TSTP Solution File: NUM817^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM817^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n095.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:50 EST 2018
% Result : Timeout 299.19s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM817^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% 0.00/0.05 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.24 % Computer : n095.star.cs.uiowa.edu
% 0.02/0.24 % Model : x86_64 x86_64
% 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24 % Memory : 32218.625MB
% 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24 % CPULimit : 300
% 0.02/0.24 % DateTime : Fri Jan 5 14:30:34 CST 2018
% 0.02/0.24 % CPUTime :
% 0.02/0.26 Python 2.7.13
% 3.49/3.71 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 3.49/3.71 FOF formula (<kernel.Constant object at 0x2b1a0fb604d0>, <kernel.Constant object at 0x2b1a0fb60dd0>) of role type named c0_type
% 3.49/3.71 Using role type
% 3.49/3.71 Declaring c0:fofType
% 3.49/3.71 FOF formula (<kernel.Constant object at 0x2b1a0fb60a28>, <kernel.DependentProduct object at 0x2b1a0f873b00>) of role type named cS_type
% 3.49/3.71 Using role type
% 3.49/3.71 Declaring cS:(fofType->fofType)
% 3.49/3.71 FOF formula (<kernel.Constant object at 0x2b1a0fb604d0>, <kernel.DependentProduct object at 0x2b1a0f873ab8>) of role type named cEVEN1_type
% 3.49/3.71 Using role type
% 3.49/3.71 Declaring cEVEN1:(fofType->Prop)
% 3.49/3.71 FOF formula (<kernel.Constant object at 0x2b1a0fb60dd0>, <kernel.DependentProduct object at 0x2b1a0f876248>) of role type named cODD1_type
% 3.49/3.71 Using role type
% 3.49/3.71 Declaring cODD1:(fofType->Prop)
% 3.49/3.71 FOF formula (((eq (fofType->Prop)) cEVEN1) (fun (Xn:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS (cS Xx))))))->(Xp Xn))))) of role definition named cEVEN1_def
% 3.49/3.71 A new definition: (((eq (fofType->Prop)) cEVEN1) (fun (Xn:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS (cS Xx))))))->(Xp Xn)))))
% 3.49/3.71 Defined: cEVEN1:=(fun (Xn:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS (cS Xx))))))->(Xp Xn))))
% 3.49/3.71 FOF formula (((eq (fofType->Prop)) cODD1) (fun (Xn:fofType)=> ((cEVEN1 Xn)->False))) of role definition named cODD1_def
% 3.49/3.71 A new definition: (((eq (fofType->Prop)) cODD1) (fun (Xn:fofType)=> ((cEVEN1 Xn)->False)))
% 3.49/3.71 Defined: cODD1:=(fun (Xn:fofType)=> ((cEVEN1 Xn)->False))
% 3.49/3.71 FOF formula (((and (forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))) (forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw))))->((ex fofType) (fun (Xn:fofType)=> (cODD1 Xn)))) of role conjecture named cTHM405
% 3.49/3.71 Conjecture to prove = (((and (forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))) (forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw))))->((ex fofType) (fun (Xn:fofType)=> (cODD1 Xn)))):Prop
% 3.49/3.71 We need to prove ['(((and (forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))) (forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw))))->((ex fofType) (fun (Xn:fofType)=> (cODD1 Xn))))']
% 3.49/3.71 Parameter fofType:Type.
% 3.49/3.71 Parameter c0:fofType.
% 3.49/3.71 Parameter cS:(fofType->fofType).
% 3.49/3.71 Definition cEVEN1:=(fun (Xn:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS (cS Xx))))))->(Xp Xn)))):(fofType->Prop).
% 3.49/3.71 Definition cODD1:=(fun (Xn:fofType)=> ((cEVEN1 Xn)->False)):(fofType->Prop).
% 3.49/3.71 Trying to prove (((and (forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))) (forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw))))->((ex fofType) (fun (Xn:fofType)=> (cODD1 Xn))))
% 3.49/3.71 Found eq_ref00:=(eq_ref0 (fun (Xn:fofType)=> (cODD1 Xn))):(((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) (fun (Xn:fofType)=> (cODD1 Xn)))
% 3.49/3.71 Found (eq_ref0 (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 3.49/3.71 Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 3.49/3.71 Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 3.49/3.71 Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 3.49/3.71 Found eta_expansion_dep000:=(eta_expansion_dep00 cODD1):(((eq (fofType->Prop)) cODD1) (fun (x:fofType)=> (cODD1 x)))
% 3.49/3.71 Found (eta_expansion_dep00 cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 3.49/3.71 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 3.49/3.71 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 3.49/3.71 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 7.18/7.38 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 7.18/7.38 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 7.18/7.38 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 7.18/7.38 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 7.18/7.38 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 7.18/7.38 Found eq_ref00:=(eq_ref0 (fun (Xn:fofType)=> (cODD1 Xn))):(((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) (fun (Xn:fofType)=> (cODD1 Xn)))
% 7.18/7.38 Found (eq_ref0 (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 7.18/7.38 Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 7.18/7.38 Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 7.18/7.38 Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> (cODD1 Xn))) b)
% 7.18/7.38 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 7.18/7.38 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 7.18/7.38 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 7.18/7.38 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (cODD1 x0))
% 7.18/7.38 Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 7.18/7.38 Found eta_expansion000:=(eta_expansion00 cODD1):(((eq (fofType->Prop)) cODD1) (fun (x:fofType)=> (cODD1 x)))
% 7.18/7.38 Found (eta_expansion00 cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 7.18/7.38 Found ((eta_expansion0 Prop) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 7.18/7.38 Found (((eta_expansion fofType) Prop) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 7.18/7.38 Found (((eta_expansion fofType) Prop) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 7.18/7.38 Found (((eta_expansion fofType) Prop) cODD1) as proof of (((eq (fofType->Prop)) cODD1) b)
% 7.18/7.38 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 7.18/7.38 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 7.18/7.38 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 7.18/7.38 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 7.18/7.38 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 7.18/7.38 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 7.18/7.38 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 7.18/7.38 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 7.18/7.38 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 7.18/7.38 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 7.18/7.38 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 66.60/66.89 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 66.60/66.89 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 66.60/66.89 Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% 66.60/66.89 Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) (cODD1 x2))
% 66.60/66.89 Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (cODD1 x)))
% 66.60/66.89 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 66.60/66.89 Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 66.60/66.89 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 66.60/66.89 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 66.60/66.89 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 66.60/66.89 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 66.60/66.89 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 66.60/66.89 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 66.60/66.89 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 66.60/66.89 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 66.60/66.89 Found ((eta_expansion_dep0 (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found (((eta_expansion_dep fofType) (fun (x3:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 83.19/83.48 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 83.19/83.48 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> (cODD1 Xn)))
% 83.19/83.48 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 83.19/83.48 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 83.19/83.48 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 83.19/83.48 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) cODD1)
% 83.19/83.48 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 83.19/83.48 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 83.19/83.48 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 83.19/83.48 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 83.19/83.48 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 83.19/83.48 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 83.19/83.48 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 83.19/83.48 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 83.19/83.48 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 96.49/96.72 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 96.49/96.72 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 96.49/96.72 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 96.49/96.72 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 96.49/96.72 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 96.49/96.72 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 96.49/96.72 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 96.49/96.72 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 96.49/96.72 Found eq_ref00:=(eq_ref0 (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))):(((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))))
% 96.49/96.72 Found (eq_ref0 (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 96.49/96.72 Found ((eq_ref Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 96.49/96.72 Found ((eq_ref Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 102.09/102.32 Found ((eq_ref Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 102.09/102.32 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 102.09/102.32 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 102.09/102.32 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 102.09/102.32 Found eq_ref00:=(eq_ref0 (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))):(((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))
% 102.09/102.32 Found (eq_ref0 (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 102.09/102.32 Found ((eq_ref Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 102.09/102.32 Found ((eq_ref Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 102.09/102.32 Found ((eq_ref Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 111.59/111.88 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 111.59/111.88 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 111.59/111.88 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 111.59/111.88 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 111.59/111.88 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 111.59/111.88 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 111.59/111.88 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 111.59/111.88 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 111.59/111.88 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 111.59/111.88 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 111.59/111.88 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 111.59/111.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 111.59/111.88 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 111.59/111.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 111.59/111.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 111.59/111.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 111.59/111.88 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 111.59/111.88 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 111.59/111.88 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 111.59/111.88 Found eq_ref00:=(eq_ref0 (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))):(((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))))
% 111.59/111.88 Found (eq_ref0 (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 118.69/118.92 Found ((eq_ref Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 118.69/118.92 Found ((eq_ref Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 118.69/118.92 Found ((eq_ref Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) as proof of (((eq Prop) (fofType->(((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))->((forall (Xu:fofType), (not (((eq fofType) (cS Xu)) c0)))->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))) b)
% 118.69/118.92 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 118.69/118.92 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 118.69/118.92 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 118.69/118.92 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 118.69/118.92 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 118.69/118.92 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 118.69/118.92 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 118.69/118.92 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 118.69/118.92 Found eq_ref00:=(eq_ref0 (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))):(((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False))))
% 123.88/124.14 Found (eq_ref0 (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 123.88/124.14 Found ((eq_ref Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 123.88/124.14 Found ((eq_ref Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 123.88/124.14 Found ((eq_ref Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) as proof of (((eq Prop) (fofType->(((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)->((forall (Xv:fofType) (Xw:fofType), ((((eq fofType) (cS Xv)) (cS Xw))->(((eq fofType) Xv) Xw)))->False)))) b)
% 123.88/124.14 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 123.88/124.14 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 123.88/124.14 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 123.88/124.14 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 123.88/124.14 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 123.88/124.14 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 123.88/124.14 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 123.88/124.14 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 123.88/124.14 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 123.88/124.14 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 123.88/124.14 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 123.88/124.14 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 123.88/124.14 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 123.88/124.14 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 123.88/124.14 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 123.88/124.14 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 123.88/124.14 Found (eq_ref00 P) as proof of (P0 c0)
% 123.88/124.14 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 123.88/124.14 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 123.88/124.14 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 123.88/124.14 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 123.88/124.14 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 123.88/124.14 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 123.88/124.14 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 123.88/124.14 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 142.26/142.52 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 142.26/142.52 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 142.26/142.52 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 142.26/142.52 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 142.26/142.52 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 142.26/142.52 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 142.26/142.52 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 142.26/142.52 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 142.26/142.52 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 142.26/142.52 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 142.26/142.52 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 142.26/142.52 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 142.26/142.52 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 142.26/142.52 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 142.26/142.52 Found (eq_ref00 P) as proof of (P0 c0)
% 142.26/142.52 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 142.26/142.52 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 142.26/142.52 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 142.26/142.52 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 142.26/142.52 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 142.26/142.52 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 142.26/142.52 Found (eq_ref00 P) as proof of (P0 c0)
% 142.26/142.52 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 142.26/142.52 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 142.26/142.52 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 142.26/142.52 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 142.26/142.52 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 142.26/142.52 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 162.25/162.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 162.25/162.59 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 162.25/162.59 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 162.25/162.59 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 162.25/162.59 Found (eq_ref00 P) as proof of (P0 c0)
% 162.25/162.59 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 162.25/162.59 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 162.25/162.59 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 162.25/162.59 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 162.25/162.59 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 162.25/162.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 162.25/162.59 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 162.25/162.59 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 162.25/162.59 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 162.25/162.59 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 162.25/162.59 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 162.25/162.59 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 162.25/162.59 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 162.25/162.59 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 162.25/162.59 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 162.25/162.59 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 162.25/162.59 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 162.25/162.59 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 162.25/162.59 Found (eq_ref00 P) as proof of (P0 c0)
% 162.25/162.59 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 191.73/192.09 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 191.73/192.09 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 191.73/192.09 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 191.73/192.09 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 191.73/192.09 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 191.73/192.09 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 191.73/192.09 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 191.73/192.09 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 191.73/192.09 Found (eq_ref00 P) as proof of (P0 c0)
% 191.73/192.09 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 191.73/192.09 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 191.73/192.09 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 191.73/192.09 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.73/192.09 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.73/192.09 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.73/192.09 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.73/192.09 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.73/192.09 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.73/192.09 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 191.73/192.09 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.73/192.09 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 191.73/192.09 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.73/192.09 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 191.73/192.09 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 191.73/192.09 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 191.73/192.09 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 191.73/192.09 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 191.73/192.09 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 191.73/192.09 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 191.73/192.09 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 191.73/192.09 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 230.62/230.96 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 230.62/230.96 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found x4:(P (cS c0))
% 230.62/230.96 Instantiate: Xu:=c0:fofType
% 230.62/230.96 Found x4 as proof of (P0 (cS Xu))
% 230.62/230.96 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 230.62/230.96 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 230.62/230.96 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 230.62/230.96 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 230.62/230.96 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 230.62/230.96 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 230.62/230.96 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 230.62/230.96 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 230.62/230.96 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 230.62/230.96 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 230.62/230.96 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 230.62/230.96 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 230.62/230.96 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 230.62/230.96 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 230.62/230.96 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 230.62/230.96 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 230.62/230.96 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 230.62/230.96 Found x4:(P (cS c0))
% 230.62/230.96 Instantiate: Xu:=c0:fofType
% 230.62/230.96 Found x4 as proof of (P0 (cS Xu))
% 230.62/230.96 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 230.62/230.96 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 230.62/230.96 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 230.62/230.96 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 230.62/230.96 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found x4:(P (cS c0))
% 299.19/299.57 Instantiate: Xu:=c0:fofType
% 299.19/299.57 Found x4 as proof of (P0 (cS Xu))
% 299.19/299.57 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 299.19/299.57 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 299.19/299.57 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found x4:(P (cS c0))
% 299.19/299.57 Instantiate: Xu:=c0:fofType
% 299.19/299.57 Found x4 as proof of (P0 (cS Xu))
% 299.19/299.57 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 299.19/299.57 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 299.19/299.57 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.19/299.57 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 299.19/299.57 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 299.19/299.57 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 299.19/299.57 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.19/299.57 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 299.19/299.57 Found x4:(P (cS c0))
% 299.19/299.57 Instantiate: Xu:=c0:fofType
% 299.19/299.57 Found x4 as proof of (P0 (cS Xu))
% 299.19/299.57 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 299.19/299.57 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 299.19/299.57 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found x4:(P (cS c0))
% 299.19/299.57 Instantiate: Xu:=c0:fofType
% 299.19/299.57 Found x4 as proof of (P0 (cS Xu))
% 299.19/299.57 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.19/299.57 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 299.19/299.57 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 299.19/299.57 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 299.19/299.57 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 299.19/299.57 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 299.19/299.57 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 299.19/299.57 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 299.19/299.57 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 299.19/299.57 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 299.19/299.57 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 299.19/299.57 Found ((eq_r
%------------------------------------------------------------------------------