TSTP Solution File: SEV181^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV181^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n090.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 13:33:51 EDT 2014
% Result : Timeout 300.09s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV181^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n090.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 08:22:36 CDT 2014
% % CPUTime : 300.09
% 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 0x2772b00>, <kernel.DependentProduct object at 0x2772c20>) of role type named cD_FOR_X5309_type
% Using role type
% Declaring cD_FOR_X5309:(((fofType->Prop)->fofType)->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->fofType)->(fofType->Prop))) cD_FOR_X5309) (fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt))))))) of role definition named cD_FOR_X5309_def
% A new definition: (((eq (((fofType->Prop)->fofType)->(fofType->Prop))) cD_FOR_X5309) (fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))))
% Defined: cD_FOR_X5309:=(fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt))))))
% FOF formula (forall (Xh:((fofType->Prop)->fofType)), ((forall (Xp:(fofType->Prop)) (Xq:(fofType->Prop)), ((((eq fofType) (Xh Xp)) (Xh Xq))->(((eq (fofType->Prop)) Xp) Xq)))->(((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh)))->False))) of role conjecture named cTHM143C_pme
% Conjecture to prove = (forall (Xh:((fofType->Prop)->fofType)), ((forall (Xp:(fofType->Prop)) (Xq:(fofType->Prop)), ((((eq fofType) (Xh Xp)) (Xh Xq))->(((eq (fofType->Prop)) Xp) Xq)))->(((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh)))->False))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xh:((fofType->Prop)->fofType)), ((forall (Xp:(fofType->Prop)) (Xq:(fofType->Prop)), ((((eq fofType) (Xh Xp)) (Xh Xq))->(((eq (fofType->Prop)) Xp) Xq)))->(((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh)))->False)))']
% Parameter fofType:Type.
% Definition cD_FOR_X5309:=(fun (Xh:((fofType->Prop)->fofType)) (Xz:fofType)=> ((ex (fofType->Prop)) (fun (Xt:(fofType->Prop))=> ((and ((Xt (Xh Xt))->False)) (((eq fofType) Xz) (Xh Xt)))))):(((fofType->Prop)->fofType)->(fofType->Prop)).
% Trying to prove (forall (Xh:((fofType->Prop)->fofType)), ((forall (Xp:(fofType->Prop)) (Xq:(fofType->Prop)), ((((eq fofType) (Xh Xp)) (Xh Xq))->(((eq (fofType->Prop)) Xp) Xq)))->(((cD_FOR_X5309 Xh) (Xh (cD_FOR_X5309 Xh)))->False)))
% Found x30:False
% Found (fun (x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1)))=> x30) as proof of False
% Found (fun (x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1)))=> x30) as proof of ((((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))->False)
% Found x30:False
% Found (fun (x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1)))=> x30) as proof of False
% Found (fun (x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1)))=> x30) as proof of ((((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))->False)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found x30:False
% Found (fun (x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1)))=> x30) as proof of False
% Found (fun (x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1)))=> x30) as proof of ((((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))->False)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh x1))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh x1))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh x1))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh x1))
% 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) 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 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) 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_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% 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 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% 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 (((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_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) 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 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(cD_FOR_X5309 Xh):(fofType->Prop);b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh a)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) (Xh (cD_FOR_X5309 Xh))) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 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) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0101:=(eq_sym010 x4):(((eq fofType) b0) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_sym0101:=(eq_sym010 x4):(((eq fofType) b0) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh a))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh a))
% Found (((eq_sym0 (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh a))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh a))
% Found (((eq_sym0 (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 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) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 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) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 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) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 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) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b0)
% Found eq_sym0101:=(eq_sym010 x4):(((eq fofType) b0) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_sym0101:=(eq_sym010 x4):(((eq fofType) b0) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found eq_sym0101:=(eq_sym010 x4):(((eq fofType) b0) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh a))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh a))
% Found (((eq_sym0 (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh a))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh a))
% Found (((eq_sym0 (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh a))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh a))
% Found (((eq_sym0 (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 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) 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) 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% 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) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=x1:(fofType->Prop);b:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_sym0100:=(eq_sym010 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym010 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym01 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_sym0101:=(eq_sym010 x4):(((eq fofType) b0) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found (eq_sym010 x4) as proof of (((eq fofType) (Xh x1)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) a0)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 a0):(((eq (fofType->Prop)) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found ((eq_ref (fofType->Prop)) a0) as proof of (((eq (fofType->Prop)) a0) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion_dep00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (eq_sym000 (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_sym00 a) (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eq_sym0 a0) a) (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((((eq_sym (fofType->Prop)) a0) a) (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((((eq_sym (fofType->Prop)) a0) a) (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found eq_ref00:=(eq_ref0 (Xh a)):(((eq fofType) (Xh a)) (Xh a))
% Found (eq_ref0 (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found ((eq_ref fofType) (Xh a)) as proof of (((eq fofType) (Xh a)) b)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh a))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh a))
% Found (((eq_sym0 (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found ((((eq_sym fofType) (Xh a)) b) x4) as proof of (((eq fofType) b) (Xh a))
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b0)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (Xh a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b) x4) as proof of (((eq fofType) b) (Xh (cD_FOR_X5309 Xh)))
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found eta_expansion000:=(eta_expansion00 a0):(((eq (fofType->Prop)) a0) (fun (x:fofType)=> (a0 x)))
% Found (eta_expansion00 a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found ((eta_expansion0 Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (((eta_expansion fofType) Prop) a0) as proof of (((eq (fofType->Prop)) a0) a)
% Found (eq_sym000 (((eta_expansion fofType) Prop) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((eq_sym00 a) (((eta_expansion fofType) Prop) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((eq_sym0 a0) a) (((eta_expansion fofType) Prop) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((((eq_sym (fofType->Prop)) a0) a) (((eta_expansion fofType) Prop) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((((eq_sym (fofType->Prop)) a0) a) (((eta_expansion fofType) Prop) a0)) as proof of (((eq (fofType->Prop)) a) a0)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found eq_ref00:=(eq_ref0 (Xh x1)):(((eq fofType) (Xh x1)) (Xh x1))
% Found (eq_ref0 (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% Found ((eq_ref fofType) (Xh x1)) as proof of (((eq fofType) (Xh x1)) b1)
% 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 x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x500:=(x50 x4):(((eq (fofType->Prop)) a) x1)
% Found (x50 x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found ((x5 x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found (((x a) x1) x4) as proof of (((eq (fofType->Prop)) a) x1)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b0)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a:=(Xh x1):fofType;b0:=(Xh (cD_FOR_X5309 Xh)):fofType
% Found x4 as proof of (((eq fofType) b0) a)
% Found x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: b0:=(Xh (cD_FOR_X5309 Xh)):fofType;b1:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) b0) b1)
% 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 x4:(((eq fofType) (Xh (cD_FOR_X5309 Xh))) (Xh x1))
% Instantiate: a0:=(Xh (cD_FOR_X5309 Xh)):fofType;b0:=(Xh x1):fofType
% Found x4 as proof of (((eq fofType) a0) b0)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh a0))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh a0))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh a0))
% Found (((eq_sym0 (Xh a0)) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh a0))
% Found ((((eq_sym fofType) (Xh a0)) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh a0))
% Found ((((eq_sym fofType) (Xh a0)) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh a0))
% Found (x50 ((((eq_sym fofType) (Xh a0)) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) a0)
% Found ((x5 a0) ((((eq_sym fofType) (Xh a0)) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((x a) a0) ((((eq_sym fofType) (Xh a0)) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) a0)
% Found (((x a) a0) ((((eq_sym fofType) (Xh a0)) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) a0)
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a0)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a0)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a0)) x4) as proof of (((eq fofType) (Xh a0)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a0)) x4) as proof of (((eq fofType) (Xh a0)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a0)) x4) as proof of (((eq fofType) (Xh a0)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a0)) x4) as proof of (((eq fofType) (Xh a0)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a0)) x4)) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a0)) x4)) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((x a0) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a0)) x4)) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found (((x a0) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a0)) x4)) as proof of (((eq (fofType->Prop)) a0) (cD_FOR_X5309 Xh))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4) as proof of (((eq fofType) (Xh a)) (Xh (cD_FOR_X5309 Xh)))
% Found (x50 ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found ((x5 (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found (((x a) (cD_FOR_X5309 Xh)) ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) (Xh a)) x4)) as proof of (((eq (fofType->Prop)) a) (cD_FOR_X5309 Xh))
% Found eq_sym0000:=(eq_sym000 x4):(((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (eq_sym000 x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((eq_sym00 b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found (((eq_sym0 (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (Xh (cD_FOR_X5309 Xh)))
% Found ((((eq_sym fofType) (Xh (cD_FOR_X5309 Xh))) b0) x4) as proof of (((eq fofType) b0) (
% EOF
%------------------------------------------------------------------------------