ref Prop) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found x2:(P b)
% Instantiate: b0:=b:fofType
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found x2:(P cV)
% Instantiate: b0:=cV:fofType
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found x1:(P cV)
% Found x1 as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (P cU)
% Found ((eq_ref fofType) cU) as proof of (P cU)
% Found ((eq_ref fofType) cU) as proof of (P cU)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 cV)->(P1 cV))
% Found (eq_ref00 P1) as proof of (P2 cV)
% Found ((eq_ref0 cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found (((eq_ref fofType) cV) P1) as proof of (P2 cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Instantiate: b:=((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False):Prop
% Found x1 as proof of (P1 b)
% Found x2:(P b)
% Found x2 as proof of (P0 cV)
% Found x2:(P cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_sym0100 ((eq_ref Prop) (f x0))) x1) as proof of (P0 (f x0))
% Found ((eq_sym0100 ((eq_ref Prop) (f x0))) x1) as proof of (P0 (f x0))
% Found (((fun (x2:(((eq Prop) (f x0)) b))=> ((eq_sym010 x2) P0)) ((eq_ref Prop) (f x0))) x1) as proof of (P0 (f x0))
% Found (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((eq_sym01 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1) as proof of (P0 (f x0))
% Found (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1) as proof of (P0 (f x0))
% Found (fun (x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1)) as proof of (P0 (f x0))
% Found (fun (P0:(Prop->Prop)) (x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1)) as proof of ((P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))->(P0 (f x0)))
% Found (fun (P0:(Prop->Prop)) (x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found (eq_sym000 (fun (P0:(Prop->Prop)) (x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((eq_sym00 (f x0)) (fun (P0:(Prop->Prop)) (x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (((eq_sym0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) (fun (P0:(Prop->Prop)) (x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> ((((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found ((((eq_sym Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) (fun (P0:(Prop->Prop)) (x1:(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((fun (x2:(((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))=> (((((eq_sym Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) x2) P0)) ((eq_ref Prop) (f x0))) x1))) as proof of (((eq Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (P cV)
% Found ((eq_ref fofType) cV) as proof of (P cV)
% Found ((eq_ref fofType) cV) as proof of (P cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (P cV)
% Found ((eq_ref fofType) cV) as proof of (P cV)
% Found ((eq_ref fofType) cV) as proof of (P cV)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b00)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b00)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b00)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found x1:(P cV)
% Instantiate: b:=cV:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found x2:(P cU)
% Instantiate: b0:=cU:fofType
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cU)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (P b0)
% Found ((eq_ref fofType) cU) as proof of (P b0)
% Found ((eq_ref fofType) cU) as proof of (P b0)
% Found ((eq_ref fofType) cU) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b00)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b00)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b00)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x2:(P cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found x2:(P cV)
% Instantiate: b:=cV:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P cU)->(P cU))
% Found (eq_ref00 P) as proof of (P0 cU)
% Found ((eq_ref0 cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found (((eq_ref fofType) cU) P) as proof of (P0 cU)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) cV)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) cV)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) cV)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) cV)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cU)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b1)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% Found (eq_sym010 ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found ((eq_sym01 b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0))) as proof of (((eq Prop) b) (f x0))
% Found ((eq_trans0000 ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found (((eq_trans000 (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) b) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found ((((eq_trans00 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found (((((eq_trans0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0)))) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found ((eq_sym0000 ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)))=> ((eq_sym000 x1) (fun (x3:Prop)=> ((P0 (f x0))->(P0 x3))))) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)))=> (((eq_sym00 (f x0)) x1) (fun (x3:Prop)=> ((P0 (f x0))->(P0 x3))))) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)))=> ((((eq_sym0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) x1) (fun (x3:Prop)=> ((P0 (f x0))->(P0 x3))))) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) (((eq_sym0 (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (((fun (x1:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)))=> (((((eq_sym Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) x1) (fun (x3:Prop)=> ((P0 (f x0))->(P0 x3))))) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) ((((eq_sym Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) (((eq_ref Prop) (f x0)) P0)) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found (fun (P0:(Prop->Prop))=> (((fun (x1:(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)))=> (((((eq_sym Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) x1) (fun (x3:Prop)=> ((P0 (f x0))->(P0 x3))))) ((((((eq_trans Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) (f x0)) ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))) ((((eq_sym Prop) (f x0)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((eq_ref Prop) (f x0))))) (((eq_ref Prop) (f x0)) P0))) as proof of ((P0 (f x0))->(P0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)))
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 cV):(((eq fofType) cV) cV)
% Found (eq_ref0 cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found ((eq_ref fofType) cV) as proof of (((eq fofType) cV) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) cV)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 cU):(((eq fofType) cU) cU)
% Found (eq_ref0 cU) as proof of (((eq fofType) cU) b00)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b00)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b00)
% Found ((eq_ref fofType) cU) as proof of (((eq fofType) cU) b00)
% Found x1:(P cU)
% Instantiate: a:=cU:fofType
% Found x1 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% Found eq_ref00:=(eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)):(((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False))
% Found (eq_ref0 ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found ((eq_ref Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) as proof of (((eq Prop) ((forall (Xx:(fofType->fofType)) (Xy:(fofType->fofType)), (((eq (fofType->fofType)) ((x0 Xx) Xy)) ((x0 Xy) Xx)))->False)) b)
% Found eq_ref000:=(eq_ref00 P):((P cV)->(P cV))
% Found (eq_ref00 P) as proof of (P0 cV)
% Found ((eq_ref0 cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found (((eq_ref fofType) cV) P) as proof of (P0 cV)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x2:(P cU)
% Instantiate: a:=cU:fofType
% Found x2 as proof of (P0 a)
% Found x2:(P cU)
% Instantiate: a:=cU:fofType
% Found x2 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cV)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (
% EOF
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