TSTP Solution File: SEU938^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU938^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n098.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:24 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 : SEU938^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n098.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:43:51 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 0x1918320>, <kernel.Constant object at 0x19185a8>) of role type named a
% Using role type
% Declaring a:fofType
% FOF formula (<kernel.Constant object at 0x1918ef0>, <kernel.Single object at 0x1918320>) of role type named b
% Using role type
% Declaring b:fofType
% FOF formula (<kernel.Constant object at 0x1919440>, <kernel.DependentProduct object at 0x196d950>) of role type named h
% Using role type
% Declaring h:(fofType->fofType)
% FOF formula (((and ((and (((eq fofType) (h a)) a)) (not (((eq fofType) (h b)) a)))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->((forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_6:(fofType->fofType)), ((Xp Xj_6)->(Xp (fun (Xx:fofType)=> (Xj (Xj_6 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_7:(fofType->fofType)), ((Xp Xj_7)->(Xp (fun (Xx:fofType)=> (Xj (Xj_7 Xx)))))))->(Xp Xk)))))->False)) of role conjecture named cTHM196_pme
% Conjecture to prove = (((and ((and (((eq fofType) (h a)) a)) (not (((eq fofType) (h b)) a)))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->((forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_6:(fofType->fofType)), ((Xp Xj_6)->(Xp (fun (Xx:fofType)=> (Xj (Xj_6 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_7:(fofType->fofType)), ((Xp Xj_7)->(Xp (fun (Xx:fofType)=> (Xj (Xj_7 Xx)))))))->(Xp Xk)))))->False)):Prop
% We need to prove ['(((and ((and (((eq fofType) (h a)) a)) (not (((eq fofType) (h b)) a)))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->((forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_6:(fofType->fofType)), ((Xp Xj_6)->(Xp (fun (Xx:fofType)=> (Xj (Xj_6 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_7:(fofType->fofType)), ((Xp Xj_7)->(Xp (fun (Xx:fofType)=> (Xj (Xj_7 Xx)))))))->(Xp Xk)))))->False))']
% Parameter fofType:Type.
% Parameter a:fofType.
% Parameter b:fofType.
% Parameter h:(fofType->fofType).
% Trying to prove (((and ((and (((eq fofType) (h a)) a)) (not (((eq fofType) (h b)) a)))) (forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), ((forall (Xx:fofType), (((eq fofType) (Xf Xx)) (Xg Xx)))->(((eq (fofType->fofType)) Xf) Xg))))->((forall (Xj:(fofType->fofType)) (Xk:(fofType->fofType)), ((forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_6:(fofType->fofType)), ((Xp Xj_6)->(Xp (fun (Xx:fofType)=> (Xj (Xj_6 Xx)))))))->(Xp (fun (Xx:fofType)=> (Xk (Xj Xx))))))->(forall (Xp:((fofType->fofType)->Prop)), (((and (Xp Xj)) (forall (Xj_7:(fofType->fofType)), ((Xp Xj_7)->(Xp (fun (Xx:fofType)=> (Xj (Xj_7 Xx)))))))->(Xp Xk)))))->False))
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h 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_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 (h a)):(((eq fofType) (h a)) (h a))
% Found (eq_ref0 (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found eq_ref00:=(eq_ref0 (h a)):(((eq fofType) (h a)) (h a))
% Found (eq_ref0 (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x5:(P (h b))
% Instantiate: b0:=(h b):fofType
% Found x5 as proof of (P0 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 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h (h a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (h a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (h a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (h a)))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=(h a):fofType
% Found x3 as proof of (((eq fofType) b0) a)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found x5:(P (h b))
% Instantiate: b0:=(h b):fofType
% Found x5 as proof of (P0 b0)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found x50:(P (h b))
% Instantiate: b0:=(h b):fofType
% Found x50 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h (h a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (h a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (h a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (h a)))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found x5:(P (h b))
% Instantiate: b0:=(h b):fofType
% Found x5 as proof of (P0 b0)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=(h a):fofType
% Found x3 as proof of (((eq fofType) b0) a)
% Found x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 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 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found x5:(P a)
% Instantiate: b0:=a:fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) 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_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found ((eq_ref fofType) (h b)) as proof of (P b)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h 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 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 (h b0)):(((eq fofType) (h b0)) (h b0))
% Found (eq_ref0 (h b0)) as proof of (P b0)
% Found ((eq_ref fofType) (h b0)) as proof of (P b0)
% Found ((eq_ref fofType) (h b0)) as proof of (P b0)
% Found ((eq_ref fofType) (h b0)) as proof of (P 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_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h (h a)))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found x5:(P (h a))
% Instantiate: b0:=(h a):fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found x30:=(x3 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found x5:(P (h a))
% Instantiate: b0:=(h a):fofType
% Found x5 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref00:=(eq_ref0 (h a)):(((eq fofType) (h a)) (h a))
% Found (eq_ref0 (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found x5:(P (h b))
% Instantiate: a0:=b:fofType
% Found x5 as proof of (P0 (h a0))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: a0:=(h a):fofType
% Found x3 as proof of (((eq fofType) a0) a)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: a0:=(h a):fofType
% Found x3 as proof of (((eq fofType) a0) a)
% Found x5:(P (h b))
% Instantiate: a0:=b:fofType
% Found x5 as proof of (P0 a0)
% Found x50:(P (h b))
% Instantiate: a0:=b:fofType
% Found x50 as proof of (P0 a0)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: a0:=(h a):fofType
% Found x3 as proof of (((eq fofType) a0) a)
% Found x50:(P (h b))
% Instantiate: a0:=b:fofType
% Found x50 as proof of (P0 (h a0))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: a0:=(h a):fofType
% Found x3 as proof of (((eq fofType) a0) a)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x5:(P (h b))
% Instantiate: a0:=b:fofType
% Found x5 as proof of (P0 a0)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: a0:=(h a):fofType
% Found x3 as proof of (((eq fofType) a0) a)
% Found x5:(P (h b))
% Instantiate: a0:=b:fofType
% Found x5 as proof of (P0 (h a0))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: a0:=(h a):fofType
% Found x3 as proof of (((eq fofType) a0) a)
% Found eq_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h (h a)))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x30:=(x3 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x30:=(x3 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (h a)):(((eq fofType) (h a)) (h a))
% Found (eq_ref0 (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found ((eq_ref fofType) (h a)) as proof of (P a)
% Found eq_ref00:=(eq_ref0 (h (h a))):(((eq fofType) (h (h a))) (h (h a)))
% Found (eq_ref0 (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref00:=(eq_ref0 (h (h a))):(((eq fofType) (h (h a))) (h (h a)))
% Found (eq_ref0 (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (h a))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (h a))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (h a))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (h a))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b00)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b00)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b00)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b00)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 (h a))->(P1 (h a)))
% Found (eq_ref00 P1) as proof of (P2 (h a))
% Found ((eq_ref0 (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h a))
% Found eq_ref000:=(eq_ref00 P1):((P1 (h a))->(P1 (h a)))
% Found (eq_ref00 P1) as proof of (P2 (h a))
% Found ((eq_ref0 (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h a))
% Found eq_ref000:=(eq_ref00 P1):((P1 (h a))->(P1 (h a)))
% Found (eq_ref00 P1) as proof of (P2 (h a))
% Found ((eq_ref0 (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h a))
% Found eq_ref000:=(eq_ref00 P1):((P1 (h a))->(P1 (h a)))
% Found (eq_ref00 P1) as proof of (P2 (h a))
% Found ((eq_ref0 (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h a))
% Found (((eq_ref fofType) (h a)) P1) as proof of (P2 (h 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) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h 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 x30:=(x3 (fun (x5:fofType)=> (P (h b)))):((P (h b))->(P (h b)))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found (x3 (fun (x5:fofType)=> (P (h b)))) as proof of (P0 (h b))
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x30:=(x3 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) 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) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref00:=(eq_ref0 (h (h a))):(((eq fofType) (h (h a))) (h (h a)))
% Found (eq_ref0 (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% 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 (h (h a))):(((eq fofType) (h (h a))) (h (h a)))
% Found (eq_ref0 (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found ((eq_ref fofType) (h (h a))) as proof of (((eq fofType) (h (h a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 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_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h (h a)))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found eq_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h (h a)))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found eq_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h a))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=(h a):fofType
% Found x3 as proof of (((eq fofType) b0) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h (h a)))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h (h a)))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h (h a)))
% Found eq_ref000:=(eq_ref00 P):((P (h (h a)))->(P (h (h a))))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h (h a))) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h (h a))) P) as proof of (P0 (h 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) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% 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 (h (h a))):(((eq fofType) (h (h a))) (h (h a)))
% Found (eq_ref0 (h (h a))) as proof of (P (h a))
% Found ((eq_ref fofType) (h (h a))) as proof of (P (h a))
% Found ((eq_ref fofType) (h (h a))) as proof of (P (h a))
% Found eq_ref00:=(eq_ref0 (h (h a))):(((eq fofType) (h (h a))) (h (h a)))
% Found (eq_ref0 (h (h a))) as proof of (P (h a))
% Found ((eq_ref fofType) (h (h a))) as proof of (P (h a))
% Found ((eq_ref fofType) (h (h a))) as proof of (P (h a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h a))
% 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 x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found x3:(((eq fofType) (h a)) a)
% Found x3 as proof of (((eq fofType) (h a)) a)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x5:(P (h b))
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 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 (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found ((eq_ref fofType) (h b)) as proof of (((eq fofType) (h b)) b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (h b)):(((eq fofType) (h b)) (h b))
% Found (eq_ref0 (h b)) as proof of (P b0)
% Found ((eq_ref fofType) (h b)) as proof of (P b0)
% Found ((eq_ref fofType) (h b)) as proof of (P b0)
% Found ((eq_ref fofType) (h b)) as proof of (P 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 x5:(P b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P0 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_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found eq_ref000:=(eq_ref00 P0):((P0 (h b))->(P0 (h b)))
% Found (eq_ref00 P0) as proof of (P (h b))
% Found ((eq_ref0 (h b)) P0) as proof of (P (h b))
% Found (((eq_ref fofType) (h b)) P0) as proof of (P (h b))
% Found (((eq_ref fofType) (h b)) P0) as proof of (P (h b))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=(h a):fofType
% Found x3 as proof of (((eq fofType) b0) a)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P (h b))->(P (h b)))
% Found (eq_ref00 P) as proof of (P0 (h b))
% Found ((eq_ref0 (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found (((eq_ref fofType) (h b)) P) as proof of (P0 (h b))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found x3:(((eq fofType) (h a)) a)
% Instantiate: b0:=a:fofType
% Found x3 as proof of (((eq fofType) (h a)) b0)
% Found eq_ref000:=(eq_ref00 P):((P (h a))->(P (h a)))
% Found (eq_ref00 P) as proof of (P0 (h a))
% Found ((eq_ref0 (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found (((eq_ref fofType) (h a)) P) as proof of (P0 (h a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h b))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Fou
% EOF
%------------------------------------------------------------------------------