TSTP Solution File: ALG281^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ALG281^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n111.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 13:18:22 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG281^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n111.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 09:06:31 CDT 2014
% % CPUTime : 300.02
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x122b248>, <kernel.Constant object at 0x122bb48>) of role type named cE
% Using role type
% Declaring cE:fofType
% FOF formula (<kernel.Constant object at 0x122b518>, <kernel.DependentProduct object at 0xe4bf80>) of role type named cJ
% Using role type
% Declaring cJ:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1283440>, <kernel.DependentProduct object at 0xe4b3f8>) of role type named cP
% Using role type
% Declaring cP:(fofType->(fofType->fofType))
% FOF formula (((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType), (((eq fofType) ((cP X) (cJ X))) cE))) of role conjecture named cTHM16_pme
% Conjecture to prove = (((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType), (((eq fofType) ((cP X) (cJ X))) cE))):Prop
% We need to prove ['(((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType), (((eq fofType) ((cP X) (cJ X))) cE)))']
% Parameter fofType:Type.
% Parameter cE:fofType.
% Parameter cJ:(fofType->fofType).
% Parameter cP:(fofType->(fofType->fofType)).
% Trying to prove (((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType), (((eq fofType) ((cP X) (cJ X))) cE)))
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x0:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x2:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% 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 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x0:(P cE)
% Instantiate: b:=cE:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found x0:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% 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) 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 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x4:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x2:(P cE)
% Instantiate: b:=cE:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found x0:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x2:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) 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 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x2:(P cE)
% Instantiate: b:=cE:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found x0:(P cE)
% Instantiate: b:=cE:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Xy)) Xy))->(P ((cP (cJ Xy)) Xy)))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found ((eq_ref0 ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Found x30:=(x3 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: b:=cE:fofType
% Found x30 as proof of (((eq fofType) ((cP cE) cE)) b)
% Found x4:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x4 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 ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: b:=cE:fofType
% Found x40 as proof of (((eq fofType) ((cP cE) cE)) b)
% Found x0:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found x2:(P ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x2 as proof of (P0 b)
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: b:=cE:fofType
% Found x40 as proof of (((eq fofType) ((cP cE) cE)) b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Xy)) Xy))->(P ((cP (cJ Xy)) Xy)))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found ((eq_ref0 ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% 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 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x4:(P cE)
% Instantiate: b:=cE:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) 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 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% 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 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) 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 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found eq_ref000:=(eq_ref00 P):((P ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found x4:(P cE)
% Instantiate: b:=cE:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found x4:(P cE)
% Instantiate: b:=cE:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:(P cE)
% Instantiate: b:=cE:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found x2:(P cE)
% Instantiate: b:=cE:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found x2:(P cE)
% Instantiate: b:=cE:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Xy)) Xy))->(P ((cP (cJ Xy)) Xy)))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found ((eq_ref0 ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) cE)
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% 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) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found x30:=(x3 ((cP X) (cJ X))):(((eq fofType) ((cP cE) ((cP X) (cJ X)))) ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x30 as proof of (((eq fofType) ((cP cE) ((cP X) (cJ X)))) b)
% Found x4:(P cE)
% Instantiate: b:=cE:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Xy)) Xy))->(P ((cP (cJ Xy)) Xy)))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found ((eq_ref0 ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Xy)) Xy))->(P ((cP (cJ Xy)) Xy)))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found ((eq_ref0 ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found x30:=(x3 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x30 as proof of (((eq fofType) a) cE)
% Found x30:=(x3 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x30 as proof of (((eq fofType) a) cE)
% Found x30:=(x3 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x30 as proof of (((eq fofType) a) cE)
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x40 as proof of (((eq fofType) a) cE)
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x40 as proof of (((eq fofType) a) cE)
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x40 as proof of (((eq fofType) a) cE)
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x40 as proof of (((eq fofType) a) cE)
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x40 as proof of (((eq fofType) a) cE)
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found x40:=(x4 cE):(((eq fofType) ((cP cE) cE)) cE)
% Instantiate: a:=((cP cE) cE):fofType
% Found x40 as proof of (((eq fofType) a) cE)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found x4:(P cE)
% Instantiate: b:=cE:fofType
% Found x4 as proof of (P0 b)
% Found x30:=(x3 ((cP X) (cJ X))):(((eq fofType) ((cP cE) ((cP X) (cJ X)))) ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x30 as proof of (((eq fofType) ((cP cE) ((cP X) (cJ X)))) b)
% Found x4:(P cE)
% Instantiate: b:=cE:fofType
% Found x4 as proof of (P0 b)
% Found x30:=(x3 ((cP X) (cJ X))):(((eq fofType) ((cP cE) ((cP X) (cJ X)))) ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x30 as proof of (((eq fofType) ((cP cE) ((cP X) (cJ X)))) b)
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% 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 ((cP X) (cJ X)))->(P ((cP X) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP X) (cJ X)))
% Found ((eq_ref0 ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found (((eq_ref fofType) ((cP X) (cJ X))) P) as proof of (P0 ((cP X) (cJ X)))
% Found x0:(P cE)
% Instantiate: b:=cE:fofType
% Found x0 as proof of (P0 b)
% Found x40:=(x4 ((cP X) (cJ X))):(((eq fofType) ((cP cE) ((cP X) (cJ X)))) ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x40 as proof of (((eq fofType) ((cP cE) ((cP X) (cJ X)))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Xy)) Xy))->(P ((cP (cJ Xy)) Xy)))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found ((eq_ref0 ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Xy)) Xy))->(P ((cP (cJ Xy)) Xy)))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found ((eq_ref0 ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found (((eq_ref fofType) ((cP (cJ Xy)) Xy)) P) as proof of (P0 ((cP (cJ Xy)) Xy))
% Found x2:(P cE)
% Instantiate: b:=cE:fofType
% Found x2 as proof of (P0 b)
% Found x40:=(x4 ((cP X) (cJ X))):(((eq fofType) ((cP cE) ((cP X) (cJ X)))) ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x40 as proof of (((eq fofType) ((cP cE) ((cP X) (cJ X)))) b)
% Found x2:(P cE)
% Instantiate: b:=cE:fofType
% Found x2 as proof of (P0 b)
% Found x40:=(x4 ((cP X) (cJ X))):(((eq fofType) ((cP cE) ((cP X) (cJ X)))) ((cP X) (cJ X)))
% Instantiate: b:=((cP X) (cJ X)):fofType
% Found x40 as proof of (((eq fofType) ((cP cE) ((cP X) (cJ X)))) b)
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP X) (cJ X)))
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found x10:=(x1 Xy):(((eq fofType) ((cP (cJ Xy)) Xy)) cE)
% Instantiate: b:=cE:fofType
% Found x10 as proof of (((eq fofType) ((cP (cJ Xy)) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP X) (cJ X)))
% Found eq_ref00:=(eq_ref0 cE):(((eq fofType) cE) cE)
% Found (eq_ref0 cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) b0)
% Found ((eq_ref fofType) cE) as proof of (((eq fofType) cE) 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) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) cE)
% 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 cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found eq_ref000:=(eq_ref00 P):((P cE)->(P cE))
% Found (eq_ref00 P) as proof of (P0 cE)
% Found ((eq_ref0 cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found (((eq_ref fofType) cE) P) as proof of (P0 cE)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Xy)) Xy))
% Found eq_ref00:=(eq_ref0 ((cP X) (cJ X))):(((eq fofType) ((cP X) (cJ X))) ((cP X) (cJ X)))
% Found (eq_ref0 ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X))) as proof of (((eq fofType) ((cP X) (cJ X))) b)
% Found ((eq_ref fofType) ((cP X) (cJ X)
% EOF
%------------------------------------------------------------------------------