TSTP Solution File: NUN023^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUN023^2 : TPTP v6.4.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 16091.75MB
% OS : Linux 3.10.0-327.10.1.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Mar 28 10:08:06 EDT 2016
% Result : Timeout 290.39s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN023^2 : TPTP v6.4.0. Released v6.4.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.22 % Computer : n003.star.cs.uiowa.edu
% 0.02/0.22 % Model : x86_64 x86_64
% 0.02/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.22 % Memory : 16091.75MB
% 0.02/0.22 % OS : Linux 3.10.0-327.10.1.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Mar 25 14:05:57 CDT 2016
% 0.02/0.23 % CPUTime :
% 0.08/0.47 Python 2.7.8
% 3.10/3.66 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 3.10/3.66 FOF formula (<kernel.Constant object at 0x2aabdfd553f8>, <kernel.Constant object at 0x2aabdfd55998>) of role type named n6
% 3.10/3.66 Using role type
% 3.10/3.66 Declaring zero:fofType
% 3.10/3.66 FOF formula (<kernel.Constant object at 0x2aabdfd55b48>, <kernel.DependentProduct object at 0x2aabdda699e0>) of role type named n7
% 3.10/3.66 Using role type
% 3.10/3.66 Declaring s:(fofType->fofType)
% 3.10/3.66 FOF formula (<kernel.Constant object at 0x2aabdfd553f8>, <kernel.DependentProduct object at 0x2aabdddfc200>) of role type named n8
% 3.10/3.66 Using role type
% 3.10/3.66 Declaring ite:(Prop->(fofType->(fofType->fofType)))
% 3.10/3.66 FOF formula (<kernel.Constant object at 0x2aabdddfc908>, <kernel.DependentProduct object at 0x2aabdda69878>) of role type named n9
% 3.10/3.66 Using role type
% 3.10/3.66 Declaring h:(fofType->fofType)
% 3.10/3.66 FOF formula (((and ((and (forall (X100:Prop) (U:fofType) (V:fofType), (X100->(((eq fofType) (((ite X100) U) V)) U)))) (forall (X100:Prop) (U:fofType) (V:fofType), ((X100->False)->(((eq fofType) (((ite X100) U) V)) V))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) zero))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))) of role conjecture named n10
% 3.10/3.66 Conjecture to prove = (((and ((and (forall (X100:Prop) (U:fofType) (V:fofType), (X100->(((eq fofType) (((ite X100) U) V)) U)))) (forall (X100:Prop) (U:fofType) (V:fofType), ((X100->False)->(((eq fofType) (((ite X100) U) V)) V))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) zero))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))):Prop
% 3.10/3.66 We need to prove ['(((and ((and (forall (X100:Prop) (U:fofType) (V:fofType), (X100->(((eq fofType) (((ite X100) U) V)) U)))) (forall (X100:Prop) (U:fofType) (V:fofType), ((X100->False)->(((eq fofType) (((ite X100) U) V)) V))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) zero))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))))']
% 3.10/3.66 Parameter fofType:Type.
% 3.10/3.66 Parameter zero:fofType.
% 3.10/3.66 Parameter s:(fofType->fofType).
% 3.10/3.66 Parameter ite:(Prop->(fofType->(fofType->fofType))).
% 3.10/3.66 Parameter h:(fofType->fofType).
% 3.10/3.66 Trying to prove (((and ((and (forall (X100:Prop) (U:fofType) (V:fofType), (X100->(((eq fofType) (((ite X100) U) V)) U)))) (forall (X100:Prop) (U:fofType) (V:fofType), ((X100->False)->(((eq fofType) (((ite X100) U) V)) V))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) zero))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))))
% 3.10/3.66 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 3.10/3.66 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 3.10/3.66 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 3.10/3.66 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 3.10/3.66 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 3.10/3.66 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 3.10/3.66 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 3.10/3.66 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 3.10/3.66 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 3.10/3.66 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 3.10/3.66 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 3.10/3.66 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 3.10/3.66 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 3.10/3.66 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 3.10/3.66 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 7.40/7.97 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 7.40/7.97 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 7.40/7.97 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 7.40/7.97 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 7.40/7.97 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 7.40/7.97 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 7.40/7.97 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 7.40/7.97 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 7.40/7.97 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.40/7.97 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 7.40/7.97 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 7.40/7.97 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 11.83/12.39 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 11.83/12.39 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 11.83/12.39 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 11.83/12.39 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 11.83/12.39 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 11.83/12.39 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 11.83/12.39 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 11.83/12.39 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 11.83/12.39 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 11.83/12.39 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 11.83/12.39 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 11.83/12.39 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 16.87/17.42 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 16.87/17.42 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 16.87/17.42 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 16.87/17.42 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 16.87/17.42 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 16.87/17.42 Found eq_ref00:=(eq_ref0 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 16.87/17.42 Found (eq_ref0 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) (fun (x:(fofType->fofType))=> ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 16.87/17.42 Found (eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 16.87/17.42 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 21.24/21.83 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 21.24/21.83 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 21.24/21.83 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 21.24/21.83 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 21.24/21.83 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 21.24/21.83 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 21.24/21.83 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 21.24/21.83 Found eta_expansion000:=(eta_expansion00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) (fun (x:(fofType->fofType))=> ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 21.24/21.83 Found (eta_expansion00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 21.24/21.83 Found ((eta_expansion0 Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 21.24/21.83 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 21.24/21.83 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 25.24/25.84 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 25.24/25.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 25.24/25.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 25.24/25.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 25.24/25.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 25.24/25.84 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero)))
% 25.24/25.84 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 25.24/25.84 Found eta_expansion000:=(eta_expansion00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) (fun (x:(fofType->fofType))=> ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 25.24/25.84 Found (eta_expansion00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 25.24/25.84 Found ((eta_expansion0 Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 25.24/25.84 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 25.24/25.84 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 25.24/25.84 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 25.24/25.84 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 25.24/25.84 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 25.24/25.84 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 25.24/25.84 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 25.24/25.84 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 25.24/25.84 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 30.12/30.73 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 30.12/30.73 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 30.12/30.73 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 30.12/30.73 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 30.12/30.73 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 30.12/30.73 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero)))
% 30.12/30.73 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 30.12/30.73 Found eta_expansion000:=(eta_expansion00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) (fun (x:(fofType->fofType))=> ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 30.12/30.73 Found (eta_expansion00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 30.12/30.73 Found ((eta_expansion0 Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 30.12/30.73 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 30.12/30.73 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 34.26/34.84 Found (((eta_expansion (fofType->fofType)) Prop) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 34.26/34.84 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 34.26/34.84 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 34.26/34.84 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 34.26/34.84 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 34.26/34.84 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 34.26/34.84 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) (fun (x:(fofType->fofType))=> ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 34.26/34.84 Found (eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 34.26/34.84 Found ((eta_expansion_dep0 (fun (x5:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 34.26/34.84 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 34.26/34.84 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 34.26/34.84 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero)))) b)
% 34.26/34.84 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 34.26/34.84 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 34.26/34.84 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 34.26/34.84 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 34.26/34.84 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 34.26/34.84 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 34.26/34.84 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 34.26/34.84 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 34.26/34.84 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 34.26/34.84 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 37.77/38.32 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 37.77/38.32 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 37.77/38.32 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 37.77/38.32 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 37.77/38.32 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 37.77/38.32 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 37.77/38.32 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 37.77/38.32 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 37.77/38.32 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 37.77/38.32 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 37.77/38.32 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero)))
% 37.77/38.32 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))))
% 37.77/38.32 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 37.77/38.32 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 37.77/38.32 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 37.77/38.32 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 37.77/38.32 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 37.77/38.32 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 37.77/38.32 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 37.77/38.32 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 45.13/45.70 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 45.13/45.70 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 45.13/45.70 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 45.13/45.70 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 45.13/45.70 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 45.13/45.70 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 45.13/45.70 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 45.13/45.70 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 45.13/45.70 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 45.13/45.70 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 45.13/45.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 45.13/45.70 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 45.13/45.70 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 45.13/45.70 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 45.13/45.70 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 45.13/45.70 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 45.13/45.70 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 45.13/45.70 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 45.13/45.70 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 45.13/45.70 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 45.13/45.70 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 45.13/45.70 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 56.30/56.87 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 56.30/56.87 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 56.30/56.87 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 56.30/56.87 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 56.30/56.87 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 56.30/56.87 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 56.30/56.87 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 56.30/56.87 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 56.30/56.87 Found eq_ref000:=(eq_ref00 P):((P (x4 zero))->(P (x4 zero)))
% 56.30/56.87 Found (eq_ref00 P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found ((eq_ref0 (x4 zero)) P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 56.30/56.87 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 56.30/56.87 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 56.30/56.87 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 56.30/56.87 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 56.30/56.87 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 56.30/56.87 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 56.30/56.87 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 56.30/56.87 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 56.30/56.87 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 56.30/56.87 Found eq_ref000:=(eq_ref00 P):((P (x4 zero))->(P (x4 zero)))
% 56.30/56.87 Found (eq_ref00 P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found ((eq_ref0 (x4 zero)) P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 56.30/56.87 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 64.04/64.60 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 64.04/64.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 64.04/64.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 64.04/64.60 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 64.04/64.60 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 64.04/64.60 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 64.04/64.60 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 64.04/64.60 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 64.04/64.60 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 64.04/64.60 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 64.04/64.60 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 64.04/64.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 64.04/64.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 64.04/64.60 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 64.04/64.60 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 64.04/64.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 64.04/64.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 64.04/64.60 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 64.04/64.60 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 64.04/64.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 64.04/64.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 64.04/64.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 73.71/74.25 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 73.71/74.25 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 73.71/74.25 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 73.71/74.25 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 73.71/74.25 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 73.71/74.25 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 73.71/74.25 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 73.71/74.25 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 73.71/74.25 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 73.71/74.25 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 73.71/74.25 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 73.71/74.25 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 73.71/74.25 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 73.71/74.25 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 73.71/74.25 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 73.71/74.25 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 73.71/74.25 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 73.71/74.25 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 73.71/74.25 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 73.71/74.25 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 73.71/74.25 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 73.71/74.25 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 73.71/74.25 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 73.71/74.25 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.67 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 85.12/85.67 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.67 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.67 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.67 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.12/85.67 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 85.12/85.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 85.12/85.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 85.12/85.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 85.12/85.67 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 85.12/85.67 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.67 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.12/85.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 85.12/85.68 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 85.12/85.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.12/85.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.12/85.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 85.12/85.68 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 85.12/85.68 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 85.12/85.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.12/85.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 85.12/85.68 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 85.12/85.68 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 85.12/85.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 85.12/85.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 85.12/85.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 100.46/100.99 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 100.46/100.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 100.46/100.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 100.46/100.99 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 100.46/100.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 100.46/100.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 100.46/100.99 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 100.46/100.99 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 100.46/100.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 100.46/100.99 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 100.46/100.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 100.46/100.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 100.46/100.99 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 100.46/100.99 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 100.46/100.99 Found (eq_ref0 b) as proof of (((eq fofType) b) (x4 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x4 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x4 zero))
% 100.46/100.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x4 zero))
% 100.46/100.99 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 100.46/100.99 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 100.46/100.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 124.18/124.75 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 124.18/124.75 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.75 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 124.18/124.75 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 124.18/124.75 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 124.18/124.75 Found (eq_ref0 b) as proof of (((eq fofType) b) (x4 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x4 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x4 zero))
% 124.18/124.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x4 zero))
% 124.18/124.75 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 124.18/124.75 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.75 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 124.18/124.76 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 124.18/124.76 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 124.18/124.76 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 124.18/124.76 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 124.18/124.76 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 124.18/124.76 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 124.18/124.76 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 124.18/124.76 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 124.18/124.76 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 135.55/136.06 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 135.55/136.06 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 135.55/136.06 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 135.55/136.06 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 135.55/136.06 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 135.55/136.06 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 135.55/136.06 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 135.55/136.06 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 135.55/136.06 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 135.55/136.06 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 135.55/136.06 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 135.55/136.06 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 135.55/136.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 135.55/136.06 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 135.55/136.06 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 138.70/139.22 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 138.70/139.22 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 138.70/139.22 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 138.70/139.22 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 138.70/139.22 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 138.70/139.22 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 138.70/139.22 Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 138.70/139.22 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 138.70/139.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 138.70/139.22 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 138.70/139.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 138.70/139.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 138.70/139.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 138.70/139.22 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 138.70/139.22 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 138.70/139.22 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 138.70/139.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 138.70/139.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 138.70/139.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 138.70/139.22 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 138.70/139.22 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 138.70/139.22 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 138.70/139.22 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 138.70/139.22 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 148.84/149.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 148.84/149.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 148.84/149.35 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 148.84/149.35 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 148.84/149.35 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 148.84/149.35 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 148.84/149.35 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 148.84/149.35 Found eq_ref00:=(eq_ref0 (((eq fofType) (x0 (s zero))) zero)):(((eq Prop) (((eq fofType) (x0 (s zero))) zero)) (((eq fofType) (x0 (s zero))) zero))
% 148.84/149.35 Found (eq_ref0 (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 148.84/149.35 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 148.84/149.35 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 148.84/149.35 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 148.84/149.35 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 148.84/149.35 Found (eta_expansion00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.84/149.35 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.84/149.35 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.84/149.35 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.84/149.35 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.84/149.35 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 148.84/149.35 Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 148.84/149.35 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 148.84/149.35 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 148.84/149.35 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 148.84/149.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 148.84/149.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 148.84/149.35 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 148.84/149.35 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 160.94/161.48 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 160.94/161.48 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 160.94/161.48 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 160.94/161.48 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 160.94/161.48 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 160.94/161.48 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 160.94/161.48 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 160.94/161.48 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 160.94/161.48 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 160.94/161.48 Found eq_ref00:=(eq_ref0 (((eq fofType) (x0 (s zero))) zero)):(((eq Prop) (((eq fofType) (x0 (s zero))) zero)) (((eq fofType) (x0 (s zero))) zero))
% 160.94/161.48 Found (eq_ref0 (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 160.94/161.48 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 160.94/161.48 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 160.94/161.48 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 160.94/161.48 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 160.94/161.48 Found (eta_expansion00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 160.94/161.48 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 160.94/161.48 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 160.94/161.48 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 160.94/161.48 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 160.94/161.48 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 160.94/161.48 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 160.94/161.48 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 160.94/161.48 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 173.07/173.62 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 173.07/173.62 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 173.07/173.62 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 173.07/173.62 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 173.07/173.62 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 173.07/173.62 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 173.07/173.62 Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% 173.07/173.62 Found iff_refl as proof of b
% 173.07/173.62 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 173.07/173.62 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 173.07/173.62 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 173.07/173.62 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 173.07/173.62 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 173.07/173.62 Found ((conj00 ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 173.07/173.62 Found (((conj0 b) ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 173.07/173.62 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 173.07/173.62 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 173.07/173.62 Found eta_expansion000:=(eta_expansion00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 173.07/173.62 Found (eta_expansion00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 173.07/173.62 Found ((eta_expansion0 Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 173.07/173.62 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 173.07/173.62 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 173.07/173.62 Found (((eta_expansion (fofType->fofType)) Prop) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 173.07/173.62 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 173.07/173.62 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 173.07/173.62 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 173.07/173.62 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 182.98/183.47 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 182.98/183.47 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 182.98/183.47 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 182.98/183.47 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 182.98/183.47 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 182.98/183.47 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 182.98/183.47 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 182.98/183.47 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 182.98/183.47 Found eq_ref00:=(eq_ref0 (((eq fofType) (x2 (s zero))) zero)):(((eq Prop) (((eq fofType) (x2 (s zero))) zero)) (((eq fofType) (x2 (s zero))) zero))
% 182.98/183.47 Found (eq_ref0 (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 182.98/183.47 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 182.98/183.47 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 182.98/183.47 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 182.98/183.47 Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% 182.98/183.47 Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% 182.98/183.47 Found iff_refl as proof of b
% 182.98/183.47 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 182.98/183.47 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 182.98/183.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 182.98/183.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 182.98/183.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 182.98/183.47 Found ((conj00 ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 182.98/183.47 Found (((conj0 b) ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 182.98/183.47 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 182.98/183.47 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) iff_refl) as proof of (P b)
% 182.98/183.47 Found x1:(P (x0 zero))
% 182.98/183.47 Instantiate: b:=(x0 zero):fofType
% 182.98/183.47 Found x1 as proof of (P0 b)
% 182.98/183.47 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 182.98/183.47 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 182.98/183.47 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 182.98/183.47 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 182.98/183.47 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 182.98/183.47 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 182.98/183.47 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 182.98/183.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 182.98/183.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 182.98/183.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 182.98/183.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 182.98/183.47 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 182.98/183.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 182.98/183.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 182.98/183.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 182.98/183.47 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 182.98/183.47 Found (eq_ref0 (x0 (s zero))) as proof of b
% 182.98/183.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 182.98/183.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 182.98/183.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 182.98/183.47 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 182.98/183.47 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 191.48/191.99 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 191.48/191.99 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 191.48/191.99 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 191.48/191.99 Found eq_ref00:=(eq_ref0 (((eq fofType) (x0 (s zero))) zero)):(((eq Prop) (((eq fofType) (x0 (s zero))) zero)) (((eq fofType) (x0 (s zero))) zero))
% 191.48/191.99 Found (eq_ref0 (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 191.48/191.99 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 191.48/191.99 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 191.48/191.99 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 191.48/191.99 Found eq_ref00:=(eq_ref0 (((eq fofType) (x2 (s zero))) zero)):(((eq Prop) (((eq fofType) (x2 (s zero))) zero)) (((eq fofType) (x2 (s zero))) zero))
% 191.48/191.99 Found (eq_ref0 (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 191.48/191.99 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 191.48/191.99 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 191.48/191.99 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 191.48/191.99 Found x1:(P (x0 zero))
% 191.48/191.99 Instantiate: b:=(x0 zero):fofType
% 191.48/191.99 Found x1 as proof of (P0 b)
% 191.48/191.99 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 191.48/191.99 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 191.48/191.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 191.48/191.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 191.48/191.99 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 191.48/191.99 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 191.48/191.99 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 191.48/191.99 Found ((eta_expansion_dep0 (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 191.48/191.99 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 191.48/191.99 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 191.48/191.99 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 191.48/191.99 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 191.48/191.99 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 191.48/191.99 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 191.48/191.99 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 191.48/191.99 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 191.48/191.99 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 191.48/191.99 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 191.48/191.99 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 191.48/191.99 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 201.35/201.83 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 201.35/201.83 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 201.35/201.83 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 201.35/201.83 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 201.35/201.83 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 201.35/201.83 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 201.35/201.83 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 201.35/201.83 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 201.35/201.83 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 201.35/201.83 Found (eq_ref0 (x0 (s zero))) as proof of b
% 201.35/201.83 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 201.35/201.83 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 201.35/201.83 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 201.35/201.83 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 201.35/201.83 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 201.35/201.83 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 201.35/201.83 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 201.35/201.83 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 201.35/201.83 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 201.35/201.83 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 201.35/201.83 Found eq_ref00:=(eq_ref0 (((eq fofType) (x0 (s zero))) zero)):(((eq Prop) (((eq fofType) (x0 (s zero))) zero)) (((eq fofType) (x0 (s zero))) zero))
% 201.35/201.83 Found (eq_ref0 (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 201.35/201.83 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 201.35/201.83 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 201.35/201.83 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 201.35/201.83 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 201.35/201.83 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 201.35/201.83 Found or_ind as proof of b
% 201.35/201.83 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 201.35/201.83 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 201.35/201.83 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 201.35/201.83 Found ((conj00 ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 201.35/201.83 Found (((conj0 b) ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 201.35/201.83 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 201.35/201.83 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 201.35/201.83 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 201.35/201.83 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 201.35/201.83 Found ((eta_expansion_dep0 (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 201.35/201.83 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 201.35/201.83 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 205.08/205.61 Found (((eta_expansion_dep (fofType->fofType)) (fun (x5:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 205.08/205.61 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 205.08/205.61 Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 205.08/205.61 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (H:(fofType->fofType))=> ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))))
% 205.08/205.61 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 205.08/205.61 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 205.08/205.61 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 205.08/205.61 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 205.08/205.61 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 205.08/205.61 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 205.08/205.61 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 205.08/205.61 Found or_ind as proof of b
% 205.08/205.61 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 205.08/205.61 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 205.08/205.61 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 205.08/205.61 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 205.08/205.61 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 205.08/205.61 Found ((conj00 ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 205.08/205.61 Found (((conj0 b) ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 205.08/205.61 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 205.08/205.61 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 205.08/205.61 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 205.08/205.61 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 205.08/205.61 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 205.08/205.61 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 205.08/205.61 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 205.08/205.61 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 205.08/205.61 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 205.08/205.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 205.08/205.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 209.67/210.16 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 209.67/210.16 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 209.67/210.16 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 209.67/210.16 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 209.67/210.16 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 209.67/210.16 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 209.67/210.16 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 209.67/210.16 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 209.67/210.16 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 209.67/210.16 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 209.67/210.16 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 209.67/210.16 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 209.67/210.16 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 209.67/210.16 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 209.67/210.16 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 209.67/210.16 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 209.67/210.16 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 209.67/210.16 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 209.67/210.16 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 209.67/210.16 Found (eq_ref0 b) as proof of (P b)
% 209.67/210.16 Found ((eq_ref fofType) b) as proof of (P b)
% 209.67/210.16 Found ((eq_ref fofType) b) as proof of (P b)
% 209.67/210.16 Found ((eq_ref fofType) b) as proof of (P b)
% 209.67/210.16 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 209.67/210.16 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found eq_ref00:=(eq_ref0 (((eq fofType) (x4 (s zero))) zero)):(((eq Prop) (((eq fofType) (x4 (s zero))) zero)) (((eq fofType) (x4 (s zero))) zero))
% 209.67/210.16 Found (eq_ref0 (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 209.67/210.16 Found ((eq_ref Prop) (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 209.67/210.16 Found ((eq_ref Prop) (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 209.67/210.16 Found ((eq_ref Prop) (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 209.67/210.16 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 209.67/210.16 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 209.67/210.16 Found or_ind as proof of b
% 209.67/210.16 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 209.67/210.16 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 209.67/210.16 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 209.67/210.16 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 209.67/210.16 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 209.67/210.16 Found ((conj00 ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 209.67/210.16 Found (((conj0 b) ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 209.67/210.16 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 209.67/210.16 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) or_ind) as proof of (P b)
% 209.67/210.16 Found x3:(P (x2 zero))
% 209.67/210.16 Instantiate: b:=(x2 zero):fofType
% 209.67/210.16 Found x3 as proof of (P0 b)
% 209.67/210.16 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 209.67/210.16 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 209.67/210.16 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 209.67/210.16 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 215.88/216.36 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 215.88/216.36 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 215.88/216.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 215.88/216.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 215.88/216.36 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 215.88/216.36 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 215.88/216.36 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 215.88/216.36 Found (eq_ref0 (x2 (s zero))) as proof of b
% 215.88/216.36 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 215.88/216.36 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 215.88/216.36 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 215.88/216.36 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 215.88/216.36 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 215.88/216.36 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 215.88/216.36 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 215.88/216.36 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 215.88/216.36 Found x1:(P (s zero))
% 215.88/216.36 Instantiate: b:=(s zero):fofType
% 215.88/216.36 Found x1 as proof of (P0 b)
% 215.88/216.36 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 215.88/216.36 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 215.88/216.36 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 215.88/216.36 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found eq_ref00:=(eq_ref0 (((eq fofType) (x0 (s zero))) zero)):(((eq Prop) (((eq fofType) (x0 (s zero))) zero)) (((eq fofType) (x0 (s zero))) zero))
% 215.88/216.36 Found (eq_ref0 (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 215.88/216.36 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 215.88/216.36 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 215.88/216.36 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 215.88/216.36 Found eq_ref00:=(eq_ref0 (((eq fofType) (x2 (s zero))) zero)):(((eq Prop) (((eq fofType) (x2 (s zero))) zero)) (((eq fofType) (x2 (s zero))) zero))
% 215.88/216.36 Found (eq_ref0 (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 215.88/216.36 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 215.88/216.36 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 215.88/216.36 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 215.88/216.36 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 215.88/216.36 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 215.88/216.36 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 215.88/216.36 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 215.88/216.36 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 219.12/219.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 219.12/219.60 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 219.12/219.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% 219.12/219.60 Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% 219.12/219.60 Found or_ind as proof of b
% 219.12/219.60 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 219.12/219.60 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 219.12/219.60 Found ((conj00 ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 219.12/219.60 Found (((conj0 b) ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 219.12/219.60 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 219.12/219.60 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) or_ind) as proof of (P b)
% 219.12/219.60 Found x3:(P (x0 zero))
% 219.12/219.60 Instantiate: b:=(x0 zero):fofType
% 219.12/219.60 Found x3 as proof of (P0 b)
% 219.12/219.60 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 219.12/219.60 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 219.12/219.60 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 219.12/219.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 219.12/219.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 219.12/219.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 219.12/219.60 Found (eq_ref0 b) as proof of (P b)
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (P b)
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (P b)
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (P b)
% 219.12/219.60 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 219.12/219.60 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 219.12/219.60 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 219.12/219.60 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 219.12/219.60 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 219.12/219.60 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 223.75/224.23 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 223.75/224.23 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 223.75/224.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 223.75/224.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 223.75/224.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 223.75/224.23 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 223.75/224.23 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found eq_ref00:=(eq_ref0 (((eq fofType) (x4 (s zero))) zero)):(((eq Prop) (((eq fofType) (x4 (s zero))) zero)) (((eq fofType) (x4 (s zero))) zero))
% 223.75/224.23 Found (eq_ref0 (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 223.75/224.23 Found ((eq_ref Prop) (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 223.75/224.23 Found ((eq_ref Prop) (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 223.75/224.23 Found ((eq_ref Prop) (((eq fofType) (x4 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x4 (s zero))) zero)) b)
% 223.75/224.23 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 223.75/224.23 Found (eq_ref0 (x0 (s zero))) as proof of b
% 223.75/224.23 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 223.75/224.23 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 223.75/224.23 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 223.75/224.23 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 223.75/224.23 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 223.75/224.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 223.75/224.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 223.75/224.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 223.75/224.23 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 223.75/224.23 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 223.75/224.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 223.75/224.23 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 223.75/224.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 223.75/224.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 223.75/224.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 223.75/224.23 Found x3:(P (x2 zero))
% 223.75/224.23 Instantiate: b:=(x2 zero):fofType
% 223.75/224.23 Found x3 as proof of (P0 b)
% 223.75/224.23 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 223.75/224.23 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 223.75/224.23 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 223.75/224.23 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 223.75/224.23 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 223.75/224.23 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 223.75/224.23 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 223.75/224.23 Found x1:(P (s zero))
% 223.75/224.23 Instantiate: b:=(s zero):fofType
% 223.75/224.23 Found x1 as proof of (P0 b)
% 223.75/224.23 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 223.75/224.23 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 223.75/224.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 230.61/231.14 Found (eq_ref0 (x2 (s zero))) as proof of b
% 230.61/231.14 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 230.61/231.14 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 230.61/231.14 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 230.61/231.14 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 230.61/231.14 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 230.61/231.14 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 230.61/231.14 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 230.61/231.14 Found x3:(P (x0 zero))
% 230.61/231.14 Instantiate: b:=(x0 zero):fofType
% 230.61/231.14 Found x3 as proof of (P0 b)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 230.61/231.14 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 230.61/231.14 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 230.61/231.14 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 230.61/231.14 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 230.61/231.14 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 230.61/231.14 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (((eq fofType) (x0 (s zero))) zero)):(((eq Prop) (((eq fofType) (x0 (s zero))) zero)) (((eq fofType) (x0 (s zero))) zero))
% 230.61/231.14 Found (eq_ref0 (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 230.61/231.14 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 230.61/231.14 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 230.61/231.14 Found ((eq_ref Prop) (((eq fofType) (x0 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x0 (s zero))) zero)) b)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (((eq fofType) (x2 (s zero))) zero)):(((eq Prop) (((eq fofType) (x2 (s zero))) zero)) (((eq fofType) (x2 (s zero))) zero))
% 230.61/231.14 Found (eq_ref0 (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 230.61/231.14 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 230.61/231.14 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 230.61/231.14 Found ((eq_ref Prop) (((eq fofType) (x2 (s zero))) zero)) as proof of (((eq Prop) (((eq fofType) (x2 (s zero))) zero)) b)
% 230.61/231.14 Found x1:(P (x0 zero))
% 230.61/231.14 Instantiate: b:=(x0 zero):fofType
% 230.61/231.14 Found x1 as proof of (P0 b)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 230.61/231.14 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 230.61/231.14 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 230.61/231.14 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 230.61/231.14 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 230.61/231.14 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 230.61/231.14 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 230.61/231.14 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (s zero))
% 230.61/231.14 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 234.89/235.37 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 234.89/235.37 Found (eq_ref0 a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 234.89/235.37 Found (eq_ref0 a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 234.89/235.37 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 234.89/235.37 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 234.89/235.37 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 234.89/235.37 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 234.89/235.37 Found x3:(P (x0 zero))
% 234.89/235.37 Instantiate: b:=(x0 zero):fofType
% 234.89/235.37 Found x3 as proof of (P0 b)
% 234.89/235.37 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 234.89/235.37 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 234.89/235.37 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 234.89/235.37 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 234.89/235.37 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 234.89/235.37 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 234.89/235.37 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 234.89/235.37 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 234.89/235.37 Found (eq_ref0 (x0 (s zero))) as proof of b
% 234.89/235.37 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 234.89/235.37 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 234.89/235.37 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 234.89/235.37 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 234.89/235.37 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 234.89/235.37 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 234.89/235.37 Found eq_ref000:=(eq_ref00 P):((P (x4 zero))->(P (x4 zero)))
% 234.89/235.37 Found (eq_ref00 P) as proof of (P0 (x4 zero))
% 234.89/235.37 Found ((eq_ref0 (x4 zero)) P) as proof of (P0 (x4 zero))
% 234.89/235.37 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 243.18/243.68 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 243.18/243.68 Found ex_intro0:=(ex_intro (fofType->fofType)):(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P)))
% 243.18/243.68 Instantiate: b:=(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P))):Prop
% 243.18/243.68 Found ex_intro0 as proof of b
% 243.18/243.68 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 243.18/243.68 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 243.18/243.68 Found ((conj00 ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 243.18/243.68 Found (((conj0 b) ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 243.18/243.68 Found ((((conj (((eq fofType) (x4 zero)) (s zero))) b) ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 243.18/243.68 Found ((((conj (((eq fofType) (x4 zero)) (s zero))) b) ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 243.18/243.68 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 243.18/243.68 Found (eq_ref0 (x0 (s zero))) as proof of b
% 243.18/243.68 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 243.18/243.68 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 243.18/243.68 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 243.18/243.68 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 243.18/243.68 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 243.18/243.68 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 243.18/243.68 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 243.18/243.68 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 243.18/243.68 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 243.18/243.68 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 243.18/243.68 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 243.18/243.68 Found (eq_ref00 P) as proof of (P0 b)
% 243.18/243.68 Found ((eq_ref0 b) P) as proof of (P0 b)
% 243.18/243.68 Found (((eq_ref fofType) b) P) as proof of (P0 b)
% 243.18/243.68 Found (((eq_ref fofType) b) P) as proof of (P0 b)
% 243.18/243.68 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 243.18/243.68 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 243.18/243.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 243.18/243.68 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 243.18/243.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 243.18/243.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 243.18/243.68 Found x3:(P (x0 zero))
% 243.18/243.68 Instantiate: b:=(x0 zero):fofType
% 243.18/243.68 Found x3 as proof of (P0 b)
% 243.18/243.68 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 243.18/243.68 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 243.18/243.68 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 248.09/248.54 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 248.09/248.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 248.09/248.54 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 248.09/248.54 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 248.09/248.54 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b0)
% 248.09/248.54 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 248.09/248.54 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 248.09/248.54 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 248.09/248.54 Found (eq_ref0 b) as proof of (P b)
% 248.09/248.54 Found ((eq_ref fofType) b) as proof of (P b)
% 248.09/248.54 Found ((eq_ref fofType) b) as proof of (P b)
% 248.09/248.54 Found ((eq_ref fofType) b) as proof of (P b)
% 248.09/248.54 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 248.09/248.54 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 248.09/248.54 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 248.09/248.54 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 248.09/248.54 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 248.09/248.54 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 248.09/248.54 Found x1:(P (x0 zero))
% 248.09/248.54 Instantiate: b:=(x0 zero):fofType
% 248.09/248.54 Found x1 as proof of (P0 b)
% 248.09/248.54 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 248.09/248.54 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 248.09/248.54 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 248.09/248.54 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 248.09/248.54 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 248.09/248.54 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 248.09/248.54 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 248.09/248.54 Found ex_intro0:=(ex_intro (fofType->fofType)):(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P)))
% 248.09/248.54 Instantiate: b:=(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P))):Prop
% 248.09/248.54 Found ex_intro0 as proof of b
% 248.09/248.54 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 248.09/248.54 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 248.09/248.54 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 248.09/248.54 Found ((conj00 ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 248.09/248.54 Found (((conj0 b) ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 248.09/248.54 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 248.09/248.54 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 256.06/256.51 Found ex_intro0:=(ex_intro (fofType->fofType)):(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P)))
% 256.06/256.51 Instantiate: b:=(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P))):Prop
% 256.06/256.51 Found ex_intro0 as proof of b
% 256.06/256.51 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 256.06/256.51 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 256.06/256.51 Found ((conj00 ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 256.06/256.51 Found (((conj0 b) ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 256.06/256.51 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 256.06/256.51 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 256.06/256.51 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 256.06/256.51 Found (eq_ref0 a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 256.06/256.51 Found (eq_ref0 a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) zero)
% 256.06/256.51 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 256.06/256.51 Found (eq_ref0 (x0 (s zero))) as proof of b
% 256.06/256.51 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 256.06/256.51 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 256.06/256.51 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 256.06/256.51 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 256.06/256.51 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 256.06/256.51 Found eq_ref000:=(eq_ref00 P):((P (s zero))->(P (s zero)))
% 256.06/256.51 Found (eq_ref00 P) as proof of (P0 (s zero))
% 256.06/256.51 Found ((eq_ref0 (s zero)) P) as proof of (P0 (s zero))
% 256.06/256.51 Found (((eq_ref fofType) (s zero)) P) as proof of (P0 (s zero))
% 256.06/256.51 Found (((eq_ref fofType) (s zero)) P) as proof of (P0 (s zero))
% 256.06/256.51 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 256.06/256.51 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 256.06/256.51 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 256.06/256.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 256.06/256.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 256.06/256.51 Found eq_ref000:=(eq_ref00 P):((P (x4 zero))->(P (x4 zero)))
% 256.06/256.51 Found (eq_ref00 P) as proof of (P0 (x4 zero))
% 256.06/256.51 Found ((eq_ref0 (x4 zero)) P) as proof of (P0 (x4 zero))
% 256.06/256.51 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 256.06/256.51 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 256.06/256.51 Found ex_intro0:=(ex_intro (fofType->fofType)):(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P)))
% 256.06/256.51 Instantiate: b:=(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P))):Prop
% 256.06/256.51 Found ex_intro0 as proof of b
% 256.06/256.51 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 256.06/256.51 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 256.06/256.51 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 256.06/256.51 Found ((conj00 ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 256.06/256.51 Found (((conj0 b) ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 258.95/259.41 Found ((((conj (((eq fofType) (x4 zero)) (s zero))) b) ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 258.95/259.41 Found ((((conj (((eq fofType) (x4 zero)) (s zero))) b) ((eq_ref fofType) (x4 zero))) ex_intro0) as proof of (P b)
% 258.95/259.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 258.95/259.41 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 258.95/259.41 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 258.95/259.41 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 258.95/259.41 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 258.95/259.41 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 258.95/259.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 258.95/259.41 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 258.95/259.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 258.95/259.41 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 258.95/259.41 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 258.95/259.41 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 258.95/259.41 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 258.95/259.41 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 258.95/259.41 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 258.95/259.41 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 258.95/259.41 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 265.40/265.85 Found x3:(P (s zero))
% 265.40/265.85 Instantiate: b:=(s zero):fofType
% 265.40/265.85 Found x3 as proof of (P0 b)
% 265.40/265.85 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 265.40/265.85 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 265.40/265.85 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 265.40/265.85 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 265.40/265.85 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 265.40/265.85 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 265.40/265.85 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 265.40/265.85 Found (eq_ref0 (x4 (s zero))) as proof of b
% 265.40/265.85 Found ((eq_ref fofType) (x4 (s zero))) as proof of b
% 265.40/265.85 Found ((eq_ref fofType) (x4 (s zero))) as proof of b
% 265.40/265.85 Found ((eq_ref fofType) (x4 (s zero))) as proof of b
% 265.40/265.85 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 265.40/265.85 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 265.40/265.85 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 265.40/265.85 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 265.40/265.85 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 265.40/265.85 Found x5:(P (x4 zero))
% 265.40/265.85 Instantiate: b:=(x4 zero):fofType
% 265.40/265.85 Found x5 as proof of (P0 b)
% 265.40/265.85 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 265.40/265.85 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 265.40/265.85 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 265.40/265.85 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 265.40/265.85 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 265.40/265.85 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 265.40/265.85 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 265.40/265.85 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 265.40/265.85 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 265.40/265.85 Found (eq_ref0 b) as proof of (P b)
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (P b)
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (P b)
% 265.40/265.85 Found ((eq_ref fofType) b) as proof of (P b)
% 265.40/265.85 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 265.40/265.85 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 265.40/265.85 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 276.59/277.05 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 276.59/277.05 Found (eq_ref00 P) as proof of (P0 b)
% 276.59/277.05 Found ((eq_ref0 b) P) as proof of (P0 b)
% 276.59/277.05 Found (((eq_ref fofType) b) P) as proof of (P0 b)
% 276.59/277.05 Found (((eq_ref fofType) b) P) as proof of (P0 b)
% 276.59/277.05 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 276.59/277.05 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 276.59/277.05 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 276.59/277.05 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 276.59/277.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 276.59/277.05 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 276.59/277.05 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 276.59/277.05 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 276.59/277.05 Found (eq_ref0 b) as proof of (P b)
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (P b)
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (P b)
% 276.59/277.05 Found ((eq_ref fofType) b) as proof of (P b)
% 276.59/277.05 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 276.59/277.05 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 276.59/277.05 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 276.59/277.05 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 276.59/277.05 Found ex_intro0:=(ex_intro (fofType->fofType)):(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P)))
% 276.59/277.05 Instantiate: b:=(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P))):Prop
% 276.59/277.05 Found ex_intro0 as proof of b
% 276.59/277.05 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 276.59/277.05 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 276.59/277.05 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 276.59/277.05 Found ((conj00 ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 276.59/277.05 Found (((conj0 b) ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 276.59/277.05 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 276.59/277.05 Found ((((conj (((eq fofType) (x0 zero)) (s zero))) b) ((eq_ref fofType) (x0 zero))) ex_intro0) as proof of (P b)
% 276.59/277.05 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 276.59/277.05 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 276.59/277.05 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 279.74/280.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.74/280.23 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 279.74/280.23 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 279.74/280.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.74/280.23 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 279.74/280.23 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 279.74/280.23 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 279.74/280.23 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 279.74/280.23 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 279.74/280.23 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 279.74/280.23 Found ex_intro0:=(ex_intro (fofType->fofType)):(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P)))
% 279.74/280.23 Instantiate: b:=(forall (P:((fofType->fofType)->Prop)) (x:(fofType->fofType)), ((P x)->((ex (fofType->fofType)) P))):Prop
% 279.74/280.23 Found ex_intro0 as proof of b
% 279.74/280.23 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 279.74/280.23 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 279.74/280.23 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 279.74/280.23 Found ((conj00 ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 279.74/280.23 Found (((conj0 b) ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 279.74/280.23 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 279.74/280.23 Found ((((conj (((eq fofType) (x2 zero)) (s zero))) b) ((eq_ref fofType) (x2 zero))) ex_intro0) as proof of (P b)
% 279.74/280.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.74/280.23 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 279.74/280.23 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.74/280.23 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 279.74/280.23 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 279.74/280.23 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 279.74/280.23 Found x3:(P (s zero))
% 279.74/280.23 Instantiate: b:=(s zero):fofType
% 279.74/280.23 Found x3 as proof of (P0 b)
% 279.74/280.23 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 279.74/280.23 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 285.02/285.52 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.02/285.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.02/285.52 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 285.02/285.52 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 285.02/285.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.02/285.52 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.02/285.52 Found x5:(P (x0 zero))
% 285.02/285.52 Instantiate: b:=(x0 zero):fofType
% 285.02/285.52 Found x5 as proof of (P0 b)
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 285.02/285.52 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 285.02/285.52 Found (eq_ref0 (x0 (s zero))) as proof of b
% 285.02/285.52 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 285.02/285.52 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 285.02/285.52 Found ((eq_ref fofType) (x0 (s zero))) as proof of b
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 285.02/285.52 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 285.02/285.52 Found eq_ref000:=(eq_ref00 P):((P (s zero))->(P (s zero)))
% 285.02/285.52 Found (eq_ref00 P) as proof of (P0 (s zero))
% 285.02/285.52 Found ((eq_ref0 (s zero)) P) as proof of (P0 (s zero))
% 285.02/285.52 Found (((eq_ref fofType) (s zero)) P) as proof of (P0 (s zero))
% 285.02/285.52 Found (((eq_ref fofType) (s zero)) P) as proof of (P0 (s zero))
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 285.02/285.52 Found (eq_ref0 (x2 (s zero))) as proof of b
% 285.02/285.52 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 285.02/285.52 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 285.02/285.52 Found ((eq_ref fofType) (x2 (s zero))) as proof of b
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 285.02/285.52 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 285.02/285.52 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 285.02/285.52 Found x5:(P (x2 zero))
% 285.02/285.52 Instantiate: b:=(x2 zero):fofType
% 285.02/285.52 Found x5 as proof of (P0 b)
% 285.02/285.52 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 285.02/285.52 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.02/285.52 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.39/290.92 Found (eq_ref0 b) as proof of (P b)
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (P b)
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (P b)
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (P b)
% 290.39/290.92 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 290.39/290.92 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 290.39/290.92 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 290.39/290.92 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 290.39/290.92 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 290.39/290.92 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 290.39/290.92 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 290.39/290.92 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.39/290.92 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.39/290.92 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 290.39/290.92 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 290.39/290.92 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 290.39/290.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.39/290.92 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 290.39/290.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.39/290.92 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 290.39/290.92 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 290.39/290.92 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 290.39/290.92 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 290.39/290.92 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 290.39/290.92 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 299.40/299.88 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.40/299.88 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found x3:(P (s zero))
% 299.40/299.88 Instantiate: b:=(s zero):fofType
% 299.40/299.88 Found x3 as proof of (P0 b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 299.40/299.88 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 299.40/299.88 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.40/299.88 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 299.40/299.88 Found (eq_ref0 (x4 (s zero))) as proof of b
% 299.40/299.88 Found ((eq_ref fofType) (x4 (s zero))) as proof of b
% 299.40/299.88 Found ((eq_ref fofType) (x4 (s zero))) as proof of b
% 299.40/299.88 Found ((eq_ref fofType) (x4 (s zero))) as proof of b
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 299.40/299.88 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 299.40/299.88 Found x5:(P (x4 zero))
% 299.40/299.88 Instantiate: b:=(x4 zero):fofType
% 299.40/299.88 Found x5 as proof of (P0 b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 299.40/299.88 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.40/299.88 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 299.40/299.88 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b0)
% 299.40/299.88 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b0)
% 299.40/299.88 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b0)
% 299.40/299.88 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b0)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 299.40/299.88 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 299.40/299.88 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (s zero))
% 299.40/299.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.40/299.88 Found (eq_ref0 b) as proof of (P b)
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (P b)
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (P b)
% 299.40/299.88 Found ((eq_ref fofType) b) as proof of (P b)
% 299.40/299.88 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 299.40/299.88 Found (eq_ref0 (s zero)) as proof
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