TSTP Solution File: NUM816^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM816^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n163.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 13:11:49 EST 2018
% Result : Timeout 292.81s
% 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 : NUM816^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% 0.02/0.04 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n163.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.25 % DateTime : Fri Jan 5 14:30:34 CST 2018
% 0.02/0.25 % CPUTime :
% 0.02/0.25 Python 2.7.13
% 14.40/14.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 14.40/14.61 FOF formula (<kernel.Constant object at 0x2ae4822ad488>, <kernel.Constant object at 0x2ae4822ad518>) of role type named c0_type
% 14.40/14.61 Using role type
% 14.40/14.61 Declaring c0:fofType
% 14.40/14.61 FOF formula (<kernel.Constant object at 0x2ae4822ad878>, <kernel.DependentProduct object at 0x2ae4822b1320>) of role type named cS_type
% 14.40/14.61 Using role type
% 14.40/14.61 Declaring cS:(fofType->fofType)
% 14.40/14.61 FOF formula (<kernel.Constant object at 0x2ae4822a1170>, <kernel.DependentProduct object at 0x2ae4822b1830>) of role type named cEVEN1_type
% 14.40/14.61 Using role type
% 14.40/14.61 Declaring cEVEN1:(fofType->Prop)
% 14.40/14.61 FOF formula (<kernel.Constant object at 0x2ae4822ad518>, <kernel.DependentProduct object at 0x2ae4822b1878>) of role type named cODD1_type
% 14.40/14.61 Using role type
% 14.40/14.61 Declaring cODD1:(fofType->Prop)
% 14.40/14.61 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
% 14.40/14.61 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)))))
% 14.40/14.61 Defined: cEVEN1:=(fun (Xn:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS (cS Xx))))))->(Xp Xn))))
% 14.40/14.61 FOF formula (((eq (fofType->Prop)) cODD1) (fun (Xn:fofType)=> ((cEVEN1 Xn)->False))) of role definition named cODD1_def
% 14.40/14.61 A new definition: (((eq (fofType->Prop)) cODD1) (fun (Xn:fofType)=> ((cEVEN1 Xn)->False)))
% 14.40/14.61 Defined: cODD1:=(fun (Xn:fofType)=> ((cEVEN1 Xn)->False))
% 14.40/14.61 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))))->(cODD1 (cS c0))) of role conjecture named cTHM406
% 14.40/14.61 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))))->(cODD1 (cS c0))):Prop
% 14.40/14.61 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))))->(cODD1 (cS c0)))']
% 14.40/14.61 Parameter fofType:Type.
% 14.40/14.61 Parameter c0:fofType.
% 14.40/14.61 Parameter cS:(fofType->fofType).
% 14.40/14.61 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).
% 14.40/14.61 Definition cODD1:=(fun (Xn:fofType)=> ((cEVEN1 Xn)->False)):(fofType->Prop).
% 14.40/14.61 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))))->(cODD1 (cS c0)))
% 14.40/14.61 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 14.40/14.61 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 14.40/14.61 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 14.40/14.61 Found x30:(P (cS (cS Xu)))
% 14.40/14.61 Instantiate: Xu:=Xx:fofType
% 14.40/14.61 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 14.40/14.61 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 14.40/14.61 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 17.32/17.51 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 17.32/17.51 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found x30:(P (cS (cS Xu)))
% 17.32/17.51 Instantiate: Xu:=Xx:fofType
% 17.32/17.51 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 17.32/17.51 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 17.32/17.51 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found x4:(P (cS (cS Xu)))
% 17.32/17.51 Instantiate: Xu:=Xx:fofType
% 17.32/17.51 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 17.32/17.51 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 17.32/17.51 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found x4:(P (cS (cS Xu)))
% 17.32/17.51 Instantiate: Xu:=Xx:fofType
% 17.32/17.51 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 17.32/17.51 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 17.32/17.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 17.32/17.51 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 17.32/17.51 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 17.32/17.51 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 21.25/21.51 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 21.25/21.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 21.25/21.51 Found x30:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 21.25/21.51 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found x30:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 21.25/21.51 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x4:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 21.25/21.51 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 21.25/21.51 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 21.25/21.51 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x3:(P (cS (cS Xu)))
% 21.25/21.51 Instantiate: Xu:=Xx:fofType
% 21.25/21.51 Found x3 as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 21.25/21.51 Found x4:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 30.05/30.24 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 30.05/30.24 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 30.05/30.24 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 30.05/30.24 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 30.05/30.24 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 30.05/30.24 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 30.05/30.24 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 30.05/30.24 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found x3:(P (cS (cS Xu)))
% 30.05/30.24 Instantiate: Xu:=Xx:fofType
% 30.05/30.24 Found x3 as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 30.05/30.24 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 30.05/30.24 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 30.05/30.24 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 30.05/30.24 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 30.05/30.24 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 30.05/30.24 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 30.05/30.24 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 30.05/30.24 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 30.05/30.24 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 30.05/30.24 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 30.05/30.24 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 30.05/30.24 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 30.05/30.24 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 30.05/30.24 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 30.05/30.24 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 30.05/30.24 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 30.05/30.24 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 38.49/38.70 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 38.49/38.70 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 38.49/38.70 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 38.49/38.70 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 38.49/38.70 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 38.49/38.70 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 38.49/38.70 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 38.49/38.70 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 38.49/38.70 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 38.49/38.70 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 38.49/38.70 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 38.49/38.70 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 38.49/38.70 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 38.49/38.70 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 38.49/38.70 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 38.49/38.70 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 38.49/38.70 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 38.49/38.70 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 38.49/38.70 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 38.49/38.70 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 38.49/38.70 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)))))
% 39.60/39.81 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)
% 39.60/39.81 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)
% 39.60/39.81 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)
% 39.60/39.81 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)
% 39.60/39.81 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 39.60/39.81 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 39.60/39.81 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 39.60/39.81 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 39.60/39.81 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 39.60/39.81 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 39.60/39.81 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 39.60/39.81 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 39.60/39.81 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 39.60/39.81 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 39.60/39.81 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 39.60/39.81 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 39.60/39.81 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found x4:(P (cS (cS Xx)))
% 41.50/41.70 Instantiate: Xu:=Xx:fofType
% 41.50/41.70 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 41.50/41.70 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 41.50/41.70 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found x4:(P (cS (cS Xx)))
% 41.50/41.70 Instantiate: Xu:=Xx:fofType
% 41.50/41.70 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 41.50/41.70 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 41.50/41.70 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 41.50/41.70 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 41.50/41.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 41.50/41.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 41.50/41.70 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 41.50/41.70 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found x4:(P (cS (cS Xx)))
% 41.50/41.70 Instantiate: Xu:=Xx:fofType
% 41.50/41.70 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 41.50/41.70 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 41.50/41.70 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 41.50/41.70 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 41.50/41.70 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 41.50/41.70 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 42.76/43.00 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 42.76/43.00 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 42.76/43.00 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 42.76/43.00 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 42.76/43.00 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 42.76/43.00 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 42.76/43.00 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 42.76/43.00 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 42.76/43.00 Found x4:(P (cS (cS Xx)))
% 42.76/43.00 Instantiate: Xu:=Xx:fofType
% 42.76/43.00 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 42.76/43.00 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 42.76/43.00 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 42.76/43.00 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))))
% 42.76/43.00 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)
% 42.76/43.00 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)
% 42.76/43.00 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)
% 42.76/43.00 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)
% 42.76/43.00 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 42.76/43.00 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 50.41/50.58 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 50.41/50.58 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 50.41/50.58 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found x3:(P (cS (cS Xu)))
% 50.41/50.58 Found x3 as proof of (P (cS (cS c0)))
% 50.41/50.58 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 50.41/50.58 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 50.41/50.58 Found x3:(P (cS (cS Xu)))
% 50.41/50.58 Instantiate: Xu:=Xx:fofType
% 50.41/50.58 Found x3 as proof of (P (cS (cS Xx)))
% 50.41/50.58 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 50.41/50.58 Found x3:(P (cS (cS Xu)))
% 50.41/50.58 Found x3 as proof of (P (cS (cS c0)))
% 50.41/50.58 Found x3:(P (cS (cS Xu)))
% 50.41/50.58 Instantiate: Xu:=Xx:fofType
% 50.41/50.58 Found x3 as proof of (P (cS (cS Xx)))
% 50.41/50.58 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 50.41/50.58 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 50.41/50.58 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 50.41/50.58 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 50.41/50.58 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 50.41/50.58 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)))))
% 50.41/50.58 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)
% 52.50/52.70 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)
% 52.50/52.70 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)
% 52.50/52.70 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)
% 52.50/52.70 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 52.50/52.70 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 52.50/52.70 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 52.50/52.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 52.50/52.70 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 52.50/52.70 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 52.50/52.70 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 52.50/52.70 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 52.50/52.70 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 52.50/52.70 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 52.50/52.70 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 52.50/52.70 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 52.50/52.70 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 52.50/52.70 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 52.50/52.70 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 52.50/52.70 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 52.50/52.70 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 52.50/52.70 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 52.50/52.70 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 55.74/55.93 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 55.74/55.93 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 Found (eq_sym000 ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 55.74/55.93 Found ((eq_sym00 (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 55.74/55.93 Found (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 55.74/55.93 Found ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 55.74/55.93 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx))))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 55.74/55.93 Found eq_ref000:=(eq_ref00 P):((P (cS Xu))->(P (cS Xu)))
% 55.74/55.93 Found (eq_ref00 P) as proof of (P0 (cS Xu))
% 55.74/55.93 Found ((eq_ref0 (cS Xu)) P) as proof of (P0 (cS Xu))
% 55.74/55.93 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 55.74/55.93 Found (((eq_ref fofType) (cS Xu)) P) as proof of (P0 (cS Xu))
% 55.74/55.93 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 55.74/55.93 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 Found x4:(P (cS (cS Xx)))
% 55.74/55.93 Instantiate: Xu:=Xx:fofType
% 55.74/55.93 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 55.74/55.93 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 55.74/55.93 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 55.74/55.93 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 55.74/55.93 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS c0))))
% 55.74/55.93 Found x4:(P (cS (cS Xx)))
% 55.74/55.93 Instantiate: Xu:=Xx:fofType
% 55.74/55.93 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 55.74/55.93 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 55.74/55.93 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 55.74/55.93 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 55.74/55.93 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))))
% 56.53/56.73 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)
% 56.53/56.73 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)
% 56.53/56.73 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)
% 56.53/56.73 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)
% 56.53/56.73 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 56.53/56.73 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 56.53/56.73 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 56.53/56.73 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 56.53/56.73 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 56.53/56.73 Found (eq_sym000 ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 56.53/56.73 Found ((eq_sym00 (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 56.53/56.73 Found (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 56.53/56.73 Found ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 56.53/56.73 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx))))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 56.53/56.73 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 56.53/56.73 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 56.53/56.73 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 56.53/56.73 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 56.53/56.73 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 56.53/56.73 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 63.00/63.21 Found x4:(P (cS (cS Xx)))
% 63.00/63.21 Instantiate: Xu:=Xx:fofType
% 63.00/63.21 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 63.00/63.21 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 63.00/63.21 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 63.00/63.21 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 63.00/63.21 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xx)))->(P (cS (cS Xx))))
% 63.00/63.21 Found (eq_ref00 P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found ((eq_ref0 (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found (((eq_ref fofType) (cS (cS Xx))) P) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xx))) P)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 63.00/63.21 Found x4:(P (cS (cS Xx)))
% 63.00/63.21 Instantiate: Xu:=Xx:fofType
% 63.00/63.21 Found (fun (x4:(P (cS (cS Xx))))=> x4) as proof of (P (cS (cS Xu)))
% 63.00/63.21 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of ((P (cS (cS Xx)))->(P (cS (cS Xu))))
% 63.00/63.21 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu)))) (P:(fofType->Prop)) (x4:(P (cS (cS Xx))))=> x4) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 63.00/63.21 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 63.00/63.21 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 63.00/63.21 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 63.00/63.21 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 63.00/63.21 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 63.00/63.21 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 63.00/63.21 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 63.00/63.21 Found x3:(P (cS (cS Xu)))
% 63.00/63.21 Found x3 as proof of (P (cS (cS c0)))
% 63.00/63.21 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 73.04/73.30 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 73.04/73.30 Found (eq_ref00 P) as proof of (P0 c0)
% 73.04/73.30 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 73.04/73.30 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 73.04/73.30 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 73.04/73.30 Found x3:(P (cS (cS Xu)))
% 73.04/73.30 Instantiate: Xu:=Xx:fofType
% 73.04/73.30 Found x3 as proof of (P (cS (cS Xx)))
% 73.04/73.30 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 73.04/73.30 Found x3:(P (cS (cS Xu)))
% 73.04/73.30 Found x3 as proof of (P (cS (cS c0)))
% 73.04/73.30 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 73.04/73.30 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 73.04/73.30 Found x3:(P (cS (cS Xu)))
% 73.04/73.30 Instantiate: Xu:=Xx:fofType
% 73.04/73.30 Found x3 as proof of (P (cS (cS Xx)))
% 73.04/73.30 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 73.04/73.30 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 73.04/73.30 Found (eq_ref00 P) as proof of (P0 c0)
% 73.04/73.30 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 73.04/73.30 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 73.04/73.30 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 73.04/73.30 Found eq_ref00:=(eq_ref0 (fofType->(False->False))):(((eq Prop) (fofType->(False->False))) (fofType->(False->False)))
% 73.04/73.30 Found (eq_ref0 (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 73.04/73.30 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 73.04/73.30 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 73.04/73.30 Found ((eq_ref Prop) (fofType->(False->False))) as proof of (((eq Prop) (fofType->(False->False))) b)
% 73.04/73.30 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 73.04/73.30 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 73.04/73.30 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 73.04/73.30 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 73.04/73.30 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 73.04/73.30 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 73.04/73.30 Found (eq_sym000 ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 73.04/73.30 Found ((eq_sym00 (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 73.04/73.30 Found (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 73.04/73.30 Found ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 73.04/73.30 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx))))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 73.04/73.30 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 73.04/73.30 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.13/82.38 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.13/82.38 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.13/82.38 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.13/82.38 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 82.13/82.38 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 82.13/82.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 82.13/82.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 82.13/82.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 82.13/82.38 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 82.13/82.38 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.13/82.38 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.13/82.38 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.13/82.38 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.13/82.38 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 82.19/82.38 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 82.19/82.38 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 82.19/82.38 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 82.19/82.38 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 82.19/82.38 Found (eq_sym000 ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found ((eq_sym00 (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((eq_sym fofType) (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx))))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 82.19/82.38 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.19/82.38 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.19/82.38 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.19/82.38 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) b)
% 82.19/82.38 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 82.19/82.38 Found (eq_ref0 b) as proof of (((eq fofType) b) c0)
% 82.19/82.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 82.19/82.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 82.19/82.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c0)
% 82.19/82.38 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 82.19/82.38 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 82.19/82.38 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 82.19/82.38 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 82.19/82.38 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 82.19/82.38 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 82.19/82.38 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 82.19/82.38 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 82.19/82.38 Found (eq_ref00 P) as proof of (P0 c0)
% 82.19/82.38 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 82.19/82.38 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 82.19/82.38 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 82.19/82.38 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 82.19/82.38 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 82.19/82.38 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 82.19/82.38 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found x30:(P (cS (cS Xu)))
% 89.91/90.17 Instantiate: Xu:=Xx:fofType
% 89.91/90.17 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 89.91/90.17 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 89.91/90.17 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 89.91/90.17 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 89.91/90.17 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 89.91/90.17 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 89.91/90.17 Found eq_ref000:=(eq_ref00 P):((P c0)->(P c0))
% 89.91/90.17 Found (eq_ref00 P) as proof of (P0 c0)
% 89.91/90.17 Found ((eq_ref0 c0) P) as proof of (P0 c0)
% 89.91/90.17 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 89.91/90.17 Found (((eq_ref fofType) c0) P) as proof of (P0 c0)
% 89.91/90.17 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 89.91/90.17 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found x30:(P (cS (cS Xu)))
% 89.91/90.17 Instantiate: Xu:=Xx:fofType
% 89.91/90.17 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 89.91/90.17 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 89.91/90.17 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 89.91/90.17 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 89.91/90.17 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 89.91/90.17 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 89.91/90.17 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 89.91/90.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 89.91/90.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 89.91/90.17 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 89.91/90.17 Found eq_ref00:=(eq_ref0 (cS (cS c0))):(((eq fofType) (cS (cS c0))) (cS (cS c0)))
% 89.91/90.17 Found (eq_ref0 (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 89.91/90.17 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 89.91/90.17 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS c0)))
% 89.91/90.17 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 89.91/90.17 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 89.91/90.17 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 97.62/97.90 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 97.62/97.90 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 97.62/97.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 97.62/97.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 97.62/97.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 97.62/97.90 Found eq_ref00:=(eq_ref0 (cS (cS c0))):(((eq fofType) (cS (cS c0))) (cS (cS c0)))
% 97.62/97.90 Found (eq_ref0 (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 97.62/97.90 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 97.62/97.90 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 97.62/97.90 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 97.62/97.90 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found x4:(P (cS (cS Xu)))
% 97.62/97.90 Instantiate: Xu:=Xx:fofType
% 97.62/97.90 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 97.62/97.90 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 97.62/97.90 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 97.62/97.90 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 97.62/97.90 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 97.62/97.90 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 97.62/97.90 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 97.62/97.90 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 97.62/97.90 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 97.62/97.90 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 97.62/97.90 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 97.62/97.90 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found x4:(P (cS (cS Xu)))
% 107.81/108.05 Instantiate: Xu:=Xx:fofType
% 107.81/108.05 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 107.81/108.05 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 107.81/108.05 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 107.81/108.05 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 107.81/108.05 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 107.81/108.05 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 107.81/108.05 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 107.81/108.05 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 107.81/108.05 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 107.81/108.05 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 107.81/108.05 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 107.81/108.05 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 107.81/108.05 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 107.81/108.05 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 107.81/108.05 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 107.81/108.05 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 107.81/108.05 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 107.81/108.05 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 107.81/108.05 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 107.81/108.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 107.81/108.05 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 107.81/108.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 107.81/108.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 107.81/108.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 111.41/111.67 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 111.41/111.67 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 111.41/111.67 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 111.41/111.67 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 111.41/111.67 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 111.41/111.67 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 111.41/111.67 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 111.41/111.67 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 111.41/111.67 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 111.41/111.67 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 111.41/111.67 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found x30:(P (cS (cS Xu)))
% 111.41/111.67 Instantiate: Xu:=Xx:fofType
% 111.41/111.67 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 111.41/111.67 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))):((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 111.41/111.67 Found (eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 111.41/111.67 Found ((eq_substitution000 (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 111.41/111.67 Found (((eq_substitution00 (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 111.41/111.67 Found ((((eq_substitution0 fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 111.41/111.67 Found (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 111.41/111.67 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 111.41/111.67 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of (forall (Xx:fofType), ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx))))))
% 111.41/111.67 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 111.41/111.67 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found (fun (x3:((P (cS (cS Xu)))->(P Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 111.41/111.67 Found x30:(P (cS (cS Xu)))
% 111.41/111.67 Instantiate: Xu:=Xx:fofType
% 111.41/111.67 Found (fun (x30:(P (cS (cS Xu))))=> x30) as proof of (P (cS (cS Xx)))
% 111.41/111.67 Found (fun (x3:((P (cS (cS Xu)))->(P Xx))) (x30:(P (cS (cS Xu))))=> x30) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 113.67/113.92 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 113.67/113.92 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 113.67/113.92 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) b)
% 113.67/113.92 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 113.67/113.92 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS c0))
% 113.67/113.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 113.67/113.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 113.67/113.92 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS c0))
% 113.67/113.92 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 113.67/113.92 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 113.67/113.92 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 113.67/113.92 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))):((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 113.67/113.92 Found (eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 113.67/113.92 Found ((eq_substitution000 (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 113.67/113.92 Found (((eq_substitution00 (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 113.67/113.92 Found ((((eq_substitution0 fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 113.67/113.92 Found (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 113.67/113.92 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 121.40/121.64 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of (forall (Xx:fofType), ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx))))))
% 121.40/121.64 Found eq_ref00:=(eq_ref0 (cS (cS c0))):(((eq fofType) (cS (cS c0))) (cS (cS c0)))
% 121.40/121.64 Found (eq_ref0 (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 121.40/121.64 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 121.40/121.64 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 121.40/121.64 Found eq_ref00:=(eq_ref0 (cS (cS c0))):(((eq fofType) (cS (cS c0))) (cS (cS c0)))
% 121.40/121.64 Found (eq_ref0 (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 121.40/121.64 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 121.40/121.64 Found ((eq_ref fofType) (cS (cS c0))) as proof of (((eq fofType) (cS (cS c0))) (cS (cS Xu)))
% 121.40/121.64 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 121.40/121.64 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 121.40/121.64 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 121.40/121.64 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 121.40/121.64 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 121.40/121.64 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 121.40/121.64 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 121.40/121.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 121.40/121.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 121.40/121.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 121.40/121.64 Found x3:(P (cS c0))
% 121.40/121.64 Instantiate: Xu:=c0:fofType
% 121.40/121.64 Found x3 as proof of (P0 (cS Xu))
% 121.40/121.64 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 121.40/121.64 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 121.40/121.64 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 121.40/121.64 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 121.40/121.64 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found ((eq_substitution0000 (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found (((eq_substitution000 (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 121.40/121.64 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 121.40/121.64 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 121.40/121.64 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 121.40/121.64 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 121.40/121.64 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 121.40/121.64 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 125.35/125.62 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 125.35/125.62 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 125.35/125.62 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 125.35/125.62 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 125.35/125.62 Found x3:(P (cS (cS Xu)))
% 125.35/125.62 Instantiate: Xu:=Xx:fofType
% 125.35/125.62 Found x3 as proof of (P (cS (cS Xx)))
% 125.35/125.62 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 125.35/125.62 Found x3:(P (cS (cS Xu)))
% 125.35/125.62 Instantiate: Xu:=Xx:fofType
% 125.35/125.62 Found x3 as proof of (P (cS (cS Xx)))
% 125.35/125.62 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 125.35/125.62 Found x3:(P (cS (cS Xu)))
% 125.35/125.62 Instantiate: Xu:=Xx:fofType
% 125.35/125.62 Found x3 as proof of (P (cS (cS Xx)))
% 125.35/125.62 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 125.35/125.62 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 125.35/125.62 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 125.35/125.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 125.35/125.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 125.35/125.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 125.35/125.62 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 125.35/125.62 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 125.35/125.62 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 125.35/125.62 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 125.35/125.62 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 125.35/125.62 Found x4:(P (cS (cS Xu)))
% 125.35/125.62 Instantiate: Xu:=Xx:fofType
% 125.35/125.62 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 125.35/125.62 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 125.35/125.62 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 125.35/125.62 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 125.35/125.62 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 125.35/125.62 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 125.35/125.62 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 125.35/125.62 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 125.35/125.62 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 125.35/125.62 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 125.35/125.62 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 125.35/125.62 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 125.35/125.62 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found ((eq_substitution0000 (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found (((eq_substitution000 (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 125.35/125.62 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found x3:(P (cS c0))
% 129.07/129.30 Instantiate: Xu:=c0:fofType
% 129.07/129.30 Found x3 as proof of (P0 (cS Xu))
% 129.07/129.30 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 129.07/129.30 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 129.07/129.30 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 129.07/129.30 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 129.07/129.30 Found x3:(P (cS (cS Xu)))
% 129.07/129.30 Instantiate: Xu:=Xx:fofType
% 129.07/129.30 Found x3 as proof of (P (cS (cS Xx)))
% 129.07/129.30 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 129.07/129.30 Found x3:(P (cS (cS Xu)))
% 129.07/129.30 Instantiate: Xu:=Xx:fofType
% 129.07/129.30 Found x3 as proof of (P (cS (cS Xx)))
% 129.07/129.30 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 129.07/129.30 Found x3:(P (cS (cS Xu)))
% 129.07/129.30 Instantiate: Xu:=Xx:fofType
% 129.07/129.30 Found x3 as proof of (P (cS (cS Xx)))
% 129.07/129.30 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 129.07/129.30 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 129.07/129.30 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 129.07/129.30 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 129.07/129.30 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 129.07/129.30 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 129.07/129.30 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 129.07/129.30 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found x4:(P (cS (cS Xu)))
% 141.74/141.98 Instantiate: Xu:=Xx:fofType
% 141.74/141.98 Found (fun (x4:(P (cS (cS Xu))))=> x4) as proof of (P (cS (cS Xx)))
% 141.74/141.98 Found (fun (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 141.74/141.98 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P:(fofType->Prop)) (x4:(P (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 141.74/141.98 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 141.74/141.98 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 141.74/141.98 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 141.74/141.98 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 141.74/141.98 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 141.74/141.98 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 141.74/141.98 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 141.74/141.98 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 141.74/141.98 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 141.74/141.98 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 141.74/141.98 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 141.74/141.98 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 141.74/141.98 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 141.74/141.98 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 141.74/141.98 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 141.74/141.98 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 141.74/141.98 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 141.74/141.98 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 141.74/141.98 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 141.74/141.98 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 141.74/141.98 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 141.74/141.98 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 141.74/141.98 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 141.74/141.98 Found x300:(P (cS (cS Xu)))
% 141.74/141.98 Instantiate: Xu:=Xx:fofType
% 141.74/141.98 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of (P (cS (cS Xx)))
% 141.74/141.98 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 141.74/141.98 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 141.74/141.98 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 141.74/141.98 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 141.74/141.98 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 141.74/141.98 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 146.05/146.30 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 146.05/146.30 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 146.05/146.30 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 146.05/146.30 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 146.05/146.30 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 146.05/146.30 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 146.05/146.30 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 146.05/146.30 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 146.05/146.30 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 146.05/146.30 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))):((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 146.05/146.30 Found (eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 146.05/146.30 Found ((eq_substitution000 (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 146.05/146.30 Found (((eq_substitution00 (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 146.05/146.30 Found ((((eq_substitution0 fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 146.05/146.30 Found (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 146.05/146.30 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 146.05/146.30 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of (forall (Xx:fofType), ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx))))))
% 146.05/146.30 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 146.05/146.30 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 146.05/146.30 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 146.05/146.30 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 150.35/150.64 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 150.35/150.64 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 150.35/150.64 Found x300:(P (cS (cS Xu)))
% 150.35/150.64 Instantiate: Xu:=Xx:fofType
% 150.35/150.64 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of (P (cS (cS Xx)))
% 150.35/150.64 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 150.35/150.64 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 150.35/150.64 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 150.35/150.64 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 150.35/150.64 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 150.35/150.64 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 150.35/150.64 Found (eq_sym010 ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found ((eq_sym01 (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> (((eq_sym0 (cS (cS Xu))) (cS (cS Xx))) ((eq_ref fofType) (cS (cS Xu))))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 150.35/150.64 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))):((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 150.35/150.64 Found (eq_substitution0000 (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 150.35/150.64 Found ((eq_substitution000 (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 150.35/150.64 Found (((eq_substitution00 (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 157.44/157.75 Found ((((eq_substitution0 fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 157.44/157.75 Found (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5)))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 157.44/157.75 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx)))))
% 157.44/157.75 Found (fun (Xx:fofType)=> (((((eq_substitution fofType) fofType) (cS (cS Xx))) (cS Xx)) (fun (x5:fofType)=> (cS (cS x5))))) as proof of (forall (Xx:fofType), ((((eq fofType) (cS (cS Xx))) (cS Xx))->(((eq fofType) (cS (cS (cS (cS Xx))))) (cS (cS (cS Xx))))))
% 157.44/157.75 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 157.44/157.75 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.44/157.75 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found x3:(P (cS c0))
% 157.44/157.75 Instantiate: Xu:=c0:fofType
% 157.44/157.75 Found x3 as proof of (P0 (cS Xu))
% 157.44/157.75 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 157.44/157.75 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 157.44/157.75 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 157.44/157.75 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 157.44/157.75 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found ((eq_substitution0000 (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found (((eq_substitution000 (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 157.44/157.75 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 157.44/157.75 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS Xu))
% 157.44/157.75 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 157.44/157.75 Found (eq_ref0 c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) b)
% 157.44/157.75 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 157.44/157.75 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 157.44/157.75 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 157.44/157.75 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 157.44/157.75 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found x30:(P1 (cS (cS Xu)))
% 162.56/162.82 Instantiate: Xu:=Xx:fofType
% 162.56/162.82 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 162.56/162.82 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 162.56/162.82 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found x30:(P1 (cS (cS Xu)))
% 162.56/162.82 Instantiate: Xu:=Xx:fofType
% 162.56/162.82 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 162.56/162.82 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 162.56/162.82 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 162.56/162.82 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 162.56/162.82 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 162.56/162.82 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 162.56/162.82 Found x3:(P (cS c0))
% 162.56/162.82 Instantiate: Xu:=c0:fofType
% 162.56/162.82 Found x3 as proof of (P0 (cS Xu))
% 162.56/162.82 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 162.56/162.82 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 162.56/162.82 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 162.56/162.82 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 162.56/162.82 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found ((eq_substitution0000 (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found (((eq_substitution000 (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) (fun (x7:fofType)=> (cS (cS Xu)))) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 162.56/162.82 Found x30:(P1 (cS (cS Xu)))
% 162.56/162.82 Instantiate: Xu:=Xx:fofType
% 162.56/162.82 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 162.56/162.82 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 162.56/162.82 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 162.56/162.82 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 162.56/162.82 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 172.76/173.07 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 172.76/173.07 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 172.76/173.07 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 172.76/173.07 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 172.76/173.07 Found x30:(P1 (cS (cS Xu)))
% 172.76/173.07 Instantiate: Xu:=Xx:fofType
% 172.76/173.07 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 172.76/173.07 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 172.76/173.07 Found x3:(P (cS (cS Xu)))
% 172.76/173.07 Instantiate: Xu:=Xx:fofType
% 172.76/173.07 Found x3 as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found x3:(P (cS (cS Xu)))
% 172.76/173.07 Instantiate: Xu:=Xx:fofType
% 172.76/173.07 Found x3 as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found x3:(P (cS (cS Xu)))
% 172.76/173.07 Instantiate: Xu:=Xx:fofType
% 172.76/173.07 Found x3 as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 172.76/173.07 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 172.76/173.07 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 172.76/173.07 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 172.76/173.07 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 172.76/173.07 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 172.76/173.07 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 172.76/173.07 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 172.76/173.07 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 172.76/173.07 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 172.76/173.07 Found x3:(P (cS (cS Xu)))
% 172.76/173.07 Instantiate: Xu:=Xx:fofType
% 172.76/173.07 Found x3 as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found x3:(P (cS (cS Xu)))
% 172.76/173.07 Instantiate: Xu:=Xx:fofType
% 172.76/173.07 Found x3 as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found x3:(P (cS (cS Xu)))
% 172.76/173.07 Instantiate: Xu:=Xx:fofType
% 172.76/173.07 Found x3 as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 172.76/173.07 Found eq_ref00:=(eq_ref0 (cS Xu)):(((eq fofType) (cS Xu)) (cS Xu))
% 172.76/173.07 Found (eq_ref0 (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found ((eq_ref fofType) (cS Xu)) as proof of (((eq fofType) (cS Xu)) (cS Xx))
% 172.76/173.07 Found (eq_substitution00000 ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 172.76/173.07 Found (((eq_substitution000 (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 180.64/180.90 Found ((((eq_substitution00 (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 180.64/180.90 Found (((((eq_substitution0 fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 180.64/180.90 Found ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 180.64/180.90 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((((((eq_substitution fofType) fofType) (cS Xu)) (cS Xx)) cS) ((eq_ref fofType) (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 180.64/180.90 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 180.64/180.90 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 180.64/180.90 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 180.64/180.90 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 180.64/180.90 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 180.64/180.90 Instantiate: Xu:=Xx:fofType
% 180.64/180.90 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 180.64/180.90 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.64/180.90 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.64/180.90 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.64/180.90 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.64/180.90 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.64/180.90 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.64/180.90 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.64/180.90 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 180.64/180.90 Instantiate: Xu:=Xx:fofType
% 180.64/180.90 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 180.64/180.90 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.64/180.90 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.66/180.90 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.66/180.90 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.66/180.90 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.66/180.90 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.66/180.90 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.66/180.90 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 180.66/180.90 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 180.66/180.90 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 180.66/180.90 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 180.66/180.90 Found x4:(P1 (cS (cS Xu)))
% 180.66/180.90 Instantiate: Xu:=Xx:fofType
% 180.66/180.90 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 180.66/180.90 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 180.66/180.90 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 180.66/180.90 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 180.66/180.90 Instantiate: Xu:=Xx:fofType
% 180.66/180.90 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 180.66/180.90 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.66/180.90 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.66/180.90 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.66/180.90 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 180.66/180.90 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.66/180.90 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 180.66/180.90 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 184.73/184.98 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 184.73/184.98 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 184.73/184.98 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 184.73/184.98 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 184.73/184.98 Found x4:(P1 (cS (cS Xu)))
% 184.73/184.98 Instantiate: Xu:=Xx:fofType
% 184.73/184.98 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 184.73/184.98 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 184.73/184.98 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 184.73/184.98 Instantiate: Xu:=Xx:fofType
% 184.73/184.98 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 184.73/184.98 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 184.73/184.98 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 184.73/184.98 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 184.73/184.98 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 184.73/184.98 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 184.73/184.98 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 184.73/184.98 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 184.73/184.98 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 184.73/184.98 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 184.73/184.98 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 184.73/184.98 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 184.73/184.98 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 184.73/184.98 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 184.73/184.98 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 184.73/184.98 Found x300:(P (cS (cS Xu)))
% 184.73/184.98 Instantiate: Xu:=Xx:fofType
% 184.73/184.98 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of (P (cS (cS Xx)))
% 184.73/184.98 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 184.73/184.98 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 184.73/184.98 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 184.73/184.98 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 191.36/191.68 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found x4:(P1 (cS (cS Xu)))
% 191.36/191.68 Instantiate: Xu:=Xx:fofType
% 191.36/191.68 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 191.36/191.68 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found x4:(P1 (cS (cS Xu)))
% 191.36/191.68 Instantiate: Xu:=Xx:fofType
% 191.36/191.68 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 191.36/191.68 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 191.36/191.68 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.36/191.68 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.36/191.68 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found x3:(P (cS (cS Xu)))
% 191.36/191.68 Instantiate: Xu:=Xx:fofType
% 191.36/191.68 Found x3 as proof of (P (cS (cS Xx)))
% 191.36/191.68 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 191.36/191.68 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 191.36/191.68 Found (eq_ref00 P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 191.36/191.68 Found ((eq_ref0 (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 191.36/191.68 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 191.36/191.68 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 191.36/191.68 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 191.36/191.68 Found x300:(P (cS (cS Xu)))
% 191.36/191.68 Instantiate: Xu:=Xx:fofType
% 191.36/191.68 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of (P (cS (cS Xx)))
% 191.36/191.68 Found (fun (x300:(P (cS (cS Xu))))=> x300) as proof of ((P (cS (cS Xu)))->(P (cS (cS Xx))))
% 191.36/191.68 Found x3:(((eq fofType) (cS (cS Xu))) Xx)
% 191.36/191.68 Found x3 as proof of (((eq fofType) (cS (cS Xu))) Xx)
% 191.36/191.68 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 191.36/191.68 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 191.36/191.68 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 206.50/206.77 Found eq_ref00:=(eq_ref0 (cS (cS Xu))):(((eq fofType) (cS (cS Xu))) (cS (cS Xu)))
% 206.50/206.77 Found (eq_ref0 (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 206.50/206.77 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 206.50/206.77 Found ((eq_ref fofType) (cS (cS Xu))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 206.50/206.77 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> ((eq_ref fofType) (cS (cS Xu)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 206.50/206.77 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 206.50/206.77 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 206.50/206.77 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 206.50/206.77 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 206.50/206.77 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 206.50/206.77 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 206.50/206.77 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 206.50/206.77 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 206.50/206.77 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 206.50/206.77 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 206.50/206.77 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 206.50/206.77 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 206.50/206.77 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 206.50/206.77 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 206.50/206.77 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 206.50/206.77 Found (eq_ref00 P) as proof of (P0 c0)
% 206.50/206.77 Found ((eq_ref0 (cS c0)) P) as proof of (P0 c0)
% 206.50/206.77 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 206.50/206.77 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 206.50/206.77 Found x3:(((eq fofType) (cS (cS Xu))) Xx)
% 206.50/206.77 Found x3 as proof of (((eq fofType) (cS (cS Xu))) Xx)
% 206.50/206.77 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 206.50/206.77 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 206.50/206.77 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 206.50/206.77 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 206.50/206.77 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 206.50/206.77 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 206.50/206.77 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 217.59/217.88 Found (eq_ref00 P) as proof of (P0 c0)
% 217.59/217.88 Found ((eq_ref0 (cS c0)) P) as proof of (P0 c0)
% 217.59/217.88 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 217.59/217.88 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 217.59/217.88 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 217.59/217.88 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 217.59/217.88 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 217.59/217.88 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 217.59/217.88 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 217.59/217.88 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 217.59/217.88 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 217.59/217.88 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 217.59/217.88 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 217.59/217.88 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 217.59/217.88 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 217.59/217.88 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.59/217.88 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found x30:(P1 (cS (cS Xu)))
% 217.65/217.90 Instantiate: Xu:=Xx:fofType
% 217.65/217.90 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 217.65/217.90 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found x30:(P1 (cS (cS Xu)))
% 217.65/217.90 Instantiate: Xu:=Xx:fofType
% 217.65/217.90 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found x30:(P1 (cS (cS Xu)))
% 217.65/217.90 Instantiate: Xu:=Xx:fofType
% 217.65/217.90 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found x30:(P1 (cS (cS Xu)))
% 217.65/217.90 Instantiate: Xu:=Xx:fofType
% 217.65/217.90 Found (fun (x30:(P1 (cS (cS Xu))))=> x30) as proof of (P1 (cS (cS Xx)))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx))) (x30:(P1 (cS (cS Xu))))=> x30) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 217.65/217.90 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 217.65/217.90 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found (fun (x3:((P1 (cS (cS Xu)))->(P1 Xx)))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 217.65/217.90 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 235.09/235.37 Found (eq_ref0 (cS c0)) as proof of (P c0)
% 235.09/235.37 Found ((eq_ref fofType) (cS c0)) as proof of (P c0)
% 235.09/235.37 Found ((eq_ref fofType) (cS c0)) as proof of (P c0)
% 235.09/235.37 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 235.09/235.37 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 235.09/235.37 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 235.09/235.37 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 235.09/235.37 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 235.09/235.37 Found (eq_ref0 (cS c0)) as proof of (P c0)
% 235.09/235.37 Found ((eq_ref fofType) (cS c0)) as proof of (P c0)
% 235.09/235.37 Found ((eq_ref fofType) (cS c0)) as proof of (P c0)
% 235.09/235.37 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 235.09/235.37 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 235.09/235.37 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 235.09/235.37 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found x3:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found eq_ref00:=(eq_ref0 c0):(((eq fofType) c0) c0)
% 235.09/235.37 Found (eq_ref0 c0) as proof of (((eq fofType) c0) c0)
% 235.09/235.37 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 235.09/235.37 Found ((eq_ref fofType) c0) as proof of (((eq fofType) c0) c0)
% 235.09/235.37 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 235.09/235.37 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 235.09/235.37 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 235.09/235.37 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 235.09/235.37 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 235.09/235.37 Found x4:(P1 (cS (cS Xu)))
% 235.09/235.37 Instantiate: Xu:=Xx:fofType
% 235.09/235.37 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 235.09/235.37 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 235.09/235.37 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 240.20/240.46 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 240.20/240.46 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 240.20/240.46 Found x4:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 240.20/240.46 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 240.20/240.46 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 240.20/240.46 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (x4:(P1 Xx))=> x3) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 240.20/240.46 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 240.20/240.46 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 240.20/240.46 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 240.20/240.46 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 240.20/240.46 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 240.20/240.46 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 240.20/240.46 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 240.20/240.46 Found x4:(P1 (cS (cS Xu)))
% 240.20/240.46 Instantiate: Xu:=Xx:fofType
% 240.20/240.46 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 240.20/240.46 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 244.99/245.33 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 244.99/245.33 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 244.99/245.33 Found x4:(P1 (cS (cS Xu)))
% 244.99/245.33 Instantiate: Xu:=Xx:fofType
% 244.99/245.33 Found (fun (x4:(P1 (cS (cS Xu))))=> x4) as proof of (P1 (cS (cS Xx)))
% 244.99/245.33 Found (fun (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop)) (x4:(P1 (cS (cS Xu))))=> x4) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 244.99/245.33 Found eq_ref000:=(eq_ref00 P1):((P1 (cS (cS Xu)))->(P1 (cS (cS Xu))))
% 244.99/245.33 Found (eq_ref00 P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found ((eq_ref0 (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (((eq_ref fofType) (cS (cS Xu))) P1) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (fun (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of ((P1 (cS (cS Xu)))->(P1 (cS (cS Xx))))
% 244.99/245.33 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx)) (P1:(fofType->Prop))=> (((eq_ref fofType) (cS (cS Xu))) P1)) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 244.99/245.33 Found x3:(((eq fofType) Xx) (cS (cS Xu)))
% 244.99/245.33 Instantiate: Xu:=Xx:fofType
% 244.99/245.33 Found x3 as proof of (((eq fofType) Xx) (cS (cS Xx)))
% 244.99/245.33 Found (eq_sym010 x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 244.99/245.33 Found ((eq_sym01 (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 244.99/245.33 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 244.99/245.33 Found (((eq_sym0 Xx) (cS (cS Xx))) x3) as proof of (((eq fofType) (cS (cS Xx))) Xx)
% 244.99/245.33 Found (x30 (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3)) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((x3 ((eq fofType) (cS (cS Xx)))) (((eq_sym0 Xx) (cS (cS Xx))) x3))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found x3:(P (cS (cS Xu)))
% 244.99/245.33 Instantiate: Xu:=Xx:fofType
% 244.99/245.33 Found x3 as proof of (P (cS (cS Xx)))
% 244.99/245.33 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 244.99/245.33 Found eq_ref00:=(eq_ref0 (cS Xx)):(((eq fofType) (cS Xx)) (cS Xx))
% 244.99/245.33 Found (eq_ref0 (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 244.99/245.33 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 244.99/245.33 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 244.99/245.33 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 244.99/245.33 Found (eq_substitution00000 ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found (((eq_substitution000 (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found ((((eq_substitution00 (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found (((((eq_substitution0 fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 244.99/245.33 Found ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found eq_ref00:=(eq_ref0 (cS Xx)):(((eq fofType) (cS Xx)) (cS Xx))
% 251.93/252.20 Found (eq_ref0 (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 251.93/252.20 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 251.93/252.20 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 251.93/252.20 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 251.93/252.20 Found (eq_substitution00000 ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found (((eq_substitution000 (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found ((((eq_substitution00 (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found (((((eq_substitution0 fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 251.93/252.20 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 251.93/252.20 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 251.93/252.20 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 251.93/252.20 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 251.93/252.20 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 251.93/252.20 Found x3:(((eq fofType) (cS (cS Xu))) Xx)
% 251.93/252.20 Found x3 as proof of (((eq fofType) (cS (cS Xu))) Xx)
% 251.93/252.20 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 251.93/252.20 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 251.93/252.20 Found (eq_sym020 ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 251.93/252.20 Found ((eq_sym02 (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 251.93/252.20 Found (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 251.93/252.20 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx))))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 251.93/252.20 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 251.93/252.20 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 260.78/261.08 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 260.78/261.08 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 260.78/261.08 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 260.78/261.08 Found eq_ref00:=(eq_ref0 (cS Xx)):(((eq fofType) (cS Xx)) (cS Xx))
% 260.78/261.08 Found (eq_ref0 (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found (eq_substitution00000 ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found (((eq_substitution000 (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found ((((eq_substitution00 (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found (((((eq_substitution0 fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found eq_ref00:=(eq_ref0 (cS Xx)):(((eq fofType) (cS Xx)) (cS Xx))
% 260.78/261.08 Found (eq_ref0 (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found ((eq_ref fofType) (cS Xx)) as proof of (((eq fofType) (cS Xx)) (cS Xu))
% 260.78/261.08 Found (eq_substitution00000 ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found ((eq_substitution0000 cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found (((eq_substitution000 (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found ((((eq_substitution00 (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found (((((eq_substitution0 fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found (fun (x3:(((eq fofType) Xx) (cS (cS Xu))))=> ((((((eq_substitution fofType) fofType) (cS Xx)) (cS Xu)) cS) ((eq_ref fofType) (cS Xx)))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 260.78/261.08 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 260.78/261.08 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 260.78/261.08 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 260.78/261.08 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 260.78/261.08 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 260.78/261.08 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 260.78/261.08 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 260.78/261.08 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 260.78/261.08 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 260.78/261.08 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 260.78/261.08 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 260.78/261.08 Found (eq_ref00 P) as proof of (P0 c0)
% 260.78/261.08 Found ((eq_ref0 (cS c0)) P) as proof of (P0 c0)
% 260.78/261.08 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 260.78/261.08 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 260.78/261.08 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 260.78/261.08 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 260.78/261.08 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 260.78/261.08 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 260.78/261.08 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 260.78/261.08 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 292.81/293.10 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 292.81/293.10 Found (eq_ref0 b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 292.81/293.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 292.81/293.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 292.81/293.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cS (cS Xu)))
% 292.81/293.10 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 292.81/293.10 Found (eq_ref0 (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (((eq fofType) (cS c0)) b)
% 292.81/293.10 Found x3:(((eq fofType) (cS (cS Xu))) Xx)
% 292.81/293.10 Found x3 as proof of (((eq fofType) (cS (cS Xu))) Xx)
% 292.81/293.10 Found eq_ref00:=(eq_ref0 (cS (cS Xx))):(((eq fofType) (cS (cS Xx))) (cS (cS Xx)))
% 292.81/293.10 Found (eq_ref0 (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 292.81/293.10 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 292.81/293.10 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 292.81/293.10 Found ((eq_ref fofType) (cS (cS Xx))) as proof of (((eq fofType) (cS (cS Xx))) (cS (cS Xu)))
% 292.81/293.10 Found (eq_sym020 ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 292.81/293.10 Found ((eq_sym02 (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 292.81/293.10 Found (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx)))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 292.81/293.10 Found (fun (x3:(((eq fofType) (cS (cS Xu))) Xx))=> (((eq_sym0 (cS (cS Xx))) (cS (cS Xu))) ((eq_ref fofType) (cS (cS Xx))))) as proof of (((eq fofType) (cS (cS Xu))) (cS (cS Xx)))
% 292.81/293.10 Found eq_ref000:=(eq_ref00 P):((P (cS (cS Xu)))->(P (cS (cS Xu))))
% 292.81/293.10 Found (eq_ref00 P) as proof of (P0 (cS (cS Xu)))
% 292.81/293.10 Found ((eq_ref0 (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 292.81/293.10 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 292.81/293.10 Found (((eq_ref fofType) (cS (cS Xu))) P) as proof of (P0 (cS (cS Xu)))
% 292.81/293.10 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 292.81/293.10 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 292.81/293.10 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 292.81/293.10 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 292.81/293.10 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 292.81/293.10 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 292.81/293.10 Found (eq_ref00 P) as proof of (P0 c0)
% 292.81/293.10 Found ((eq_ref0 (cS c0)) P) as proof of (P0 c0)
% 292.81/293.10 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 292.81/293.10 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 c0)
% 292.81/293.10 Found eq_ref000:=(eq_ref00 P):((P (cS c0))->(P (cS c0)))
% 292.81/293.10 Found (eq_ref00 P) as proof of (P0 (cS c0))
% 292.81/293.10 Found ((eq_ref0 (cS c0)) P) as proof of (P0 (cS c0))
% 292.81/293.10 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 292.81/293.10 Found (((eq_ref fofType) (cS c0)) P) as proof of (P0 (cS c0))
% 292.81/293.10 Found x3:(P (cS (cS Xu)))
% 292.81/293.10 Instantiate: Xu:=Xx:fofType
% 292.81/293.10 Found x3 as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found x3:(P (cS (cS Xu)))
% 292.81/293.10 Instantiate: Xu:=Xx:fofType
% 292.81/293.10 Found x3 as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 292.81/293.10 Found (eq_ref0 (cS c0)) as proof of (P c0)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (P c0)
% 292.81/293.10 Found ((eq_ref fofType) (cS c0)) as proof of (P c0)
% 292.81/293.10 Found x3:(P (cS (cS Xu)))
% 292.81/293.10 Instantiate: Xu:=Xx:fofType
% 292.81/293.10 Found x3 as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found x3:(P (cS (cS Xu)))
% 292.81/293.10 Instantiate: Xu:=Xx:fofType
% 292.81/293.10 Found x3 as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found (fun (x4:(P Xx))=> x3) as proof of (P (cS (cS Xx)))
% 292.81/293.10 Found eq_ref00:=(eq_ref0 (cS c0)):(((eq fofType) (cS c0)) (cS c0))
% 292.81/293.10 Found (eq_ref0 (cS c0)) as proof of
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