TSTP Solution File: NUN025^3 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUN025^3 : TPTP v6.4.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 299.27s
% 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 : NUN025^3 : TPTP v6.4.0. Released v6.4.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.22 % Computer : n018.star.cs.uiowa.edu
% 0.03/0.22 % Model : x86_64 x86_64
% 0.03/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.22 % Memory : 16091.75MB
% 0.03/0.22 % OS : Linux 3.10.0-327.10.1.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Mar 25 14:09:12 CDT 2016
% 0.03/0.23 % CPUTime :
% 0.03/0.24 Python 2.7.8
% 2.20/2.38 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 2.20/2.38 FOF formula (<kernel.Constant object at 0x2aab3380f290>, <kernel.Constant object at 0x2aab33ad6290>) of role type named n6
% 2.20/2.38 Using role type
% 2.20/2.38 Declaring zero:fofType
% 2.20/2.38 FOF formula (<kernel.Constant object at 0x2aab3380f878>, <kernel.DependentProduct object at 0x2aab33ad6680>) of role type named n7
% 2.20/2.38 Using role type
% 2.20/2.38 Declaring s:(fofType->fofType)
% 2.20/2.38 FOF formula (<kernel.Constant object at 0x2aab3380f290>, <kernel.DependentProduct object at 0x2aab33ad6488>) of role type named n8
% 2.20/2.38 Using role type
% 2.20/2.38 Declaring ite:(Prop->(fofType->(fofType->fofType)))
% 2.20/2.38 FOF formula (<kernel.Constant object at 0x2aab3380f878>, <kernel.DependentProduct object at 0x2aab33ad64d0>) of role type named n9
% 2.20/2.38 Using role type
% 2.20/2.38 Declaring h:(fofType->fofType)
% 2.20/2.38 FOF formula (((and ((and ((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), (not (((eq fofType) (s X)) zero))))) (forall (X:fofType), (not (((eq fofType) (s X)) X))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) (((ite (((eq fofType) X) (s zero))) zero) (s zero))))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero)))))) of role conjecture named n10
% 2.20/2.38 Conjecture to prove = (((and ((and ((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), (not (((eq fofType) (s X)) zero))))) (forall (X:fofType), (not (((eq fofType) (s X)) X))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) (((ite (((eq fofType) X) (s zero))) zero) (s zero))))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero)))))):Prop
% 2.20/2.38 We need to prove ['(((and ((and ((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), (not (((eq fofType) (s X)) zero))))) (forall (X:fofType), (not (((eq fofType) (s X)) X))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) (((ite (((eq fofType) X) (s zero))) zero) (s zero))))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))))']
% 2.20/2.38 Parameter fofType:Type.
% 2.20/2.38 Parameter zero:fofType.
% 2.20/2.38 Parameter s:(fofType->fofType).
% 2.20/2.38 Parameter ite:(Prop->(fofType->(fofType->fofType))).
% 2.20/2.38 Parameter h:(fofType->fofType).
% 2.20/2.38 Trying to prove (((and ((and ((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), (not (((eq fofType) (s X)) zero))))) (forall (X:fofType), (not (((eq fofType) (s X)) X))))) (forall (X:fofType), (((eq fofType) (h X)) (((ite (((eq fofType) X) zero)) (s zero)) (((ite (((eq fofType) X) (s zero))) zero) (s zero))))))->((ex (fofType->fofType)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))))
% 2.20/2.38 Found eq_ref00:=(eq_ref0 (x0 (s (s zero)))):(((eq fofType) (x0 (s (s zero)))) (x0 (s (s zero))))
% 2.20/2.38 Found (eq_ref0 (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 2.20/2.38 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 2.20/2.38 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 7.51/7.73 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x2 (s (s zero)))):(((eq fofType) (x2 (s (s zero)))) (x2 (s (s zero))))
% 7.51/7.73 Found (eq_ref0 (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 7.51/7.73 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.51/7.73 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.51/7.73 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.51/7.73 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 7.51/7.73 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x0 (s (s zero)))):(((eq fofType) (x0 (s (s zero)))) (x0 (s (s zero))))
% 7.51/7.73 Found (eq_ref0 (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 7.51/7.73 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 7.51/7.73 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.51/7.73 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.51/7.73 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.51/7.73 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 7.51/7.73 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x4 (s (s zero)))):(((eq fofType) (x4 (s (s zero)))) (x4 (s (s zero))))
% 7.51/7.73 Found (eq_ref0 (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 7.51/7.73 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 7.51/7.73 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 7.51/7.73 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x0 (s (s zero)))):(((eq fofType) (x0 (s (s zero)))) (x0 (s (s zero))))
% 16.62/16.86 Found (eq_ref0 (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 16.62/16.86 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 16.62/16.86 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 16.62/16.86 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x2 (s (s zero)))):(((eq fofType) (x2 (s (s zero)))) (x2 (s (s zero))))
% 16.62/16.86 Found (eq_ref0 (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 16.62/16.86 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 16.62/16.86 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 16.62/16.86 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 16.62/16.86 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 16.62/16.86 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 16.62/16.86 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 16.62/16.86 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 18.92/19.18 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 18.92/19.18 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) (fun (x:(fofType->fofType))=> ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 18.92/19.18 Found (eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 18.92/19.18 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 18.92/19.18 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 18.92/19.18 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 18.92/19.18 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 18.92/19.18 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 18.92/19.18 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 18.92/19.18 Found eq_ref00:=(eq_ref0 (x6 (s (s zero)))):(((eq fofType) (x6 (s (s zero)))) (x6 (s (s zero))))
% 18.92/19.18 Found (eq_ref0 (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 18.92/19.18 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 18.92/19.18 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 18.92/19.18 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 22.44/22.64 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 22.44/22.64 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 22.44/22.64 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 22.44/22.64 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 22.44/22.64 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 22.44/22.64 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 22.44/22.64 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 22.44/22.64 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 22.44/22.64 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 22.44/22.64 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 22.44/22.64 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 22.44/22.64 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x0 (s (s zero)))):(((eq fofType) (x0 (s (s zero)))) (x0 (s (s zero))))
% 22.44/22.64 Found (eq_ref0 (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x2 (s (s zero)))):(((eq fofType) (x2 (s (s zero)))) (x2 (s (s zero))))
% 22.44/22.64 Found (eq_ref0 (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (x4 (s (s zero)))):(((eq fofType) (x4 (s (s zero)))) (x4 (s (s zero))))
% 22.44/22.64 Found (eq_ref0 (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 22.44/22.64 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 22.44/22.64 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 22.44/22.64 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 25.22/25.47 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 25.22/25.47 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and ((and (((eq fofType) (x0 zero)) (s zero))) (((eq fofType) (x0 (s zero))) zero))) (((eq fofType) (x0 (s (s zero)))) (s zero))))
% 25.22/25.47 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 25.22/25.47 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 25.22/25.47 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 25.22/25.47 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 25.22/25.47 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 25.22/25.47 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 25.22/25.47 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 25.22/25.47 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 25.22/25.47 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 25.22/25.47 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 25.22/25.47 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 34.93/35.09 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 34.93/35.09 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 34.93/35.09 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 34.93/35.09 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 34.93/35.09 Found eq_ref00:=(eq_ref0 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero)))))
% 34.93/35.09 Found (eq_ref0 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 34.93/35.09 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 34.93/35.09 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 34.93/35.09 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 34.93/35.09 Found eq_ref00:=(eq_ref0 (x6 zero)):(((eq fofType) (x6 zero)) (x6 zero))
% 34.93/35.09 Found (eq_ref0 (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 34.93/35.09 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 34.93/35.09 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 34.93/35.09 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 34.93/35.09 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 34.93/35.09 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 34.93/35.09 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 34.93/35.09 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 34.93/35.09 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 34.93/35.09 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 34.93/35.09 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 48.16/48.31 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 48.16/48.31 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 48.16/48.31 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and ((and (((eq fofType) (x2 zero)) (s zero))) (((eq fofType) (x2 (s zero))) zero))) (((eq fofType) (x2 (s (s zero)))) (s zero))))
% 48.16/48.31 Found (fun (x2:(fofType->fofType))=> ((eq_ref Prop) (f x2))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 48.16/48.31 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 48.16/48.31 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 48.16/48.31 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x6 (s zero))):(((eq fofType) (x6 (s zero))) (x6 (s zero)))
% 48.16/48.31 Found (eq_ref0 (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 48.16/48.31 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 48.16/48.31 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 48.16/48.31 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x6 zero)):(((eq fofType) (x6 zero)) (x6 zero))
% 48.16/48.31 Found (eq_ref0 (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x8 (s (s zero)))):(((eq fofType) (x8 (s (s zero)))) (x8 (s (s zero))))
% 48.16/48.31 Found (eq_ref0 (x8 (s (s zero)))) as proof of (((eq fofType) (x8 (s (s zero)))) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x8 (s (s zero)))) as proof of (((eq fofType) (x8 (s (s zero)))) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x8 (s (s zero)))) as proof of (((eq fofType) (x8 (s (s zero)))) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x8 (s (s zero)))) as proof of (((eq fofType) (x8 (s (s zero)))) (s zero))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 48.16/48.31 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 48.16/48.31 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 48.16/48.31 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 48.16/48.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 51.74/51.89 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 51.74/51.89 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 51.74/51.89 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 51.74/51.89 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 51.74/51.89 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 51.74/51.89 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 51.74/51.89 Found eq_ref00:=(eq_ref0 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero)))))
% 51.74/51.89 Found (eq_ref0 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 51.74/51.89 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 51.74/51.89 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 51.74/51.89 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 51.74/51.89 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 51.74/51.89 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 51.74/51.89 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 51.74/51.89 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 51.74/51.89 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 51.74/51.89 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 51.74/51.89 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 51.74/51.89 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 51.74/51.89 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 51.74/51.89 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 57.35/57.53 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 57.35/57.53 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 57.35/57.53 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x0 (s (s zero)))):(((eq fofType) (x0 (s (s zero)))) (x0 (s (s zero))))
% 57.35/57.53 Found (eq_ref0 (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x0 (s (s zero)))) as proof of (((eq fofType) (x0 (s (s zero)))) (s zero))
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x2 (s (s zero)))):(((eq fofType) (x2 (s (s zero)))) (x2 (s (s zero))))
% 57.35/57.53 Found (eq_ref0 (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x2 (s (s zero)))) as proof of (((eq fofType) (x2 (s (s zero)))) (s zero))
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x4 (s (s zero)))):(((eq fofType) (x4 (s (s zero)))) (x4 (s (s zero))))
% 57.35/57.53 Found (eq_ref0 (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x4 (s (s zero)))) as proof of (((eq fofType) (x4 (s (s zero)))) (s zero))
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x6 (s (s zero)))):(((eq fofType) (x6 (s (s zero)))) (x6 (s (s zero))))
% 57.35/57.53 Found (eq_ref0 (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x6 (s (s zero)))) as proof of (((eq fofType) (x6 (s (s zero)))) (s zero))
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 57.35/57.53 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 57.35/57.53 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 57.35/57.53 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 57.35/57.53 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 57.35/57.53 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 59.23/59.38 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 59.23/59.38 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 59.23/59.38 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 59.23/59.38 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 59.23/59.38 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 59.23/59.38 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 59.23/59.38 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 59.23/59.38 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 59.23/59.38 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 59.23/59.38 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 59.23/59.38 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 59.23/59.38 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 59.23/59.38 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 86.58/86.72 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 86.58/86.72 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 86.58/86.72 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 86.58/86.72 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 86.58/86.72 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 86.58/86.72 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and ((and (((eq fofType) (x4 zero)) (s zero))) (((eq fofType) (x4 (s zero))) zero))) (((eq fofType) (x4 (s (s zero)))) (s zero))))
% 86.58/86.72 Found (fun (x4:(fofType->fofType))=> ((eq_ref Prop) (f x4))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 86.58/86.72 Found eq_ref00:=(eq_ref0 (x8 zero)):(((eq fofType) (x8 zero)) (x8 zero))
% 86.58/86.72 Found (eq_ref0 (x8 zero)) as proof of (((eq fofType) (x8 zero)) (s zero))
% 86.58/86.72 Found ((eq_ref fofType) (x8 zero)) as proof of (((eq fofType) (x8 zero)) (s zero))
% 86.58/86.72 Found ((eq_ref fofType) (x8 zero)) as proof of (((eq fofType) (x8 zero)) (s zero))
% 86.58/86.72 Found eq_ref00:=(eq_ref0 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero)))))
% 86.58/86.72 Found (eq_ref0 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 86.58/86.72 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 101.30/101.48 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 101.30/101.48 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 101.30/101.48 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 101.30/101.48 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 101.30/101.48 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x6 zero)):(((eq fofType) (x6 zero)) (x6 zero))
% 101.30/101.48 Found (eq_ref0 (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 101.30/101.48 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 101.30/101.48 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 101.30/101.48 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 101.30/101.48 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 101.30/101.48 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x8 (s zero))):(((eq fofType) (x8 (s zero))) (x8 (s zero)))
% 101.30/101.48 Found (eq_ref0 (x8 (s zero))) as proof of (((eq fofType) (x8 (s zero))) zero)
% 101.30/101.48 Found ((eq_ref fofType) (x8 (s zero))) as proof of (((eq fofType) (x8 (s zero))) zero)
% 101.30/101.48 Found ((eq_ref fofType) (x8 (s zero))) as proof of (((eq fofType) (x8 (s zero))) zero)
% 101.30/101.48 Found ((eq_ref fofType) (x8 (s zero))) as proof of (((eq fofType) (x8 (s zero))) zero)
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x8 zero)):(((eq fofType) (x8 zero)) (x8 zero))
% 101.30/101.48 Found (eq_ref0 (x8 zero)) as proof of (((eq fofType) (x8 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x8 zero)) as proof of (((eq fofType) (x8 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x8 zero)) as proof of (((eq fofType) (x8 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x8 zero)) as proof of (((eq fofType) (x8 zero)) (s zero))
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 101.30/101.48 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 101.30/101.48 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 101.30/101.48 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 101.30/101.48 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 110.47/110.64 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 110.47/110.64 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 110.47/110.64 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 110.47/110.64 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 110.47/110.64 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 110.47/110.64 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x6 zero)):(((eq fofType) (x6 zero)) (x6 zero))
% 110.47/110.64 Found (eq_ref0 (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 110.47/110.64 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 110.47/110.64 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 110.47/110.64 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 110.47/110.64 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 110.47/110.64 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 110.47/110.64 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 110.47/110.64 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 110.47/110.64 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 110.47/110.64 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 110.47/110.64 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 110.47/110.64 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 110.47/110.64 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 110.47/110.64 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 120.23/120.35 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 120.23/120.35 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 120.23/120.35 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 120.23/120.35 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 120.23/120.35 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 120.23/120.35 Found eq_ref00:=(eq_ref0 (x6 (s zero))):(((eq fofType) (x6 (s zero))) (x6 (s zero)))
% 120.23/120.35 Found (eq_ref0 (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 120.23/120.35 Found eq_ref00:=(eq_ref0 (x6 zero)):(((eq fofType) (x6 zero)) (x6 zero))
% 120.23/120.35 Found (eq_ref0 (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 120.23/120.35 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 120.23/120.35 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 120.23/120.35 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 120.23/120.35 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 120.23/120.35 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 120.23/120.35 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 120.23/120.35 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) ((and ((and (((eq fofType) (x6 zero)) (s zero))) (((eq fofType) (x6 (s zero))) zero))) (((eq fofType) (x6 (s (s zero)))) (s zero))))
% 120.23/120.35 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 120.23/120.35 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 120.23/120.35 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 120.23/120.35 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 120.23/120.35 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 124.22/124.40 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 124.22/124.40 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 124.22/124.40 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 124.22/124.40 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 124.22/124.40 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 124.22/124.40 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 124.22/124.40 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 124.22/124.40 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) zero)
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 124.22/124.40 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) (s zero))
% 124.22/124.40 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 124.22/124.40 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 124.22/124.40 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 124.22/124.40 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 124.22/124.40 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 125.92/126.06 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 125.92/126.06 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 125.92/126.06 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 125.92/126.06 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 125.92/126.06 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 125.92/126.06 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 125.92/126.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 125.92/126.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 125.92/126.06 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 125.92/126.06 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 125.92/126.06 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 125.92/126.06 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 125.92/126.06 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 125.92/126.06 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) zero)
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 125.92/126.06 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) (s zero))
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x6 (s zero))):(((eq fofType) (x6 (s zero))) (x6 (s zero)))
% 125.92/126.06 Found (eq_ref0 (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 125.92/126.06 Found ((eq_ref fofType) (x6 (s zero))) as proof of (((eq fofType) (x6 (s zero))) zero)
% 125.92/126.06 Found eq_ref00:=(eq_ref0 (x6 zero)):(((eq fofType) (x6 zero)) (x6 zero))
% 125.92/126.06 Found (eq_ref0 (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 125.92/126.06 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 165.02/165.10 Found ((eq_ref fofType) (x6 zero)) as proof of (((eq fofType) (x6 zero)) (s zero))
% 165.02/165.10 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 165.02/165.10 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 165.02/165.10 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 165.02/165.10 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 165.02/165.10 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) zero)
% 165.02/165.10 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 165.02/165.10 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 165.02/165.10 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 165.02/165.10 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 165.02/165.10 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) (s zero))
% 165.02/165.10 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 165.02/165.10 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 165.02/165.10 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 165.02/165.10 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 165.02/165.10 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 165.02/165.10 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))):(((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) (fun (x:(fofType->fofType))=> ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 165.02/165.10 Found (eta_expansion_dep00 (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 165.02/165.10 Found ((eta_expansion_dep0 (fun (x9:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 165.02/165.10 Found (((eta_expansion_dep (fofType->fofType)) (fun (x9:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 165.02/165.10 Found (((eta_expansion_dep (fofType->fofType)) (fun (x9:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 165.02/165.10 Found (((eta_expansion_dep (fofType->fofType)) (fun (x9:(fofType->fofType))=> Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (H:(fofType->fofType))=> ((and ((and (((eq fofType) (H zero)) (s zero))) (((eq fofType) (H (s zero))) zero))) (((eq fofType) (H (s (s zero)))) (s zero))))) b)
% 165.02/165.10 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 165.02/165.10 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 186.84/186.91 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 186.84/186.91 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 186.84/186.91 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 186.84/186.91 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 186.84/186.91 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 186.84/186.91 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 186.84/186.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 186.84/186.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 186.84/186.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 186.84/186.91 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 186.84/186.91 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 186.84/186.91 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 186.84/186.91 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 186.84/186.91 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 186.84/186.91 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 186.84/186.91 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 186.84/186.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 186.84/186.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 186.84/186.91 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 186.84/186.91 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 186.84/186.91 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 186.84/186.91 Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% 186.84/186.91 Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found (fun (x8:(fofType->fofType))=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found (fun (x8:(fofType->fofType))=> ((eq_ref Prop) (f x8))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 186.84/186.91 Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% 186.84/186.91 Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found (fun (x8:(fofType->fofType))=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and ((and (((eq fofType) (x8 zero)) (s zero))) (((eq fofType) (x8 (s zero))) zero))) (((eq fofType) (x8 (s (s zero)))) (s zero))))
% 186.84/186.91 Found (fun (x8:(fofType->fofType))=> ((eq_ref Prop) (f x8))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) ((and ((and (((eq fofType) (x zero)) (s zero))) (((eq fofType) (x (s zero))) zero))) (((eq fofType) (x (s (s zero)))) (s zero)))))
% 207.14/207.20 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 207.14/207.20 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 207.14/207.20 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 207.14/207.20 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 207.14/207.20 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 207.14/207.20 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 207.14/207.20 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 207.14/207.20 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 207.14/207.20 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (s zero)))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (s zero)))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (s zero)))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (s zero)))
% 207.14/207.20 Found eq_ref00:=(eq_ref0 zero):(((eq fofType) zero) zero)
% 207.14/207.20 Found (eq_ref0 zero) as proof of (((eq fofType) zero) b)
% 207.14/207.20 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 207.14/207.20 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 207.14/207.20 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 207.14/207.20 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 207.14/207.20 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 207.14/207.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 207.14/207.20 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 207.14/207.20 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 207.14/207.20 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 207.14/207.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 207.14/207.20 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 207.14/207.20 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 207.14/207.20 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 207.14/207.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 207.14/207.20 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 207.14/207.20 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 207.14/207.20 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 207.14/207.20 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 271.60/271.68 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 271.60/271.68 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 271.60/271.68 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 271.60/271.68 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 271.60/271.68 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 271.60/271.68 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 271.60/271.68 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 271.60/271.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 271.60/271.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 271.60/271.68 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 271.60/271.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found eq_ref000:=(eq_ref00 P):((P (x4 zero))->(P (x4 zero)))
% 271.60/271.68 Found (eq_ref00 P) as proof of (P0 (x4 zero))
% 271.60/271.68 Found ((eq_ref0 (x4 zero)) P) as proof of (P0 (x4 zero))
% 271.60/271.68 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 271.60/271.68 Found (((eq_ref fofType) (x4 zero)) P) as proof of (P0 (x4 zero))
% 271.60/271.68 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 271.60/271.68 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 271.60/271.68 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 271.60/271.68 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 271.60/271.68 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 271.60/271.68 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 271.60/271.68 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 271.60/271.68 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 271.60/271.68 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 271.60/271.68 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 271.60/271.68 Found eq_ref00:=(eq_ref0 (x4 (s zero))):(((eq fofType) (x4 (s zero))) (x4 (s zero)))
% 271.60/271.68 Found (eq_ref0 (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) b)
% 271.60/271.68 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) b)
% 271.60/271.68 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) b)
% 271.60/271.68 Found ((eq_ref fofType) (x4 (s zero))) as proof of (((eq fofType) (x4 (s zero))) b)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 271.60/271.68 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 (x4 zero)):(((eq fofType) (x4 zero)) (x4 zero))
% 271.60/271.68 Found (eq_ref0 (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 271.60/271.68 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 271.60/271.68 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 271.60/271.68 Found ((eq_ref fofType) (x4 zero)) as proof of (((eq fofType) (x4 zero)) b)
% 271.60/271.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 271.60/271.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 271.60/271.68 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 271.60/271.68 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 271.60/271.68 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 285.41/285.51 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 285.41/285.51 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 285.41/285.51 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 285.41/285.51 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.41/285.51 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 zero))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 zero))
% 285.41/285.51 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 285.41/285.51 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.41/285.51 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.41/285.51 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.41/285.51 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 285.41/285.51 Found eq_ref00:=(eq_ref0 zero):(((eq fofType) zero) zero)
% 285.41/285.51 Found (eq_ref0 zero) as proof of (((eq fofType) zero) b)
% 285.41/285.51 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 285.41/285.51 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 285.41/285.51 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 285.41/285.51 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.41/285.51 Found (eq_ref0 b) as proof of (((eq fofType) b) (x2 (s zero)))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 (s zero)))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 (s zero)))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x2 (s zero)))
% 285.41/285.51 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 285.41/285.51 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 285.41/285.51 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 285.41/285.51 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 285.41/285.51 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 285.41/285.51 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.41/285.51 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 285.41/285.51 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 285.41/285.51 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.41/285.51 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.41/285.51 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.41/285.51 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 285.41/285.51 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.41/285.51 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.41/285.51 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 285.41/285.51 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 285.41/285.51 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 285.41/285.51 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 285.41/285.51 Found eq_ref00:=(eq_ref0 (x2 (s zero))):(((eq fofType) (x2 (s zero))) (x2 (s zero)))
% 299.27/299.30 Found (eq_ref0 (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 299.27/299.30 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 299.27/299.30 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 299.27/299.30 Found ((eq_ref fofType) (x2 (s zero))) as proof of (((eq fofType) (x2 (s zero))) b)
% 299.27/299.30 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.27/299.30 Found (eq_ref0 b) as proof of (((eq fofType) b) zero)
% 299.27/299.30 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 299.27/299.30 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 299.27/299.30 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) zero)
% 299.27/299.30 Found eq_ref00:=(eq_ref0 (x2 zero)):(((eq fofType) (x2 zero)) (x2 zero))
% 299.27/299.30 Found (eq_ref0 (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.27/299.30 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.27/299.30 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.27/299.30 Found ((eq_ref fofType) (x2 zero)) as proof of (((eq fofType) (x2 zero)) b)
% 299.27/299.30 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.27/299.30 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.30 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.30 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.30 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.30 Found eq_ref000:=(eq_ref00 P):((P (x2 zero))->(P (x2 zero)))
% 299.27/299.30 Found (eq_ref00 P) as proof of (P0 (x2 zero))
% 299.27/299.30 Found ((eq_ref0 (x2 zero)) P) as proof of (P0 (x2 zero))
% 299.27/299.30 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 299.27/299.30 Found (((eq_ref fofType) (x2 zero)) P) as proof of (P0 (x2 zero))
% 299.27/299.30 Found eq_ref000:=(eq_ref00 P):((P (x0 zero))->(P (x0 zero)))
% 299.27/299.30 Found (eq_ref00 P) as proof of (P0 (x0 zero))
% 299.27/299.30 Found ((eq_ref0 (x0 zero)) P) as proof of (P0 (x0 zero))
% 299.27/299.30 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 299.27/299.30 Found (((eq_ref fofType) (x0 zero)) P) as proof of (P0 (x0 zero))
% 299.27/299.30 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.27/299.30 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 zero))
% 299.27/299.30 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 zero))
% 299.27/299.31 Found eq_ref00:=(eq_ref0 (s zero)):(((eq fofType) (s zero)) (s zero))
% 299.27/299.31 Found (eq_ref0 (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.27/299.31 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.27/299.31 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.27/299.31 Found ((eq_ref fofType) (s zero)) as proof of (((eq fofType) (s zero)) b)
% 299.27/299.31 Found eq_ref00:=(eq_ref0 zero):(((eq fofType) zero) zero)
% 299.27/299.31 Found (eq_ref0 zero) as proof of (((eq fofType) zero) b)
% 299.27/299.31 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 299.27/299.31 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 299.27/299.31 Found ((eq_ref fofType) zero) as proof of (((eq fofType) zero) b)
% 299.27/299.31 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.27/299.31 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 (s zero)))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (s zero)))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (s zero)))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 (s zero)))
% 299.27/299.31 Found eq_ref00:=(eq_ref0 (x0 zero)):(((eq fofType) (x0 zero)) (x0 zero))
% 299.27/299.31 Found (eq_ref0 (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.27/299.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.27/299.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.27/299.31 Found ((eq_ref fofType) (x0 zero)) as proof of (((eq fofType) (x0 zero)) b)
% 299.27/299.31 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.27/299.31 Found (eq_ref0 b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (s zero))
% 299.27/299.31 Found eq_ref00:=(eq_ref0 (x0 (s zero))):(((eq fofType) (x0 (s zero))) (x0 (s zero)))
% 299.27/299.31 Found (eq_ref0 (x0 (s zero))) as proof of (((eq fofType) (x0 (s zero))) b)
% 299.27/299.31 Found ((eq_ref fofType) (x0 (s zero))) as proof of (((
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