TSTP Solution File: SYO546^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO546^1 : TPTP v7.5.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:52:04 EDT 2022
% Result : Timeout 296.42s 296.80s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO546^1 : TPTP v7.5.0. Released v5.2.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.19/0.33 % DateTime : Sun Mar 13 19:34:56 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.19/0.34 Python 2.7.5
% 1.83/2.02 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.83/2.02 FOF formula (<kernel.Constant object at 0x2aaec195a6c8>, <kernel.DependentProduct object at 0xd459e0>) of role type named eps
% 1.83/2.02 Using role type
% 1.83/2.02 Declaring eps:((fofType->Prop)->fofType)
% 1.83/2.02 FOF formula (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P)))) of role axiom named choiceax
% 1.83/2.02 A new axiom: (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P))))
% 1.83/2.02 FOF formula (<kernel.Constant object at 0x2aaec194af38>, <kernel.DependentProduct object at 0xd45a28>) of role type named caseoo
% 1.83/2.02 Using role type
% 1.83/2.02 Declaring case:((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 1.83/2.02 FOF formula (((eq ((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType)))))) case) (fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V))))))) of role definition named caseood
% 1.83/2.02 A new definition: (((eq ((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType)))))) case) (fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V)))))))
% 1.83/2.02 Defined: case:=(fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V))))))
% 1.83/2.02 FOF formula (<kernel.Constant object at 0x2aaec195a680>, <kernel.DependentProduct object at 0xd45710>) of role type named f
% 1.83/2.02 Using role type
% 1.83/2.02 Declaring f:(Prop->Prop)
% 1.83/2.02 FOF formula (forall (X:fofType), (((eq fofType) (((((case f) X) X) X) X)) X)) of role conjecture named conj
% 1.83/2.02 Conjecture to prove = (forall (X:fofType), (((eq fofType) (((((case f) X) X) X) X)) X)):Prop
% 1.83/2.02 Parameter fofType_DUMMY:fofType.
% 1.83/2.02 We need to prove ['(forall (X:fofType), (((eq fofType) (((((case f) X) X) X) X)) X))']
% 1.83/2.02 Parameter fofType:Type.
% 1.83/2.02 Parameter eps:((fofType->Prop)->fofType).
% 1.83/2.02 Axiom choiceax:(forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P)))).
% 1.83/2.02 Definition case:=(fun (B:(Prop->Prop)) (X:fofType) (Y:fofType) (U:fofType) (V:fofType)=> (eps (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) B) not)) (((eq fofType) Z) Y)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> A))) (((eq fofType) Z) U)))) ((and (((eq (Prop->Prop)) B) (fun (A:Prop)=> True))) (((eq fofType) Z) V)))))):((Prop->Prop)->(fofType->(fofType->(fofType->(fofType->fofType))))).
% 1.83/2.02 Parameter f:(Prop->Prop).
% 1.83/2.02 Trying to prove (forall (X:fofType), (((eq fofType) (((((case f) X) X) X) X)) X))
% 1.83/2.02 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 1.83/2.02 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 1.83/2.02 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 1.83/2.02 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 1.83/2.02 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 1.83/2.02 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 1.83/2.02 Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% 1.83/2.02 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 5.75/5.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 5.75/5.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 5.75/5.90 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 5.75/5.90 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 5.75/5.90 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 5.75/5.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 5.75/5.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 5.75/5.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 5.75/5.90 Found x:(P (((((case f) X) X) X) X))
% 5.75/5.90 Instantiate: b:=(((((case f) X) X) X) X):fofType
% 5.75/5.90 Found x as proof of (P0 b)
% 5.75/5.90 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 5.75/5.90 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 5.75/5.90 Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 5.75/5.90 Found (eq_ref0 (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) b)
% 5.75/5.90 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) b)
% 5.75/5.90 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) b)
% 5.75/5.90 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))) b)
% 5.75/5.90 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) (fun (x:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 5.75/5.90 Found (eta_expansion_dep00 (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) b)
% 5.75/5.90 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) b)
% 5.75/5.90 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) b)
% 5.75/5.90 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) b)
% 5.75/5.90 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X))) b)
% 5.75/5.90 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 5.75/5.90 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 6.86/7.04 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 6.86/7.04 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0)))
% 6.86/7.04 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 6.86/7.04 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 6.86/7.04 Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% 6.86/7.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 6.86/7.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 6.86/7.04 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 6.86/7.04 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 6.86/7.04 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 6.86/7.04 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 6.86/7.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 6.86/7.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 6.86/7.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 6.86/7.04 Found x:(P X)
% 6.86/7.04 Instantiate: b:=X:fofType
% 6.86/7.04 Found x as proof of (P0 b)
% 6.86/7.04 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 6.86/7.04 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 6.86/7.04 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 6.86/7.04 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 6.86/7.04 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 6.86/7.04 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X)))
% 6.86/7.04 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 6.86/7.04 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 6.86/7.04 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 13.94/14.12 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X))
% 13.94/14.12 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((eq fofType) (((((case f) X) X) X) X)) X)))
% 13.94/14.12 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 13.94/14.12 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 13.94/14.12 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 13.94/14.12 Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% 13.94/14.12 Found (eq_ref0 x) as proof of (((eq fofType) x) X)
% 13.94/14.12 Found ((eq_ref fofType) x) as proof of (((eq fofType) x) X)
% 13.94/14.12 Found ((eq_ref fofType) x) as proof of (((eq fofType) x) X)
% 13.94/14.12 Found ((eq_ref fofType) x) as proof of (((eq fofType) x) X)
% 13.94/14.12 Found (ex_intro000 ((eq_ref fofType) x)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq fofType) X0) X)))
% 13.94/14.12 Found ((ex_intro00 X) ((eq_ref fofType) X)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq fofType) X0) X)))
% 13.94/14.12 Found (((ex_intro0 (fun (X0:fofType)=> (((eq fofType) X0) X))) X) ((eq_ref fofType) X)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq fofType) X0) X)))
% 13.94/14.12 Found ((((ex_intro fofType) (fun (X0:fofType)=> (((eq fofType) X0) X))) X) ((eq_ref fofType) X)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq fofType) X0) X)))
% 13.94/14.12 Found ((((ex_intro fofType) (fun (X0:fofType)=> (((eq fofType) X0) X))) X) ((eq_ref fofType) X)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq fofType) X0) X)))
% 13.94/14.12 Found eq_ref00:=(eq_ref0 (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))):(((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))))
% 13.94/14.12 Found (eq_ref0 (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 13.94/14.12 Found ((eq_ref fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 13.94/14.12 Found ((eq_ref fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 13.94/14.12 Found ((eq_ref fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 21.94/22.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 21.94/22.13 Found (eq_ref0 b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 21.94/22.13 Found eta_expansion000:=(eta_expansion00 (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) (fun (x:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X))))
% 21.94/22.13 Found (eta_expansion00 (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 21.94/22.13 Found ((eta_expansion0 Prop) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 21.94/22.13 Found (((eta_expansion fofType) Prop) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 21.94/22.13 Found (((eta_expansion fofType) Prop) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 21.94/22.13 Found (((eta_expansion fofType) Prop) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 21.94/22.13 Found fofType_DUMMY:fofType
% 21.94/22.13 Found fofType_DUMMY as proof of fofType
% 21.94/22.13 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 21.94/22.13 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 21.94/22.13 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 21.94/22.13 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 21.94/22.13 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 21.94/22.13 Found fofType_DUMMY:fofType
% 21.94/22.13 Found fofType_DUMMY as proof of fofType
% 21.94/22.13 Found x2:(P b)
% 21.94/22.13 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 21.94/22.13 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 21.94/22.13 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 21.94/22.13 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 21.94/22.13 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 21.94/22.13 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X))))
% 24.21/24.41 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 24.21/24.41 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 24.21/24.41 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X))))
% 24.21/24.41 Found eq_ref000:=(eq_ref00 P0):((P0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))->(P0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 24.21/24.41 Found (eq_ref00 P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 24.21/24.41 Found ((eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 24.21/24.41 Found (((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 24.21/24.41 Found (((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 24.21/24.41 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 24.21/24.41 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 24.21/24.41 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 24.21/24.41 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 24.21/24.41 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 24.21/24.41 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 24.21/24.41 Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% 24.21/24.41 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 24.21/24.41 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 24.21/24.41 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 24.21/24.41 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 24.21/24.41 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 24.21/24.41 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 24.21/24.41 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 24.21/24.41 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 33.72/33.98 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 33.72/33.98 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 33.72/33.98 Found eq_ref00:=(eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))):(((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 33.72/33.98 Found (eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 33.72/33.98 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 33.72/33.98 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 33.72/33.98 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 33.72/33.98 Found x3:(P X)
% 33.72/33.98 Found (fun (x3:(P X))=> x3) as proof of (P X)
% 33.72/33.98 Found (fun (x3:(P X))=> x3) as proof of (P0 X)
% 33.72/33.98 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 33.72/33.98 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 33.72/33.98 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 33.72/33.98 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 33.72/33.98 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 33.72/33.98 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 33.72/33.98 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 33.72/33.98 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 33.72/33.98 Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% 33.72/33.98 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 33.72/33.98 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 33.72/33.98 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 33.72/33.98 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 33.72/33.98 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (((((case f) X) X) X) X))
% 33.72/33.98 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((((case f) X) X) X) X))
% 33.72/33.98 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((((case f) X) X) X) X))
% 33.72/33.98 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (((((case f) X) X) X) X))
% 33.72/33.98 Found X:fofType
% 33.72/33.98 Found X as proof of fofType
% 33.72/33.98 Found X:fofType
% 33.72/33.98 Found X as proof of fofType
% 33.72/33.98 Found x2:(P b)
% 33.72/33.98 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 33.72/33.98 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 33.72/33.98 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 33.72/33.98 Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 33.72/33.98 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 33.72/33.98 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 50.72/50.92 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 50.72/50.92 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 50.72/50.92 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 50.72/50.92 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 50.72/50.92 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 50.72/50.92 Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% 50.72/50.92 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 50.72/50.92 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 50.72/50.92 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 50.72/50.92 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 50.72/50.92 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 50.72/50.92 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 50.72/50.92 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 50.72/50.92 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 50.72/50.92 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (x00:fofType)=> (((eq fofType) x00) X)))->(P0 (fun (x:fofType)=> (((eq fofType) x) X))))
% 50.72/50.92 Found (eta_expansion000 P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 50.72/50.92 Found ((eta_expansion00 (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 50.72/50.92 Found (((eta_expansion0 Prop) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 50.72/50.92 Found ((((eta_expansion fofType) Prop) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 50.72/50.92 Found ((((eta_expansion fofType) Prop) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 50.72/50.92 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (x00:fofType)=> (((eq fofType) x00) X))):(((eq (fofType->Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) (fun (x:fofType)=> (((eq fofType) x) X)))
% 50.72/50.92 Found (eta_expansion_dep00 (fun (x00:fofType)=> (((eq fofType) x00) X))) as proof of (((eq (fofType->Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) b)
% 50.72/50.92 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) as proof of (((eq (fofType->Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) b)
% 50.72/50.92 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) as proof of (((eq (fofType->Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) b)
% 50.72/50.92 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) as proof of (((eq (fofType->Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) b)
% 50.72/50.92 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) as proof of (((eq (fofType->Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) b)
% 50.72/50.92 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 50.72/50.92 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))))
% 50.72/50.92 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))))
% 64.40/64.61 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))))
% 64.40/64.61 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))))
% 64.40/64.61 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (x00:fofType)=> (((eq fofType) x00) X)))->(P0 (fun (x:fofType)=> (((eq fofType) x) X))))
% 64.40/64.61 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found ((eta_expansion_dep00 (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found (((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found ((((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found ((((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (x00:fofType)=> (((eq fofType) x00) X)))->(P0 (fun (x:fofType)=> (((eq fofType) x) X))))
% 64.40/64.61 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found ((eta_expansion_dep00 (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found (((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found ((((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found ((((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (x00:fofType)=> (((eq fofType) x00) X))) P0) as proof of (P1 (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 64.40/64.61 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 64.40/64.61 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 64.40/64.61 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 64.40/64.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 64.40/64.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 64.40/64.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 64.40/64.61 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 64.40/64.61 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 64.40/64.61 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 89.39/89.61 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 89.39/89.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 89.39/89.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 89.39/89.61 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 89.39/89.61 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 89.39/89.61 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 89.39/89.61 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 89.39/89.61 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 89.39/89.61 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 89.39/89.61 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 89.39/89.61 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 89.39/89.61 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 89.39/89.61 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 89.39/89.61 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 89.39/89.61 Found ex_intro0000:=(ex_intro000 x):((ex fofType) (fun (X:fofType)=> (P0 X)))
% 89.39/89.61 Found (ex_intro000 x) as proof of ((ex fofType) (fun (X:fofType)=> (P0 X)))
% 89.39/89.61 Found ((ex_intro00 X) x) as proof of ((ex fofType) (fun (X:fofType)=> (P0 X)))
% 89.39/89.61 Found (((ex_intro0 (fun (X:fofType)=> (P0 X))) X) x) as proof of ((ex fofType) (fun (X:fofType)=> (P0 X)))
% 89.39/89.61 Found ((((ex_intro fofType) (fun (X:fofType)=> (P0 X))) X) x) as proof of ((ex fofType) (fun (X:fofType)=> (P0 X)))
% 89.39/89.61 Found ((((ex_intro fofType) (fun (X:fofType)=> (P0 X))) X) x) as proof of ((ex fofType) (fun (X:fofType)=> (P0 X)))
% 89.39/89.61 Found (choiceax0 ((((ex_intro fofType) (fun (X:fofType)=> (P0 X))) X) x)) as proof of (P0 (eps a))
% 89.39/89.61 Found (choiceax0 ((((ex_intro fofType) (fun (X:fofType)=> (P0 X))) X) x)) as proof of (P0 (eps a))
% 89.39/89.61 Found ((choiceax P0) ((((ex_intro fofType) (fun (X:fofType)=> (P0 X))) X) x)) as proof of (P0 (eps a))
% 89.39/89.61 Found ((choiceax P0) ((((ex_intro fofType) (fun (X:fofType)=> (P0 X))) X) x)) as proof of (P0 (eps a))
% 89.39/89.61 Found eq_ref00:=(eq_ref0 (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))):(((eq (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))))
% 89.39/89.61 Found (eq_ref0 (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) b)
% 89.50/89.78 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) b)
% 89.50/89.78 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) b)
% 89.50/89.78 Found ((eq_ref (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) as proof of (((eq (fofType->Prop)) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))) b)
% 89.50/89.78 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 119.20/119.50 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 119.20/119.50 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 119.20/119.50 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 119.20/119.50 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 119.20/119.50 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (x00:fofType)=> (((eq fofType) x00) X)))
% 119.20/119.50 Found eq_ref000:=(eq_ref00 P0):((P0 (((eq fofType) x) X))->(P0 (((eq fofType) x) X)))
% 119.20/119.50 Found (eq_ref00 P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found ((eq_ref0 (((eq fofType) x) X)) P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found (((eq_ref Prop) (((eq fofType) x) X)) P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found (((eq_ref Prop) (((eq fofType) x) X)) P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found eq_ref000:=(eq_ref00 P0):((P0 (((eq fofType) x) X))->(P0 (((eq fofType) x) X)))
% 119.20/119.50 Found (eq_ref00 P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found ((eq_ref0 (((eq fofType) x) X)) P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found (((eq_ref Prop) (((eq fofType) x) X)) P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found (((eq_ref Prop) (((eq fofType) x) X)) P0) as proof of (P1 (((eq fofType) x) X))
% 119.20/119.50 Found eq_ref00:=(eq_ref0 (((eq fofType) x) X)):(((eq Prop) (((eq fofType) x) X)) (((eq fofType) x) X))
% 119.20/119.50 Found (eq_ref0 (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 119.20/119.50 Found ((eq_ref Prop) (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 119.20/119.50 Found ((eq_ref Prop) (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 119.20/119.50 Found ((eq_ref Prop) (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 119.20/119.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 119.20/119.50 Found (eq_ref0 b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 119.20/119.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 119.20/119.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 119.20/119.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 163.39/163.68 Found eq_ref00:=(eq_ref0 (((eq fofType) x) X)):(((eq Prop) (((eq fofType) x) X)) (((eq fofType) x) X))
% 163.39/163.68 Found (eq_ref0 (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 163.39/163.68 Found ((eq_ref Prop) (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 163.39/163.68 Found ((eq_ref Prop) (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 163.39/163.68 Found ((eq_ref Prop) (((eq fofType) x) X)) as proof of (((eq Prop) (((eq fofType) x) X)) b)
% 163.39/163.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 163.39/163.68 Found (eq_ref0 b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 163.39/163.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 163.39/163.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 163.39/163.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 163.39/163.68 Found x:(P (((((case f) X) X) X) X))
% 163.39/163.68 Instantiate: b:=(((((case f) X) X) X) X):fofType
% 163.39/163.68 Found x as proof of (P0 b)
% 163.39/163.68 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 163.39/163.68 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 163.39/163.68 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 163.39/163.68 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 163.39/163.68 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 163.39/163.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 163.39/163.68 Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% 163.39/163.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 163.39/163.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 163.39/163.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 163.39/163.68 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 163.39/163.68 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 163.39/163.68 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 163.39/163.68 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 163.39/163.68 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 163.39/163.68 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 163.39/163.68 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 163.39/163.68 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 199.52/199.78 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 199.52/199.78 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 199.52/199.78 Found x:(P X)
% 199.52/199.78 Instantiate: b:=X:fofType
% 199.52/199.78 Found x as proof of (P0 b)
% 199.52/199.78 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 199.52/199.78 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 199.52/199.78 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 199.52/199.78 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 199.52/199.78 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 199.52/199.78 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 199.52/199.78 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 199.52/199.78 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 199.52/199.78 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 199.52/199.78 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 199.52/199.78 Found x:(P0 (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))))
% 199.52/199.78 Instantiate: b:=(((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))):fofType
% 199.52/199.78 Found x as proof of (P1 b)
% 199.52/199.78 Found eq_ref00:=(eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))):(((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 199.52/199.78 Found (eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) b)
% 199.52/199.78 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) b)
% 199.52/199.78 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) b)
% 199.52/199.78 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) b)
% 199.52/199.78 Found eq_ref000:=(eq_ref00 P0):((P0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))))->(P0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))))
% 199.52/199.78 Found (eq_ref00 P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 199.52/199.78 Found ((eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 199.81/200.13 Found (((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 199.81/200.13 Found (((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 199.81/200.13 Found eq_ref000:=(eq_ref00 P0):((P0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))))->(P0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))))
% 199.81/200.13 Found (eq_ref00 P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 202.82/203.08 Found ((eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 202.82/203.08 Found (((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 202.82/203.08 Found (((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x000:fofType)=> (((eq fofType) x000) X))))))) P0) as proof of (P1 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 202.82/203.08 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 202.82/203.08 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 202.82/203.08 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 202.82/203.08 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 202.82/203.08 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 202.82/203.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 202.82/203.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 202.82/203.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 202.82/203.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 203.59/203.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 203.59/203.86 Found eq_ref00:=(eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))):(((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 203.59/203.86 Found (eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 203.59/203.86 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 203.59/203.86 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 204.78/205.08 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 204.78/205.08 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 204.78/205.08 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 204.78/205.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 204.78/205.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 204.78/205.08 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 204.78/205.08 Found eq_ref00:=(eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))):(((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 204.78/205.08 Found (eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 207.64/207.89 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 207.64/207.89 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 207.64/207.89 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 207.64/207.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.64/207.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 207.64/207.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 207.64/207.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 207.64/207.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 207.64/207.89 Found eq_ref00:=(eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))):(((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 207.64/207.89 Found (eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 207.64/207.89 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 207.64/207.89 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 208.93/209.18 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 208.93/209.18 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 208.93/209.18 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 208.93/209.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 208.93/209.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 208.93/209.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) x) X))
% 208.93/209.18 Found eq_ref00:=(eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))):(((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))))
% 208.93/209.18 Found (eq_ref0 ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 218.00/218.28 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 218.00/218.28 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 218.00/218.28 Found ((eq_ref Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) as proof of (((eq Prop) ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) x) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))))) b)
% 218.00/218.28 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 218.00/218.28 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 218.00/218.28 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 218.00/218.28 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 218.00/218.28 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 218.00/218.28 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 218.00/218.28 Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% 218.00/218.28 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 239.69/239.99 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 239.69/239.99 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 239.69/239.99 Found x:(P (((((case f) X) X) X) X))
% 239.69/239.99 Instantiate: a:=(((((case f) X) X) X) X):fofType
% 239.69/239.99 Found x as proof of (P0 a)
% 239.69/239.99 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 239.69/239.99 Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% 239.69/239.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 239.69/239.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 239.69/239.99 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% 239.69/239.99 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 239.69/239.99 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 239.69/239.99 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 239.69/239.99 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 239.69/239.99 Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% 239.69/239.99 Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.69/239.99 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.69/239.99 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.69/239.99 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.69/239.99 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 239.69/239.99 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 239.69/239.99 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> (forall (X0:fofType), (((eq fofType) (((((case f) X0) X0) X0) X0)) X0))))
% 239.69/239.99 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 239.69/239.99 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 239.69/239.99 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 239.69/239.99 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 239.69/239.99 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 239.69/239.99 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 239.69/239.99 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 239.69/239.99 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 253.89/254.19 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 253.89/254.19 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 253.89/254.19 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 253.89/254.19 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 253.89/254.19 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 253.89/254.19 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X0:fofType)=> (((eq fofType) (((((case f) X) X) X) X)) X)))
% 253.89/254.19 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 253.89/254.19 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found eq_ref00:=(eq_ref0 (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))):(((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X))))
% 253.89/254.19 Found (eq_ref0 (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 253.89/254.19 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 253.89/254.19 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 253.89/254.19 Found ((eq_ref (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) as proof of (((eq (fofType->Prop)) (fun (X0:fofType)=> (((eq fofType) X) (((((case f) X) X) X) X)))) b)
% 253.89/254.19 Found x:(P1 X)
% 253.89/254.19 Instantiate: b:=X:fofType
% 253.89/254.19 Found x as proof of (P2 b)
% 253.89/254.19 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 253.89/254.19 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 253.89/254.19 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 253.89/254.19 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 253.89/254.19 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 253.89/254.19 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 253.89/254.19 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 253.89/254.19 Found x:(P0 (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))))
% 255.07/255.36 Instantiate: a:=(fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))))):(fofType->Prop)
% 255.07/255.36 Found x as proof of (P1 (eps a))
% 255.07/255.36 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 255.07/255.36 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (fun (x0:fofType)=> (((eq fofType) x0) X)))
% 255.07/255.36 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (x0:fofType)=> (((eq fofType) x0) X)))
% 255.07/255.36 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (x0:fofType)=> (((eq fofType) x0) X)))
% 255.07/255.36 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (x0:fofType)=> (((eq fofType) x0) X)))
% 255.07/255.36 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (x0:fofType)=> (((eq fofType) x0) X)))
% 255.07/255.36 Found fofType_DUMMY:fofType
% 255.07/255.36 Found fofType_DUMMY as proof of fofType
% 255.07/255.36 Found eq_ref00:=(eq_ref0 (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))):(((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))))
% 255.07/255.36 Found (eq_ref0 (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 255.07/255.36 Found ((eq_ref fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 255.07/255.36 Found ((eq_ref fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 255.07/255.36 Found ((eq_ref fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X)))) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))) b)
% 255.07/255.36 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 261.12/261.40 Found (eq_ref0 b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x0:fofType)=> (((eq fofType) x0) X))))
% 261.12/261.40 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 261.12/261.40 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 261.12/261.40 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 261.12/261.40 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 261.12/261.40 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 261.12/261.40 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 261.12/261.40 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 261.12/261.40 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 261.12/261.40 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 261.12/261.40 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 261.12/261.40 Found eq_ref00:=(eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))):(((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 261.12/261.40 Found (eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 261.12/261.40 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 261.12/261.40 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 261.12/261.40 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 261.12/261.40 Found x2:(P (((((case f) X) X) X) X))
% 261.12/261.40 Found (fun (x2:(P (((((case f) X) X) X) X)))=> x2) as proof of (P (((((case f) X) X) X) X))
% 261.12/261.40 Found (fun (x2:(P (((((case f) X) X) X) X)))=> x2) as proof of (P0 (((((case f) X) X) X) X))
% 266.70/267.04 Found fofType_DUMMY:fofType
% 266.70/267.04 Found fofType_DUMMY as proof of fofType
% 266.70/267.04 Found x2:(P b)
% 266.70/267.04 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 266.70/267.04 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 266.70/267.04 Found x:(P0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 266.70/267.04 Instantiate: b:=(eps (fun (x00:fofType)=> (((eq fofType) x00) X))):fofType
% 266.70/267.04 Found x as proof of (P1 b)
% 266.70/267.04 Found eq_ref00:=(eq_ref0 (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))):(((eq fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 266.70/267.04 Found (eq_ref0 (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) b)
% 266.70/267.04 Found ((eq_ref fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) b)
% 266.70/267.04 Found ((eq_ref fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) b)
% 266.70/267.04 Found ((eq_ref fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) as proof of (((eq fofType) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))) b)
% 266.70/267.04 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 266.70/267.04 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 266.70/267.04 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 266.70/267.04 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 266.70/267.04 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 266.70/267.04 Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% 266.70/267.04 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 266.70/267.04 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 281.49/281.84 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% 281.49/281.84 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 281.49/281.84 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 281.49/281.84 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 281.49/281.84 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 281.49/281.84 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b0)
% 281.49/281.84 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 281.49/281.84 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X))))
% 281.49/281.84 Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% 281.49/281.84 Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X)))
% 281.49/281.84 Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((eq fofType) X) (((((case f) X) X) X) X))))
% 281.49/281.84 Found x00:(P1 X)
% 281.49/281.84 Found (fun (x00:(P1 X))=> x00) as proof of (P1 X)
% 281.49/281.84 Found (fun (x00:(P1 X))=> x00) as proof of (P2 X)
% 281.49/281.84 Found eq_ref000:=(eq_ref00 P0):((P0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))->(P0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 281.49/281.84 Found (eq_ref00 P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 281.49/281.84 Found ((eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 281.49/281.84 Found (((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 281.49/281.84 Found (((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) P0) as proof of (P1 (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 281.49/281.84 Found x:(P b)
% 281.49/281.84 Instantiate: b0:=b:fofType
% 281.49/281.84 Found x as proof of (P0 b0)
% 281.49/281.84 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 281.49/281.84 Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% 281.49/281.84 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 281.49/281.84 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 281.49/281.84 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% 281.49/281.84 Found eq_ref00:=(eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))):(((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 281.49/281.84 Found (eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 281.49/281.84 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 281.49/281.84 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 281.49/281.84 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 281.49/281.84 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 281.49/281.84 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 282.19/282.50 Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) (fun (Z:fofType)=> ((or ((or ((or ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> False))) (((eq fofType) Z) X))) ((and (((eq (Prop->Prop)) f) not)) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> A))) (((eq fofType) Z) X)))) ((and (((eq (Prop->Prop)) f) (fun (A:Prop)=> True))) (((eq fofType) Z) X)))))
% 282.19/282.50 Found x:(P X)
% 282.19/282.50 Instantiate: b:=X:fofType
% 282.19/282.50 Found x as proof of (P0 b)
% 296.42/296.80 Found eq_ref00:=(eq_ref0 (((((case f) X) X) X) X)):(((eq fofType) (((((case f) X) X) X) X)) (((((case f) X) X) X) X))
% 296.42/296.80 Found (eq_ref0 (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 296.42/296.80 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 296.42/296.80 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 296.42/296.80 Found ((eq_ref fofType) (((((case f) X) X) X) X)) as proof of (((eq fofType) (((((case f) X) X) X) X)) b)
% 296.42/296.80 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 296.42/296.80 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))))
% 296.42/296.80 Found eq_ref00:=(eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))):(((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) (eps (fun (x00:fofType)=> (((eq fofType) x00) X))))
% 296.42/296.80 Found (eq_ref0 (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 296.42/296.80 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 296.42/296.80 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 296.42/296.80 Found ((eq_ref fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) as proof of (((eq fofType) (eps (fun (x00:fofType)=> (((eq fofType) x00) X)))) b)
% 296.42/296.80 Found x3:(P X)
% 296.42/296.80 Found (fun (x3:(P X))=> x3) as proof of (P X)
% 296.42/296.80 Found (fun (x3:(P X))=> x3) as proof of (P0 X)
% 296.42/296.80 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 296.42/296.80 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 296.42/296.80 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found x3:(P X)
% 296.42/296.80 Found (fun (x3:(P X))=> x3) as proof of (P X)
% 296.42/296.80 Found (fun (x3:(P X))=> x3) as proof of (P0 X)
% 296.42/296.80 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% 296.42/296.80 Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% 296.42/296.80 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 296.42/296.80 Found (eq_ref0 b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (((((case f) X) X) X) X))
% 296.42/296.80 Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
%------------------------------------------------------------------------------