TSTP Solution File: SEV276^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV276^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n118.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 13:33:59 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 : SEV276^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n118.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 08:42:16 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 0x114f170>, <kernel.Type object at 0x116da70>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x114f2d8>, <kernel.DependentProduct object at 0x116d878>) of role type named cR
% Using role type
% Declaring cR:(a->(a->Prop))
% FOF formula ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy)))) of role conjecture named cTHM544_pme
% Conjecture to prove = ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy))))']
% Parameter a:Type.
% Parameter cR:(a->(a->Prop)).
% Trying to prove ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), (((and ((cR Xx) Xy)) ((cR Xy) Xx))->(((eq a) Xx) Xy))))
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x1:(P Xx)
% Instantiate: b:=Xx:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x3:(P Xx)
% Instantiate: b:=Xx:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x1:(P Xx)
% Instantiate: b:=Xx:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found x1:(P Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found x3:(P Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x3:(P Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x1:(P Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x1:(P Xx)
% Instantiate: b:=Xx:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found x3:(P Xx)
% Instantiate: b:=Xx:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found x1:(P Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x1:(P Xx)
% Instantiate: b:=Xx:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x1:(P Xx)
% Instantiate: a0:=Xx:a
% Found x1 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref a) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found x1:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x1:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x3:(P Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found ((eq_ref a) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x3:(P Xx)
% Instantiate: a0:=Xx:a
% Found x3 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found x3:(P Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x1:(P b)
% Instantiate: b0:=b:a
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found x1:(P Xx)
% Instantiate: a0:=Xx:a
% Found x1 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found x1:(P Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy)->(P0 Xy))
% Found (eq_ref00 P0) as proof of (P1 Xy)
% Found ((eq_ref0 Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found x1:(P Xy)
% Instantiate: a0:=Xy:a
% Found x1 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found x1:(P b)
% Found x1 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found ((eq_ref a) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found x3:(P b)
% Instantiate: b0:=b:a
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x3:(P Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found x1:(P Xy)
% Instantiate: b0:=Xy:a
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found x1:(P Xy)
% Instantiate: b0:=Xy:a
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% 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 a) b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found x3:(P Xy)
% Instantiate: a0:=Xy:a
% Found x3 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy)->(P0 Xy))
% Found (eq_ref00 P0) as proof of (P1 Xy)
% Found ((eq_ref0 Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found x3:(P b)
% Found x3 as proof of (P0 Xx)
% Found x3:(P b)
% Found x3 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found x3:(P Xy)
% Instantiate: b:=Xy:a
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x3:(P b)
% Instantiate: b0:=b:a
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found x1:(P b)
% Instantiate: b0:=b:a
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found x1:(P Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x1:(P Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found x3:(P Xy)
% Instantiate: a0:=Xy:a
% Found x3 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy)->(P0 Xy))
% Found (eq_ref00 P0) as proof of (P1 Xy)
% Found ((eq_ref0 Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found x1:(P Xy)
% Found x1 as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found x1:(P Xy)
% Instantiate: a0:=Xy:a
% Found x1 as proof of (P0 a0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref000:=(eq_ref00 P0):((P0 Xy)->(P0 Xy))
% Found (eq_ref00 P0) as proof of (P1 Xy)
% Found ((eq_ref0 Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found (((eq_ref a) Xy) P0) as proof of (P1 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found x1:(P b)
% Instantiate: b0:=b:a
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (P b0)
% Found ((eq_ref a) b) as proof of (P b0)
% Found ((eq_ref a) b) as proof of (P b0)
% Found ((eq_ref a) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found x3:(P b)
% Instantiate: b0:=b:a
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found (((eq_ref a) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref a) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found (((eq_ref a) 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 a) b) P) as proof of (P0 b)
% Found (((eq_ref a) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P Xy)
% Found ((eq_ref a) Xy) as proof of (P Xy)
% Found ((eq_ref a) Xy) as proof of (P Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found x1:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x1:(P1 Xy)
% Instantiate: b:=Xy:a
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:a
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found (((eq_ref a) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref a) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found x3:(P b)
% Found x3 as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found ((eq_ref a) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found ((eq_ref a) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a
% EOF
%------------------------------------------------------------------------------