TSTP Solution File: SYO516^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO516^1 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n029.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 00:52:00 EDT 2022
% Result : Timeout 288.76s 289.17s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO516^1 : TPTP v7.5.0. Released v4.1.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n029.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
% 0.12/0.33 % DateTime : Sun Mar 13 14:07:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 3.55/3.74 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 3.55/3.74 FOF formula (<kernel.Constant object at 0x10d3998>, <kernel.DependentProduct object at 0x2b1be4d8b7e8>) of role type named r_type
% 3.55/3.74 Using role type
% 3.55/3.74 Declaring r:(fofType->(fofType->Prop))
% 3.55/3.74 FOF formula ((forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))))->((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))) of role conjecture named descr2
% 3.55/3.74 Conjecture to prove = ((forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))))->((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))):Prop
% 3.55/3.74 Parameter fofType_DUMMY:fofType.
% 3.55/3.74 We need to prove ['((forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))))->((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))))']
% 3.55/3.74 Parameter fofType:Type.
% 3.55/3.74 Parameter r:(fofType->(fofType->Prop)).
% 3.55/3.74 Trying to prove ((forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))))->((ex (fofType->fofType)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))))
% 3.55/3.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (x:(fofType->fofType))=> (forall (X:fofType), ((r X) (x X)))))
% 3.55/3.74 Found (eta_expansion_dep00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (x:(fofType->fofType))=> (forall (X:fofType), ((r X) (x X)))))
% 3.55/3.74 Found (eta_expansion_dep00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 3.55/3.74 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 5.23/5.46 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 5.23/5.46 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.23/5.46 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 5.23/5.46 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.23/5.46 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 5.23/5.46 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.23/5.46 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 5.23/5.46 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.23/5.46 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (X:fofType), ((r X) (x0 X))))
% 5.23/5.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 5.23/5.46 Found eq_ref00:=(eq_ref0 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (y:fofType)=> ((r x0) y)))
% 5.23/5.46 Found (eq_ref0 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 5.23/5.46 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 5.23/5.46 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 5.23/5.46 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 5.23/5.46 Found eq_ref00:=(eq_ref0 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (y:fofType)=> ((r x0) y)))
% 5.23/5.46 Found (eq_ref0 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 5.23/5.46 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 5.23/5.46 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 7.87/8.07 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 7.87/8.07 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 7.87/8.07 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 7.87/8.07 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 7.87/8.07 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 7.87/8.07 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 7.87/8.07 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 7.87/8.07 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 7.87/8.07 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 7.87/8.07 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 7.87/8.07 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 7.87/8.07 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 7.87/8.07 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 7.87/8.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 7.87/8.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 7.87/8.07 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 7.87/8.07 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 7.87/8.07 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 7.87/8.07 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 7.87/8.07 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 9.23/9.45 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 9.23/9.45 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 9.23/9.45 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 9.23/9.45 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 9.23/9.45 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 9.23/9.45 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 9.23/9.45 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 9.23/9.45 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 9.23/9.45 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 14.52/14.77 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 14.52/14.77 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 14.52/14.77 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 14.52/14.77 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 14.52/14.77 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 14.52/14.77 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 14.52/14.77 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 14.52/14.77 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 14.52/14.77 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 14.52/14.77 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 14.52/14.77 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 14.52/14.77 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 14.52/14.77 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 14.52/14.77 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 15.93/16.10 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 15.93/16.10 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 15.93/16.10 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 15.93/16.10 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 15.93/16.10 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 15.93/16.10 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 15.93/16.10 Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 15.93/16.10 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 15.93/16.10 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 15.93/16.10 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 15.93/16.10 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 15.93/16.10 Found eq_ref00:=(eq_ref0 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 15.93/16.10 Found (eq_ref0 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 15.93/16.10 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 15.93/16.10 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 15.93/16.10 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 15.93/16.10 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 15.93/16.10 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 17.83/18.07 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->fofType)->Prop)) a) (fun (x:(fofType->fofType))=> (a x)))
% 17.83/18.07 Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 17.83/18.07 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 17.83/18.07 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 17.83/18.07 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 17.83/18.07 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 17.83/18.07 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 17.83/18.07 Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 17.83/18.07 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 17.83/18.07 Found eq_ref00:=(eq_ref0 (x0 X)):(((eq fofType) (x0 X)) (x0 X))
% 17.83/18.07 Found (eq_ref0 (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 17.83/18.07 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 17.83/18.07 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 17.83/18.07 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 17.83/18.07 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 17.83/18.07 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 17.83/18.07 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 17.83/18.07 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 17.83/18.07 Found eta_expansion000:=(eta_expansion00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (x:(fofType->fofType))=> (forall (X:fofType), ((r X) (x X)))))
% 17.83/18.07 Found (eta_expansion00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 17.83/18.07 Found ((eta_expansion0 Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 17.83/18.07 Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 17.83/18.07 Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 20.53/20.76 Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 20.53/20.76 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 20.53/20.76 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 20.53/20.76 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 20.53/20.76 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 20.53/20.76 Found eq_ref00:=(eq_ref0 (x0 X)):(((eq fofType) (x0 X)) (x0 X))
% 20.53/20.76 Found (eq_ref0 (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 20.53/20.76 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 20.53/20.76 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 20.53/20.76 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 20.53/20.76 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 20.53/20.76 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 20.53/20.76 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 20.53/20.76 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (forall (X:fofType), ((r X) (x3 X))))
% 20.53/20.76 Found (fun (x3:(fofType->fofType))=> ((eq_ref Prop) (f x3))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 20.53/20.76 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 20.53/20.76 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 20.53/20.76 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 20.53/20.76 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 20.53/20.76 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 20.53/20.76 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 20.53/20.76 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 20.53/20.76 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 22.56/22.78 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 22.56/22.78 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 22.56/22.78 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 22.56/22.78 Found x0 as proof of (P b)
% 22.56/22.78 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) (fun (x:fofType)=> ((r x3) x)))
% 22.56/22.78 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 22.56/22.78 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 22.56/22.78 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 22.56/22.78 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 22.56/22.78 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 22.56/22.78 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 22.56/22.78 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 22.56/22.78 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 22.56/22.78 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 22.56/22.78 Found x0 as proof of (P f)
% 22.56/22.78 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 22.56/22.78 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 22.56/22.78 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 22.56/22.78 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 22.56/22.78 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 22.56/22.78 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 22.56/22.78 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 22.56/22.78 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 22.56/22.78 Found x0 as proof of (P f)
% 24.14/24.32 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 24.14/24.32 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 24.14/24.32 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 24.14/24.32 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 24.14/24.32 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 24.14/24.32 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 24.14/24.32 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 24.14/24.32 Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% 24.14/24.32 Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 24.14/24.32 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 24.14/24.32 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 24.14/24.32 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 24.14/24.32 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 24.14/24.32 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 24.14/24.32 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 24.14/24.32 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 24.14/24.32 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 24.14/24.32 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 24.14/24.32 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 24.14/24.32 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 24.14/24.32 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 24.14/24.32 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 24.14/24.32 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 24.14/24.32 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 24.14/24.32 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 24.14/24.32 Found x1 as proof of (P b)
% 24.14/24.32 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 24.14/24.32 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 24.14/24.32 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 24.14/24.32 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 24.14/24.32 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 26.35/26.59 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 26.35/26.59 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 26.35/26.59 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 26.35/26.59 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 26.35/26.59 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 26.35/26.59 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 26.35/26.59 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 26.35/26.59 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 26.35/26.59 Found x0 as proof of (P b)
% 26.35/26.59 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) (fun (x:fofType)=> ((r x3) x)))
% 26.35/26.59 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 26.35/26.59 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 26.35/26.59 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 26.35/26.59 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 26.35/26.59 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 26.35/26.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 26.35/26.59 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 26.35/26.59 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 26.35/26.59 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 26.35/26.59 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 26.35/26.59 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 26.35/26.59 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 26.35/26.59 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 26.35/26.59 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 26.35/26.59 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 26.35/26.59 Found x1 as proof of (P f)
% 26.35/26.59 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 26.35/26.59 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 26.35/26.59 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 26.35/26.59 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 26.35/26.59 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 26.35/26.59 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 26.35/26.59 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 26.35/26.59 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 26.35/26.59 Found x1 as proof of (P f)
% 26.35/26.59 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 26.35/26.59 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 28.17/28.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 28.17/28.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 28.17/28.39 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 28.17/28.39 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 28.17/28.39 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 28.17/28.39 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 28.17/28.39 Found x0 as proof of (P f)
% 28.17/28.39 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 28.17/28.39 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 28.17/28.39 Found x0 as proof of (P f)
% 28.17/28.39 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 28.17/28.39 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 28.17/28.39 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 28.17/28.39 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x3) x4))
% 28.17/28.39 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 28.17/28.39 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 28.17/28.39 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 28.17/28.39 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 28.17/28.39 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 28.17/28.39 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 28.17/28.39 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 28.17/28.39 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 28.17/28.39 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 28.17/28.39 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 28.17/28.39 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 28.17/28.39 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 28.17/28.39 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 28.17/28.39 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 28.17/28.39 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 28.17/28.39 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 28.17/28.39 Found x1 as proof of (P b)
% 28.17/28.39 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 28.17/28.39 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 28.17/28.39 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 28.17/28.39 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 28.17/28.39 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 28.17/28.39 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 32.84/33.08 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 32.84/33.08 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 32.84/33.08 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 32.84/33.08 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 32.84/33.08 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 32.84/33.08 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 32.84/33.08 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 32.84/33.08 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 32.84/33.08 Found x1 as proof of (P f)
% 32.84/33.08 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 32.84/33.08 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 32.84/33.08 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 32.84/33.08 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 32.84/33.08 Found x1 as proof of (P f)
% 32.84/33.08 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 32.84/33.08 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((r x0) x4))
% 32.84/33.08 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 32.84/33.08 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 32.84/33.08 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found x2:(P x1)
% 32.84/33.08 Instantiate: x1:=x':fofType
% 32.84/33.08 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 32.84/33.08 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found x2:(P x1)
% 32.84/33.08 Instantiate: x1:=x':fofType
% 32.84/33.08 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 32.84/33.08 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 32.84/33.08 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 32.84/33.08 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 32.84/33.08 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 34.56/34.79 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 34.56/34.79 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 34.56/34.79 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 34.56/34.79 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 34.56/34.79 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 34.56/34.79 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 34.56/34.79 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 34.56/34.79 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 34.56/34.79 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 34.56/34.79 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 34.56/34.79 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 34.56/34.79 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 34.56/34.79 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 34.56/34.79 Found x0 as proof of (P b)
% 34.56/34.79 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 34.56/34.79 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 34.56/34.79 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 36.74/36.93 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 36.74/36.93 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 36.74/36.93 Found x0 as proof of (P b)
% 36.74/36.93 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 36.74/36.93 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 36.74/36.93 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 36.74/36.93 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 36.74/36.93 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 36.74/36.93 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 36.74/36.93 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 36.74/36.93 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 36.74/36.93 Found x0 as proof of (P f)
% 36.74/36.93 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 36.74/36.93 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 36.74/36.93 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 36.74/36.93 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 36.74/36.93 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 36.74/36.93 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 36.74/36.93 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 36.74/36.93 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 36.74/36.93 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 36.74/36.93 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 36.74/36.93 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 36.74/36.93 Found x0 as proof of (P f)
% 36.74/36.93 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 36.74/36.93 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 36.74/36.93 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 36.74/36.93 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 38.16/38.36 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 38.16/38.36 Found x0 as proof of (P f)
% 38.16/38.36 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 38.16/38.36 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 38.16/38.36 Found x2:(P x1)
% 38.16/38.36 Instantiate: x1:=x':fofType
% 38.16/38.36 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 38.16/38.36 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 38.16/38.36 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 38.16/38.36 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 38.16/38.36 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 38.16/38.36 Found x0 as proof of (P f)
% 38.16/38.36 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 38.16/38.36 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 38.16/38.36 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 38.16/38.36 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 38.16/38.36 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 38.16/38.36 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 38.16/38.36 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 38.16/38.36 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 38.16/38.36 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 38.16/38.36 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 38.16/38.36 Found x2:(P x1)
% 38.16/38.36 Instantiate: x1:=x':fofType
% 38.16/38.36 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 38.16/38.36 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 38.16/38.36 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 38.16/38.36 Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 38.16/38.36 Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% 38.16/38.36 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 38.16/38.36 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 38.16/38.36 Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 38.16/38.36 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 38.16/38.36 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 38.16/38.36 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 38.16/38.36 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 38.16/38.36 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 38.16/38.36 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 39.37/39.60 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 39.37/39.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 39.37/39.60 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 39.37/39.60 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 39.37/39.60 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 39.37/39.60 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 39.37/39.60 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 39.37/39.60 Found x1 as proof of (P b)
% 39.37/39.60 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 39.37/39.60 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 39.37/39.60 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 39.37/39.60 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 39.37/39.60 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 39.37/39.60 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 39.37/39.60 Found x1 as proof of (P b)
% 39.37/39.60 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 42.26/42.44 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 42.26/42.44 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 42.26/42.44 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 42.26/42.44 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 42.26/42.44 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 42.26/42.44 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 42.26/42.44 Found x0 as proof of (P b)
% 42.26/42.44 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 42.26/42.44 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 42.26/42.44 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 42.26/42.44 Found x0 as proof of (P b)
% 42.26/42.44 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 42.26/42.44 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x3) y)))) b)
% 42.26/42.44 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 42.26/42.44 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 42.26/42.44 Found x1 as proof of (P f)
% 42.26/42.44 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 42.26/42.44 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 42.26/42.44 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 42.26/42.44 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 42.26/42.44 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 44.05/44.29 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 44.05/44.29 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 44.05/44.29 Found x1 as proof of (P f)
% 44.05/44.29 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 44.05/44.29 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 44.05/44.29 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 44.05/44.29 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 44.05/44.29 Found x1 as proof of (P f)
% 44.05/44.29 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 44.05/44.29 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 44.05/44.29 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 44.05/44.29 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 44.05/44.29 Found x1 as proof of (P f)
% 44.05/44.29 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 44.05/44.29 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 44.05/44.29 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 44.05/44.29 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 44.05/44.29 Found x0 as proof of (P f)
% 44.05/44.29 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 44.05/44.29 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 44.05/44.29 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 44.05/44.29 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 44.05/44.29 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 46.30/46.48 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 46.30/46.48 Found x0 as proof of (P f)
% 46.30/46.48 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 46.30/46.48 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 46.30/46.48 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 46.30/46.48 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 46.30/46.48 Found x0 as proof of (P f)
% 46.30/46.48 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 46.30/46.48 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 46.30/46.48 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 46.30/46.48 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 46.30/46.48 Found x0 as proof of (P f)
% 46.30/46.48 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 46.30/46.48 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x4))
% 46.30/46.48 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x3) y))) x)))
% 46.30/46.48 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 46.30/46.48 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 46.30/46.48 Found x1 as proof of (P b)
% 46.30/46.48 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 46.30/46.48 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 46.30/46.48 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 46.30/46.48 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 46.30/46.48 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 46.30/46.48 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 50.15/50.33 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 50.15/50.33 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 50.15/50.33 Found x1 as proof of (P b)
% 50.15/50.33 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 50.15/50.33 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 50.15/50.33 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 50.15/50.33 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 50.15/50.33 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 50.15/50.33 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 50.15/50.33 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 50.15/50.33 Found x1 as proof of (P f)
% 50.15/50.33 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 50.15/50.33 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 50.15/50.33 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 50.15/50.33 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 50.15/50.33 Found x1 as proof of (P f)
% 50.15/50.33 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 50.15/50.33 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 50.15/50.33 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 50.15/50.33 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 50.15/50.33 Found x1 as proof of (P f)
% 50.15/50.33 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 50.15/50.33 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 50.15/50.33 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 50.15/50.33 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 80.41/80.65 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 80.41/80.65 Found x1 as proof of (P f)
% 80.41/80.65 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 80.41/80.65 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 80.41/80.65 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 80.41/80.65 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 80.41/80.65 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x4))
% 80.41/80.65 Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 80.41/80.65 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 80.41/80.65 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 80.41/80.65 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 80.41/80.65 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 80.41/80.65 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 80.41/80.65 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 80.41/80.65 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 80.41/80.65 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 80.41/80.65 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 93.60/93.80 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 93.60/93.80 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 93.60/93.80 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 93.60/93.80 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 93.60/93.80 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 93.60/93.80 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 93.60/93.80 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 93.60/93.80 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 93.60/93.80 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 93.60/93.80 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 93.60/93.80 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 93.60/93.80 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 93.60/93.80 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 93.60/93.80 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 93.60/93.80 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found x5:(P x4)
% 93.60/93.80 Instantiate: x4:=x':fofType
% 93.60/93.80 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 93.60/93.80 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (fun (x00:((r x3) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 93.60/93.80 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 93.60/93.80 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 93.60/93.80 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 93.60/93.80 Found x5:(P x4)
% 93.60/93.80 Instantiate: x4:=x':fofType
% 93.60/93.80 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 93.60/93.80 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 96.81/97.04 Found (fun (x00:((r x3) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 96.81/97.04 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 96.81/97.04 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 96.81/97.04 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 96.81/97.04 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 96.81/97.04 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 96.81/97.04 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 96.81/97.04 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 96.81/97.04 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 96.81/97.04 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 96.81/97.04 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 96.81/97.04 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 96.81/97.04 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 96.81/97.04 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 96.81/97.04 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 96.81/97.04 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 96.81/97.04 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 96.81/97.04 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 96.81/97.04 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 96.81/97.04 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 96.81/97.04 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 96.81/97.04 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 96.81/97.04 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 96.81/97.04 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 96.81/97.04 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 96.81/97.04 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 96.81/97.04 Found x30:=(x3 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 98.52/98.76 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found x5:(P x4)
% 98.52/98.76 Instantiate: x4:=x':fofType
% 98.52/98.76 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 98.52/98.76 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 98.52/98.76 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found x5:(P x4)
% 98.52/98.76 Instantiate: x4:=x':fofType
% 98.52/98.76 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 98.52/98.76 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 98.52/98.76 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found x30:=(x3 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 98.52/98.76 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 98.52/98.76 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 98.52/98.76 Found (eq_ref0 x4) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 98.52/98.76 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 98.52/98.76 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 98.52/98.76 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 98.52/98.76 Found x5:(P x4)
% 98.52/98.76 Instantiate: x4:=x':fofType
% 98.52/98.76 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 98.52/98.76 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x3) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found x5:(P x4)
% 98.52/98.76 Instantiate: x4:=x':fofType
% 98.52/98.76 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 98.52/98.76 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (fun (x00:((r x3) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 98.52/98.76 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 98.52/98.76 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 98.52/98.76 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 99.52/99.81 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 99.52/99.81 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 99.52/99.81 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 99.52/99.81 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 99.52/99.81 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 99.52/99.81 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 99.52/99.81 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 99.52/99.81 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 99.52/99.81 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 99.52/99.81 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 99.52/99.81 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 99.52/99.81 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 99.52/99.81 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 99.52/99.81 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 99.52/99.81 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 99.52/99.81 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 99.52/99.81 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 99.52/99.81 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 99.52/99.81 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 99.52/99.81 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 99.52/99.81 Found x5:(P x1)
% 99.52/99.81 Instantiate: x1:=x':fofType
% 99.52/99.81 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 99.52/99.81 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 99.52/99.81 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found x5:(P x1)
% 101.41/101.65 Instantiate: x1:=x':fofType
% 101.41/101.65 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 101.41/101.65 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 101.41/101.65 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found x5:(P x1)
% 101.41/101.65 Instantiate: x1:=x':fofType
% 101.41/101.65 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 101.41/101.65 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 101.41/101.65 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 101.41/101.65 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found x5:(P x1)
% 101.41/101.65 Instantiate: x1:=x':fofType
% 101.41/101.65 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 101.41/101.65 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 101.41/101.65 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 101.41/101.65 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 101.41/101.65 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 101.41/101.65 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 101.41/101.65 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 101.41/101.65 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 101.41/101.65 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 104.48/104.68 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found x5:(P x4)
% 104.48/104.68 Instantiate: x4:=x':fofType
% 104.48/104.68 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 104.48/104.68 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 104.48/104.68 Found x5:(P x4)
% 104.48/104.68 Instantiate: x4:=x':fofType
% 104.48/104.68 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 104.48/104.68 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 104.48/104.68 Found x30:=(x3 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 104.48/104.68 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 104.48/104.68 Found x30:=(x3 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 104.48/104.68 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (x3 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x3 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 104.48/104.68 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 104.48/104.68 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 104.48/104.68 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 104.48/104.68 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 104.48/104.68 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 104.48/104.68 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 104.48/104.68 Found (eq_ref0 x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 104.48/104.68 Found (eq_ref0 x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 104.48/104.68 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found x5:(P x1)
% 104.48/104.68 Instantiate: x1:=x':fofType
% 104.48/104.68 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 104.48/104.68 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 104.48/104.68 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 104.48/104.68 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 104.48/104.68 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found x5:(P x1)
% 105.19/105.46 Instantiate: x1:=x':fofType
% 105.19/105.46 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 105.19/105.46 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 105.19/105.46 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 105.19/105.46 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 105.19/105.46 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 105.19/105.46 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found x5:(P x1)
% 105.19/105.46 Instantiate: x1:=x':fofType
% 105.19/105.46 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 105.19/105.46 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 105.19/105.46 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 105.19/105.46 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found x5:(P x1)
% 105.19/105.46 Instantiate: x1:=x':fofType
% 105.19/105.46 Found (fun (x5:(P x1))=> x5) as proof of (P x')
% 105.19/105.46 Found (fun (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x5:(P x1))=> x5) as proof of (((eq fofType) x1) x')
% 105.19/105.46 Found x40:=(x4 (fun (x5:(fofType->Prop))=> (P x1))):((P x1)->(P x1))
% 105.19/105.46 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 105.19/105.46 Found (x4 (fun (x5:(fofType->Prop))=> (P x1))) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (x4 (fun (x5:(fofType->Prop))=> (P x1)))) as proof of (((eq fofType) x1) x')
% 110.56/110.85 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 110.56/110.85 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 110.56/110.85 Found x2:(P x1)
% 110.56/110.85 Instantiate: x1:=x':fofType
% 110.56/110.85 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 110.56/110.85 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 110.56/110.85 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 110.56/110.85 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 110.56/110.85 Found x2:(P x1)
% 110.56/110.85 Instantiate: x1:=x':fofType
% 110.56/110.85 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 110.56/110.85 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 110.56/110.85 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 110.56/110.85 Found (eq_ref0 x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 110.56/110.85 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 110.56/110.85 Found (eq_ref0 x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 110.56/110.85 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 110.56/110.85 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 110.56/110.85 Found (eq_ref00 P) as proof of (P0 x1)
% 110.56/110.85 Found ((eq_ref0 x1) P) as proof of (P0 x1)
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 110.56/110.85 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 110.56/110.85 Found (eq_ref00 P) as proof of (P0 x1)
% 110.56/110.85 Found ((eq_ref0 x1) P) as proof of (P0 x1)
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 110.56/110.85 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 110.56/110.85 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 110.56/110.85 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 110.56/110.85 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.56/110.85 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.56/110.85 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.56/110.85 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.56/110.85 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of (((eq fofType) x1) x')
% 110.68/110.90 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 110.68/110.90 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found ((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found ((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found ((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 110.68/110.90 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 110.68/110.90 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 110.68/110.90 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P x'))
% 110.68/110.90 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of (((eq fofType) x1) x')
% 114.68/114.95 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 114.68/114.95 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 114.68/114.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 114.68/114.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 114.68/114.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 114.68/114.95 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found ((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found ((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found ((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 114.68/114.95 Found x2:(P x1)
% 114.68/114.95 Instantiate: x1:=x':fofType
% 114.68/114.95 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 114.68/114.95 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 114.68/114.95 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 114.68/114.95 Found x2:(P x1)
% 114.68/114.95 Instantiate: x1:=x':fofType
% 114.68/114.95 Found (fun (x2:(P x1))=> x2) as proof of (P x')
% 114.68/114.95 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 114.68/114.95 Found (fun (x00:((r x0) x')) (P:(fofType->Prop)) (x2:(P x1))=> x2) as proof of (((eq fofType) x1) x')
% 114.68/114.95 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 114.68/114.95 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 114.68/114.95 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 114.68/114.95 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 114.68/114.95 Found (eq_ref00 P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found ((eq_ref0 x1) P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (((eq_ref fofType) x1) P) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 114.68/114.95 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 114.68/114.95 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x1) P)) as proof of (((eq fofType) x1) x')
% 114.68/114.95 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 114.68/114.95 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 114.68/114.95 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 114.68/114.95 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 114.68/114.95 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 114.68/114.95 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 114.68/114.95 Found (eq_ref0 b) as proof of (((eq fofType) b) x')
% 114.68/114.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 114.68/114.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 114.68/114.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 114.68/114.95 Found ((eq_trans0000 ((eq_ref fofType) x1)) ((eq_ref fofType) b)) as proof of (((eq fofType) x1) x')
% 114.68/114.95 Found (((eq_trans000 x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((((fun (b:fofType)=> ((eq_trans00 b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (fun (x00:((r x0) x'))=> ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 114.90/115.11 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 114.90/115.11 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 114.90/115.11 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 114.90/115.11 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 114.90/115.11 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 114.90/115.11 Found (eq_ref0 b) as proof of (((eq fofType) b) x')
% 114.90/115.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 114.90/115.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 114.90/115.11 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 114.90/115.11 Found ((eq_trans0000 ((eq_ref fofType) x1)) ((eq_ref fofType) b)) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (((eq_trans000 x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((((fun (b:fofType)=> ((eq_trans00 b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (fun (x00:((r x0) x'))=> ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 114.90/115.11 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (fun (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1)) as proof of ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))->(((eq fofType) x1) x'))
% 114.90/115.11 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1)) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(((eq fofType) x1) x')))
% 114.90/115.11 Found (ex_ind00 (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((ex_ind0 (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (((fun (P:Prop) (x3:(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->P)))=> (((((ex_ind fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))) P) x3) x2)) (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 114.90/115.11 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (fun (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 114.90/115.11 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1)) as proof of ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))->(((eq fofType) x1) x'))
% 117.39/117.63 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1)) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(((eq fofType) x1) x')))
% 117.39/117.63 Found (ex_ind00 (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 117.39/117.63 Found ((ex_ind0 (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 117.39/117.63 Found (((fun (P:Prop) (x3:(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->P)))=> (((((ex_ind fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))) P) x3) x2)) (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 117.39/117.63 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 117.39/117.63 Found (eq_ref00 P) as proof of (P0 x1)
% 117.39/117.63 Found ((eq_ref0 x1) P) as proof of (P0 x1)
% 117.39/117.63 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 117.39/117.63 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 117.39/117.63 Found eq_ref000:=(eq_ref00 P):((P x1)->(P x1))
% 117.39/117.63 Found (eq_ref00 P) as proof of (P0 x1)
% 117.39/117.63 Found ((eq_ref0 x1) P) as proof of (P0 x1)
% 117.39/117.63 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 117.39/117.63 Found (((eq_ref fofType) x1) P) as proof of (P0 x1)
% 117.39/117.63 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 117.39/117.63 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found (((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found (((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found (((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of (((eq fofType) x1) x')
% 117.39/117.63 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 117.39/117.63 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 117.39/117.63 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found ((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found ((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 117.39/117.63 Found ((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 118.18/118.40 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 118.18/118.40 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found ((eq_sym0000 ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P)) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) (fun (x4:fofType)=> ((P x1)->(P x4))))) ((eq_ref fofType) x')) (((eq_ref fofType) x1) P))) as proof of (((eq fofType) x1) x')
% 118.18/118.40 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 118.18/118.40 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 118.18/118.40 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (eq_sym0000 ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found ((fun (x2:(((eq fofType) x') x1))=> ((eq_sym000 x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found ((fun (x2:(((eq fofType) x') x1))=> (((eq_sym00 x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found ((fun (x2:(((eq fofType) x') x1))=> ((((eq_sym0 x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x')) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of ((P x1)->(P x'))
% 118.18/118.40 Found (fun (x00:((r x0) x')) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) x') x1))=> (((((eq_sym fofType) x') x1) x2) P)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 118.18/118.40 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 118.18/118.40 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 118.18/118.40 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 118.18/118.40 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 118.18/118.40 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 118.18/118.40 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 118.18/118.40 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 122.56/122.78 Found (fun (x00:((r x3) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 122.56/122.78 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 122.56/122.78 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 122.56/122.78 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 122.56/122.78 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 122.56/122.78 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 122.56/122.78 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 122.56/122.78 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 122.56/122.78 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 122.56/122.78 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 122.56/122.78 Found (fun (x00:((r x3) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 122.56/122.78 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 122.56/122.78 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 122.56/122.78 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 122.56/122.78 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 122.56/122.78 Found (eq_ref0 b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_trans0000 ((eq_ref fofType) x1)) ((eq_ref fofType) b)) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found (((eq_trans000 x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found ((((fun (b:fofType)=> ((eq_trans00 b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found (fun (x00:((r x0) x'))=> ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 122.56/122.78 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 122.56/122.78 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 122.56/122.78 Found (eq_ref0 b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x')
% 122.56/122.78 Found ((eq_trans0000 ((eq_ref fofType) x1)) ((eq_ref fofType) b)) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found (((eq_trans000 x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found ((((fun (b:fofType)=> ((eq_trans00 b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found ((((fun (b:fofType)=> (((eq_trans0 x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found (fun (x00:((r x0) x'))=> ((((fun (b:fofType)=> ((((eq_trans fofType) x1) b) x')) x') ((eq_ref fofType) x1)) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 122.56/122.78 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 122.56/122.78 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 124.69/124.95 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 124.69/124.95 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found (fun (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1)) as proof of ((((eq (fofType->Prop)) (r X)) ((eq fofType) x3))->(((eq fofType) x1) x'))
% 124.69/124.95 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1)) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->(((eq fofType) x1) x')))
% 124.69/124.95 Found (ex_ind00 (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found ((ex_ind0 (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found (((fun (P:Prop) (x3:(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->P)))=> (((((ex_ind fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y)))) P) x3) x2)) (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 124.69/124.95 Found (eq_ref0 x1) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found (fun (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1)) as proof of ((((eq (fofType->Prop)) (r X)) ((eq fofType) x3))->(((eq fofType) x1) x'))
% 124.69/124.95 Found (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1)) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->(((eq fofType) x1) x')))
% 124.69/124.95 Found (ex_ind00 (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found ((ex_ind0 (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found (((fun (P:Prop) (x3:(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->P)))=> (((((ex_ind fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y)))) P) x3) x2)) (((eq fofType) x1) x')) (fun (x3:fofType) (x4:(((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))=> ((eq_ref fofType) x1))) as proof of (((eq fofType) x1) x')
% 124.69/124.95 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 124.69/124.95 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 124.69/124.95 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 124.69/124.95 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 124.69/124.95 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 124.69/124.95 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 124.69/124.95 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 124.69/124.95 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 124.69/124.95 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 124.69/124.95 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found eq_ref00:=(eq_ref0 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 129.47/129.77 Found (eq_ref0 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 129.47/129.77 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 129.47/129.77 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 129.47/129.77 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 129.47/129.77 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 129.47/129.77 Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 129.47/129.77 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 129.47/129.77 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 129.47/129.77 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 129.47/129.77 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 129.47/129.77 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 129.47/129.77 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 129.47/129.77 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 129.47/129.77 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found (fun (x00:((r x3) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 129.47/129.77 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 129.47/129.77 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found (fun (x00:((r x3) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 129.47/129.77 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 129.47/129.77 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 132.49/132.75 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 132.49/132.75 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 132.49/132.75 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 132.49/132.75 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 132.49/132.75 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 132.49/132.75 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 132.49/132.75 Found eta_expansion000:=(eta_expansion00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (x:(fofType->fofType))=> (forall (X:fofType), ((r X) (x X)))))
% 132.49/132.75 Found (eta_expansion00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 132.49/132.75 Found ((eta_expansion0 Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 132.49/132.75 Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 132.49/132.75 Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b0)
% 137.68/137.93 Found eq_ref00:=(eq_ref0 f):(((eq ((fofType->fofType)->Prop)) f) f)
% 137.68/137.93 Found (eq_ref0 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->fofType)->Prop)) f) (fun (x:(fofType->fofType))=> (f x)))
% 137.68/137.93 Found (eta_expansion00 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 137.68/137.93 Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 137.68/137.93 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) b0)
% 137.68/137.93 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 137.68/137.93 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 137.68/137.93 Found (eq_ref0 x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x4)
% 137.68/137.93 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found ((eq_sym00 x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found (((eq_sym0 x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found ((((eq_sym fofType) x') x4) ((eq_ref fofType) x')) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x4) ((eq_ref fofType) x'))) as proof of (((eq fofType) x4) x')
% 137.68/137.93 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->fofType)->Prop)) f) (fun (x:(fofType->fofType))=> (f x)))
% 137.68/137.93 Found (eta_expansion00 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 137.68/137.93 Found eq_ref00:=(eq_ref0 f):(((eq ((fofType->fofType)->Prop)) f) f)
% 141.96/142.21 Found (eq_ref0 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 141.96/142.21 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->fofType)->Prop)) a) a)
% 141.96/142.21 Found (eq_ref0 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 141.96/142.21 Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->fofType)->Prop)) b) b)
% 141.96/142.21 Found (eq_ref0 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 141.96/142.21 Found ((eq_ref ((fofType->fofType)->Prop)) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 141.96/142.21 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 141.96/142.21 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 141.96/142.21 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 141.96/142.21 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 141.96/142.21 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 141.96/142.21 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 141.96/142.21 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 141.96/142.21 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 141.96/142.21 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 141.96/142.21 Found eta_expansion000:=(eta_expansion00 f):(((eq ((fofType->fofType)->Prop)) f) (fun (x:(fofType->fofType))=> (f x)))
% 141.96/142.21 Found (eta_expansion00 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found ((eta_expansion0 Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found (((eta_expansion (fofType->fofType)) Prop) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq ((fofType->fofType)->Prop)) f) (fun (x:(fofType->fofType))=> (f x)))
% 143.45/143.72 Found (eta_expansion_dep00 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 143.45/143.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 143.45/143.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 143.45/143.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 143.45/143.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 143.45/143.72 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 143.45/143.72 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 143.45/143.72 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 143.45/143.72 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 143.45/143.72 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 143.45/143.72 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 143.45/143.72 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 143.45/143.72 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 148.85/149.13 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 148.85/149.13 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 148.85/149.13 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 148.85/149.13 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 148.85/149.13 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 148.85/149.13 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 148.85/149.13 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 148.85/149.13 Found eq_ref00:=(eq_ref0 f):(((eq ((fofType->fofType)->Prop)) f) f)
% 148.85/149.13 Found (eq_ref0 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found ((eq_ref ((fofType->fofType)->Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq ((fofType->fofType)->Prop)) f) (fun (x:(fofType->fofType))=> (f x)))
% 148.85/149.13 Found (eta_expansion_dep00 f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found ((eta_expansion_dep0 (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found (((eta_expansion_dep (fofType->fofType)) (fun (x1:(fofType->fofType))=> Prop)) f) as proof of (((eq ((fofType->fofType)->Prop)) f) b)
% 148.85/149.13 Found eq_ref00:=(eq_ref0 a):(((eq ((fofType->fofType)->Prop)) a) a)
% 148.85/149.13 Found (eq_ref0 a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.85/149.13 Found ((eq_ref ((fofType->fofType)->Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.85/149.13 Found ((eq_ref ((fofType->fofType)->Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.85/149.13 Found ((eq_ref ((fofType->fofType)->Prop)) a) as proof of (((eq ((fofType->fofType)->Prop)) a) b)
% 148.85/149.13 Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->fofType)->Prop)) b) (fun (x:(fofType->fofType))=> (b x)))
% 148.85/149.13 Found (eta_expansion00 b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 148.85/149.13 Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 148.85/149.13 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 148.85/149.13 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 148.85/149.13 Found (((eta_expansion (fofType->fofType)) Prop) b) as proof of (((eq ((fofType->fofType)->Prop)) b) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 148.85/149.13 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 148.85/149.13 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 154.17/154.46 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 154.17/154.46 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 154.17/154.46 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 154.17/154.46 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 154.17/154.46 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 154.17/154.46 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (b x0))
% 154.17/154.46 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (b x)))
% 154.17/154.46 Found eq_ref00:=(eq_ref0 (x3 X0)):(((eq fofType) (x3 X0)) (x3 X0))
% 154.17/154.46 Found (eq_ref0 (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 154.17/154.46 Found ((eq_ref fofType) (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 154.17/154.46 Found ((eq_ref fofType) (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 154.17/154.46 Found ((eq_ref fofType) (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 154.17/154.46 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 154.17/154.46 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 154.17/154.46 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 154.17/154.46 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 154.17/154.46 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 154.17/154.46 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 X))
% 154.17/154.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 X))
% 154.17/154.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 X))
% 154.17/154.46 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 X))
% 154.17/154.46 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 154.17/154.46 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 154.17/154.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 154.17/154.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 154.17/154.46 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 154.17/154.46 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 154.17/154.46 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 154.17/154.46 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 154.17/154.46 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 154.17/154.46 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 154.17/154.46 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 154.17/154.46 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 154.17/154.46 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 154.17/154.46 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 154.17/154.46 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 161.27/161.54 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 161.27/161.54 Found eq_ref00:=(eq_ref0 x'):(((eq fofType) x') x')
% 161.27/161.54 Found (eq_ref0 x') as proof of (((eq fofType) x') x1)
% 161.27/161.54 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 161.27/161.54 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 161.27/161.54 Found ((eq_ref fofType) x') as proof of (((eq fofType) x') x1)
% 161.27/161.54 Found (eq_sym000 ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 161.27/161.54 Found ((eq_sym00 x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 161.27/161.54 Found (((eq_sym0 x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 161.27/161.54 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 161.27/161.54 Found ((((eq_sym fofType) x') x1) ((eq_ref fofType) x')) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 161.27/161.54 Found (fun (x00:((r x0) x'))=> ((((eq_sym fofType) x') x1) ((eq_ref fofType) x'))) as proof of (((eq fofType) x1) x')
% 161.27/161.54 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 161.27/161.54 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 161.27/161.54 Found x0 as proof of (P a)
% 161.27/161.54 Found x2:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x1) Z)))
% 161.27/161.54 Instantiate: a:=(r X):(fofType->Prop);b:=(fun (Z:fofType)=> (((eq fofType) x1) Z)):(fofType->Prop)
% 161.27/161.54 Found x2 as proof of (((eq (fofType->Prop)) a) b)
% 161.27/161.54 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 161.27/161.54 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) b0)
% 161.27/161.54 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 161.27/161.54 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 161.27/161.54 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 161.27/161.54 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 161.27/161.54 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 161.27/161.54 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 161.27/161.54 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 161.27/161.54 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 161.27/161.54 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 161.27/161.54 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 161.27/161.54 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 161.27/161.54 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 161.27/161.54 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 161.27/161.54 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 161.27/161.54 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 161.27/161.54 Found eq_ref00:=(eq_ref0 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X)))))
% 161.27/161.54 Found (eq_ref0 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 161.27/161.54 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 161.27/161.54 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 168.95/169.23 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 168.95/169.23 Found eq_ref00:=(eq_ref0 (x0 X)):(((eq fofType) (x0 X)) (x0 X))
% 168.95/169.23 Found (eq_ref0 (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 168.95/169.23 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 168.95/169.23 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 168.95/169.23 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 168.95/169.23 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 168.95/169.23 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 168.95/169.23 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 168.95/169.23 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 168.95/169.23 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 168.95/169.23 Found (eq_ref0 b) as proof of (((eq fofType) b) (x0 X))
% 168.95/169.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 X))
% 168.95/169.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 X))
% 168.95/169.23 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (x0 X))
% 168.95/169.23 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 168.95/169.23 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 168.95/169.23 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 168.95/169.23 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 168.95/169.23 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 168.95/169.23 Found eq_ref00:=(eq_ref0 (x3 X0)):(((eq fofType) (x3 X0)) (x3 X0))
% 168.95/169.23 Found (eq_ref0 (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 168.95/169.23 Found ((eq_ref fofType) (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 168.95/169.23 Found ((eq_ref fofType) (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 168.95/169.23 Found ((eq_ref fofType) (x3 X0)) as proof of (((eq fofType) (x3 X0)) b)
% 168.95/169.23 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 168.95/169.23 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 168.95/169.23 Found eta_expansion000:=(eta_expansion00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 168.95/169.23 Found (eta_expansion00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 168.95/169.23 Found ((eta_expansion0 Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 168.95/169.23 Found (((eta_expansion fofType) Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 168.95/169.23 Found (((eta_expansion fofType) Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 168.95/169.23 Found (((eta_expansion fofType) Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 168.95/169.23 Found x3:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x2) Z)))
% 168.95/169.23 Instantiate: a:=(r X):(fofType->Prop);b:=(fun (Z:fofType)=> (((eq fofType) x2) Z)):(fofType->Prop)
% 168.95/169.23 Found x3 as proof of (((eq (fofType->Prop)) a) b)
% 168.95/169.23 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 168.95/169.23 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 168.95/169.23 Found x1 as proof of (P a)
% 168.95/169.23 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 168.95/169.23 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 168.95/169.23 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 168.95/169.23 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 174.68/174.96 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 174.68/174.96 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 174.68/174.96 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 174.68/174.96 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 174.68/174.96 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) b0)
% 174.68/174.96 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 174.68/174.96 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 174.68/174.96 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 174.68/174.96 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 174.68/174.96 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 174.68/174.96 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 174.68/174.96 Found x0 as proof of (P a)
% 174.68/174.96 Found x2:(((eq (fofType->Prop)) (r X)) ((eq fofType) x1))
% 174.68/174.96 Instantiate: a:=(r X):(fofType->Prop);b:=((eq fofType) x1):(fofType->Prop)
% 174.68/174.96 Found x2 as proof of (((eq (fofType->Prop)) a) b)
% 174.68/174.96 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 174.68/174.96 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 174.68/174.96 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 174.68/174.96 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x3) y)))
% 174.68/174.96 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 174.68/174.96 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 174.68/174.96 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 177.31/177.63 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 177.31/177.63 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 177.31/177.63 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 177.31/177.63 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 177.31/177.63 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 177.31/177.63 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 177.31/177.63 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 177.31/177.63 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 177.31/177.63 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 177.31/177.63 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found eq_ref00:=(eq_ref0 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (y:fofType)=> ((r x0) y)))
% 177.31/177.63 Found (eq_ref0 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 177.31/177.63 Found eq_ref00:=(eq_ref0 (x0 X)):(((eq fofType) (x0 X)) (x0 X))
% 179.95/180.27 Found (eq_ref0 (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 179.95/180.27 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 179.95/180.27 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 179.95/180.27 Found ((eq_ref fofType) (x0 X)) as proof of (((eq fofType) (x0 X)) b)
% 179.95/180.27 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))):(((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) (fun (x:(fofType->fofType))=> (forall (X:fofType), ((r X) (x X)))))
% 179.95/180.27 Found (eta_expansion_dep00 (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 179.95/180.27 Found ((eta_expansion_dep0 (fun (x7:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 179.95/180.27 Found (((eta_expansion_dep (fofType->fofType)) (fun (x7:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 179.95/180.27 Found (((eta_expansion_dep (fofType->fofType)) (fun (x7:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 179.95/180.27 Found (((eta_expansion_dep (fofType->fofType)) (fun (x7:(fofType->fofType))=> Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (F:(fofType->fofType))=> (forall (X:fofType), ((r X) (F X))))) b)
% 179.95/180.27 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 179.95/180.27 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 179.95/180.27 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 179.95/180.27 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 179.95/180.27 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 179.95/180.27 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 179.95/180.27 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 179.95/180.27 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 179.95/180.27 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 179.95/180.27 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 179.95/180.27 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 186.24/186.58 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 186.24/186.58 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 186.24/186.58 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 186.24/186.58 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 186.24/186.58 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 186.24/186.58 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 186.24/186.58 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 186.24/186.58 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 186.24/186.58 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 186.24/186.58 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 186.24/186.58 Found eq_ref00:=(eq_ref0 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (y:fofType)=> ((r x0) y)))
% 186.24/186.58 Found (eq_ref0 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 186.24/186.58 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 186.24/186.58 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 186.24/186.58 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 186.24/186.58 Found x3:(((eq (fofType->Prop)) (r X)) ((eq fofType) x2))
% 186.24/186.58 Instantiate: a:=(r X):(fofType->Prop);b:=((eq fofType) x2):(fofType->Prop)
% 186.24/186.58 Found x3 as proof of (((eq (fofType->Prop)) a) b)
% 186.24/186.58 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 186.24/186.58 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 186.24/186.58 Found x1 as proof of (P a)
% 186.24/186.58 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 186.24/186.58 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 186.24/186.58 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 186.24/186.58 Found eq_ref00:=(eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))):(((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x'))))
% 187.87/188.17 Found (eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found eq_ref00:=(eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))):(((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x'))))
% 187.87/188.17 Found (eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 187.87/188.17 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 187.87/188.17 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 187.87/188.17 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 187.87/188.17 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 187.87/188.17 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 187.87/188.17 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 187.87/188.17 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 187.87/188.17 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 187.87/188.17 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 187.87/188.17 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 187.87/188.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 187.87/188.17 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 187.87/188.17 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 187.87/188.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 187.87/188.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 187.87/188.17 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 187.87/188.17 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 187.87/188.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 192.60/192.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 192.60/192.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 192.60/192.88 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 192.60/192.88 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 192.60/192.88 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 192.60/192.88 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 192.60/192.88 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 192.60/192.88 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 192.60/192.88 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 192.60/192.88 Found eq_ref00:=(eq_ref0 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (y:fofType)=> ((r x0) y)))
% 192.60/192.88 Found (eq_ref0 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 192.60/192.88 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 192.60/192.88 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 192.60/192.88 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 192.60/192.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 197.61/197.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 197.61/197.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 197.61/197.88 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 197.61/197.88 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (f x0))
% 197.61/197.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (f x0))
% 197.61/197.88 Found (fun (x0:(fofType->fofType))=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (f x)))
% 197.61/197.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 197.61/197.88 Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% 197.61/197.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 197.61/197.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 197.61/197.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 197.61/197.88 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 197.61/197.88 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 197.61/197.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.61/197.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.61/197.88 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 197.61/197.88 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 197.61/197.88 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 197.61/197.88 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 197.61/197.88 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 197.61/197.88 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 197.61/197.88 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 197.61/197.88 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 197.61/197.88 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 197.61/197.88 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 197.61/197.88 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 197.61/197.88 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 197.61/197.88 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 197.61/197.88 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 197.61/197.88 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 197.61/197.88 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 197.61/197.88 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 197.61/197.88 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 200.54/200.83 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 200.54/200.83 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 200.54/200.83 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 200.54/200.83 Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% 200.54/200.83 Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) (forall (X:fofType), ((r X) (x6 X))))
% 200.54/200.83 Found (fun (x6:(fofType->fofType))=> ((eq_ref Prop) (f x6))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f x)) (forall (X:fofType), ((r X) (x X)))))
% 200.54/200.83 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 200.54/200.83 Found (eq_ref0 a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 200.54/200.83 Found (eq_ref0 a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 200.54/200.83 Found (eq_ref0 x4) as proof of (((eq fofType) x4) b)
% 200.54/200.83 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 200.54/200.83 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 200.54/200.83 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 200.54/200.83 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 200.54/200.83 Found (eq_ref0 a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 200.54/200.83 Found eq_ref00:=(eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))):(((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x'))))
% 200.54/200.83 Found (eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 200.54/200.83 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 200.54/200.83 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 200.54/200.83 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 200.54/200.83 Found eq_ref00:=(eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))):(((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x'))))
% 200.54/200.83 Found (eq_ref0 (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 200.54/200.83 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 200.54/200.83 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 210.20/210.50 Found ((eq_ref Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) as proof of (((eq Prop) (forall (x':fofType), (((r x0) x')->(((eq fofType) x1) x')))) b)
% 210.20/210.50 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 210.20/210.50 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 210.20/210.50 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 210.20/210.50 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 210.20/210.50 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 210.20/210.50 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 210.20/210.50 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 210.20/210.50 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) ((r x0) x1))
% 210.20/210.50 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 210.20/210.50 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 210.20/210.50 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 210.20/210.50 Found x3 as proof of (P b)
% 210.20/210.50 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x6) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) (fun (x:fofType)=> ((r x6) x)))
% 210.20/210.50 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 210.20/210.50 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 210.20/210.50 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 210.20/210.50 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 210.20/210.50 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 210.20/210.50 Found x20:=(x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))):((P0 (fun (y:fofType)=> ((r x3) y)))->(P0 (fun (y:fofType)=> ((r x3) y))))
% 210.20/210.50 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 210.20/210.50 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 210.20/210.50 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 210.20/210.50 Found (eq_ref0 b) as proof of (((eq fofType) b) x1)
% 210.20/210.50 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 210.20/210.50 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 210.20/210.50 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x1)
% 213.83/214.12 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 213.83/214.12 Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% 213.83/214.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 213.83/214.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 213.83/214.12 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% 213.83/214.12 Found x2:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x1) Z)))
% 213.83/214.12 Instantiate: a:=(r X):(fofType->Prop);b:=(fun (Z:fofType)=> (((eq fofType) x1) Z)):(fofType->Prop)
% 213.83/214.12 Found x2 as proof of (((eq (fofType->Prop)) a) b)
% 213.83/214.12 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 213.83/214.12 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 213.83/214.12 Found x0 as proof of (P a)
% 213.83/214.12 Found x2:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x1) Z)))
% 213.83/214.12 Instantiate: a:=(r X):(fofType->Prop);b:=(fun (Z:fofType)=> (((eq fofType) x1) Z)):(fofType->Prop)
% 213.83/214.12 Found x2 as proof of (((eq (fofType->Prop)) a) b)
% 213.83/214.12 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 213.83/214.12 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 213.83/214.12 Found x0 as proof of (P a)
% 213.83/214.12 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 213.83/214.12 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 213.83/214.12 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% 213.83/214.12 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 213.83/214.12 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 213.83/214.12 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 213.83/214.12 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 213.83/214.12 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 213.83/214.12 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 213.83/214.12 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 213.83/214.12 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) ((r x0) x1))
% 213.83/214.12 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) ((r x0) x)))
% 217.12/217.44 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 217.12/217.44 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 217.12/217.44 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 217.12/217.44 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 217.12/217.44 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 217.12/217.44 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 217.12/217.44 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 217.12/217.44 Found x3 as proof of (P f)
% 217.12/217.44 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 217.12/217.44 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 217.12/217.44 Found x3 as proof of (P f)
% 217.12/217.44 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 217.12/217.44 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 217.12/217.44 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 217.12/217.44 Found (eq_ref0 x4) as proof of (((eq fofType) x4) b)
% 217.12/217.44 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 217.12/217.44 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 217.12/217.44 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 217.12/217.44 Found ex_intro00:=(ex_intro0 (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))):(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->((ex fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))))
% 217.12/217.44 Found (ex_intro0 (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 217.12/217.44 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 217.12/217.44 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 220.69/221.06 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 220.69/221.06 Found (ex_ind00 ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))) as proof of (P a)
% 220.69/221.06 Found ((ex_ind0 (P a)) ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))) as proof of (P a)
% 220.69/221.06 Found (((fun (P0:Prop) (x2:(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->P0)))=> (((((ex_ind fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))) P0) x2) x1)) (P a)) ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))) as proof of (P a)
% 220.69/221.06 Found ex_intro00:=(ex_intro0 (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))):(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->((ex fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))))
% 220.69/221.06 Found (ex_intro0 (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 220.69/221.06 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 220.69/221.06 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 220.69/221.06 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z))))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->(P a)))
% 220.69/221.06 Found (ex_ind00 ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))) as proof of (P a)
% 220.69/221.06 Found ((ex_ind0 (P a)) ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))) as proof of (P a)
% 220.69/221.06 Found (((fun (P0:Prop) (x2:(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x) Z)))->P0)))=> (((((ex_ind fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z))))) P0) x2) x1)) (P a)) ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x3) Z)))))) as proof of (P a)
% 220.69/221.06 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 220.69/221.06 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x6) x)))
% 220.69/221.06 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 220.69/221.06 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 220.69/221.06 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x6) x)))
% 220.69/221.06 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 224.31/224.62 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 224.31/224.62 Found x4 as proof of (P b)
% 224.31/224.62 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) (fun (x:fofType)=> ((r x3) x)))
% 224.31/224.62 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 224.31/224.62 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 224.31/224.62 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 224.31/224.62 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 224.31/224.62 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 224.31/224.62 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 224.31/224.62 Found (eq_ref0 a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 224.31/224.62 Found (eq_ref0 a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found eq_ref00:=(eq_ref0 (fun (y:fofType)=> ((r x3) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) (fun (y:fofType)=> ((r x3) y)))
% 224.31/224.62 Found (eq_ref0 (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 224.31/224.62 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 224.31/224.62 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 224.31/224.62 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 224.31/224.62 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 224.31/224.62 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 224.31/224.62 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 224.31/224.62 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 224.31/224.62 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 224.31/224.62 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 224.31/224.62 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 224.31/224.62 Found (eq_ref0 a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X0)
% 224.31/224.62 Found x30:=(x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))):((P0 (fun (y:fofType)=> ((r x0) y)))->(P0 (fun (y:fofType)=> ((r x0) y))))
% 224.31/224.62 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 224.31/224.62 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 224.31/224.62 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 224.31/224.62 Found (eq_ref0 x4) as proof of (((eq fofType) x4) b)
% 224.31/224.62 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 224.31/224.62 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 224.31/224.62 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 224.31/224.62 Found eta_expansion000:=(eta_expansion00 (r X)):(((eq (fofType->Prop)) (r X)) (fun (x:fofType)=> ((r X) x)))
% 224.31/224.62 Found (eta_expansion00 (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found ((eta_expansion0 Prop) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found (((eta_expansion fofType) Prop) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found (((eta_expansion fofType) Prop) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found (((eta_expansion fofType) Prop) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found (x30 (((eta_expansion fofType) Prop) (r X))) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found ((x3 (fun (x5:(fofType->Prop))=> (((eq (fofType->Prop)) x5) (fun (y:fofType)=> ((r x0) y))))) (((eta_expansion fofType) Prop) (r X))) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found ((x3 (fun (x5:(fofType->Prop))=> (((eq (fofType->Prop)) x5) (fun (y:fofType)=> ((r x0) y))))) (((eta_expansion fofType) Prop) (r X))) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 230.01/230.42 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 230.01/230.42 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 230.01/230.42 Found x1 as proof of (P a)
% 230.01/230.42 Found x3:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x2) Z)))
% 230.01/230.42 Instantiate: a:=(r X):(fofType->Prop);b:=(fun (Z:fofType)=> (((eq fofType) x2) Z)):(fofType->Prop)
% 230.01/230.42 Found x3 as proof of (((eq (fofType->Prop)) a) b)
% 230.01/230.42 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 230.01/230.42 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 230.01/230.42 Found x1 as proof of (P a)
% 230.01/230.42 Found x3:(((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) x2) Z)))
% 230.01/230.42 Instantiate: a:=(r X):(fofType->Prop);b:=(fun (Z:fofType)=> (((eq fofType) x2) Z)):(fofType->Prop)
% 230.01/230.42 Found x3 as proof of (((eq (fofType->Prop)) a) b)
% 230.01/230.42 Found x20:=(x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))):((P0 (fun (y:fofType)=> ((r x3) y)))->(P0 (fun (y:fofType)=> ((r x3) y))))
% 230.01/230.42 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 230.01/230.42 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 230.01/230.42 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 230.01/230.42 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 230.01/230.42 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 230.01/230.42 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 230.01/230.42 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 230.01/230.42 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 230.01/230.42 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 230.01/230.42 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 230.01/230.42 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 232.49/232.81 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 232.49/232.81 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 232.49/232.81 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 232.49/232.81 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))))
% 232.49/232.81 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))):(fofType->Prop)
% 232.49/232.81 Found x3 as proof of (P b)
% 232.49/232.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x6) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) (fun (x:fofType)=> ((r x6) x)))
% 232.49/232.81 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 232.49/232.81 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 232.49/232.81 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 232.49/232.81 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 232.49/232.81 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x6) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x6) y))) b)
% 232.49/232.81 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 232.49/232.81 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 232.49/232.81 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 232.49/232.81 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 232.49/232.81 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 232.49/232.81 Found x20:=(x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))):((P0 (fun (y:fofType)=> ((r x3) y)))->(P0 (fun (y:fofType)=> ((r x3) y))))
% 232.49/232.81 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 232.49/232.81 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 232.49/232.81 Found x20:=(x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))):((P0 (fun (y:fofType)=> ((r x3) y)))->(P0 (fun (y:fofType)=> ((r x3) y))))
% 232.49/232.81 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 232.49/232.81 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 232.49/232.81 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 232.49/232.81 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 232.49/232.82 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 232.49/232.82 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 232.49/232.82 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 232.49/232.82 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 232.49/232.82 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 232.49/232.82 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 232.49/232.82 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 232.49/232.82 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 234.87/235.25 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 234.87/235.25 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 234.87/235.25 Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 234.87/235.25 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 234.87/235.25 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 234.87/235.25 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% 234.87/235.25 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 234.87/235.25 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 234.87/235.25 Found x4 as proof of (P f)
% 234.87/235.25 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 234.87/235.25 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 234.87/235.25 Found x4 as proof of (P f)
% 234.87/235.25 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 234.87/235.25 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 234.87/235.25 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 234.87/235.25 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 234.87/235.25 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 234.87/235.25 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 239.26/239.57 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 239.26/239.57 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 239.26/239.57 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 239.26/239.57 Found x2:(((eq (fofType->Prop)) (r X)) ((eq fofType) x1))
% 239.26/239.57 Instantiate: a:=(r X):(fofType->Prop);b:=((eq fofType) x1):(fofType->Prop)
% 239.26/239.57 Found x2 as proof of (((eq (fofType->Prop)) a) b)
% 239.26/239.57 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 239.26/239.57 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 239.26/239.57 Found x0 as proof of (P a)
% 239.26/239.57 Found x0:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 239.26/239.57 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 239.26/239.57 Found x0 as proof of (P a)
% 239.26/239.57 Found x2:(((eq (fofType->Prop)) (r X)) ((eq fofType) x1))
% 239.26/239.57 Instantiate: a:=(r X):(fofType->Prop);b:=((eq fofType) x1):(fofType->Prop)
% 239.26/239.57 Found x2 as proof of (((eq (fofType->Prop)) a) b)
% 239.26/239.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 239.26/239.57 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 239.26/239.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 239.26/239.57 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 239.26/239.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 239.26/239.57 Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 239.26/239.57 Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 239.26/239.57 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x3) y))))
% 239.26/239.57 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 239.26/239.57 Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% 239.26/239.57 Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.26/239.57 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.26/239.57 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.26/239.57 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 239.26/239.57 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 239.26/239.57 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 239.26/239.57 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 239.26/239.57 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 239.26/239.57 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 242.65/242.97 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 242.65/242.97 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 242.65/242.97 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 242.65/242.97 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 242.65/242.97 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 242.65/242.97 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 242.65/242.97 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 242.65/242.97 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 242.65/242.97 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 242.65/242.97 Found x4 as proof of (P b)
% 242.65/242.97 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 242.65/242.97 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 242.65/242.97 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 242.65/242.97 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 242.65/242.97 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 242.65/242.97 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 242.65/242.97 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 242.65/242.97 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 242.65/242.97 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% 242.65/242.97 Found (eq_ref0 a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found ((eq_ref fofType) a) as proof of (((eq fofType) a) X)
% 242.65/242.97 Found eta_expansion000:=(eta_expansion00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 242.65/242.97 Found (eta_expansion00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 242.65/242.97 Found ((eta_expansion0 Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 242.65/242.97 Found (((eta_expansion fofType) Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 242.65/242.97 Found (((eta_expansion fofType) Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 242.65/242.97 Found (((eta_expansion fofType) Prop) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 242.65/242.97 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 242.65/242.97 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 242.65/242.97 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 242.65/242.97 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 242.65/242.97 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 244.61/244.93 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 244.61/244.93 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))):((P0 (f x4))->(P0 (f x4)))
% 244.61/244.93 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 244.61/244.93 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 244.61/244.93 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))):((P0 (f x4))->(P0 (f x4)))
% 244.61/244.93 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 244.61/244.93 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 244.61/244.93 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 244.61/244.93 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 244.61/244.93 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 244.61/244.93 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 244.61/244.93 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 244.61/244.93 Found ex_intro00:=(ex_intro0 (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))):(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->((ex fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3))))))
% 244.61/244.93 Found (ex_intro0 (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->(P a)))
% 244.61/244.93 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->(P a)))
% 244.61/244.93 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->(P a)))
% 244.61/244.93 Found ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3)))) as proof of (forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->(P a)))
% 244.61/244.93 Found (ex_ind00 ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3))))) as proof of (P a)
% 244.61/244.93 Found ((ex_ind0 (P a)) ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3))))) as proof of (P a)
% 244.61/244.93 Found (((fun (P0:Prop) (x2:(forall (x:fofType), ((((eq (fofType->Prop)) (r X)) ((eq fofType) x))->P0)))=> (((((ex_ind fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y)))) P0) x2) x1)) (P a)) ((ex_intro fofType) (fun (x3:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) x3))))) as proof of (P a)
% 244.92/245.29 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 244.92/245.29 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 244.92/245.29 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 244.92/245.29 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 244.92/245.29 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 244.92/245.29 Found (eq_ref0 x4) as proof of (((eq fofType) x4) b)
% 244.92/245.29 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 244.92/245.29 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 244.92/245.29 Found ((eq_ref fofType) x4) as proof of (((eq fofType) x4) b)
% 244.92/245.29 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 244.92/245.29 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 249.98/250.33 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 249.98/250.33 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 249.98/250.33 Found (eq_ref0 b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 249.98/250.33 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 249.98/250.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 249.98/250.33 Found (eq_ref0 b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 249.98/250.33 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 249.98/250.33 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 249.98/250.33 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 249.98/250.33 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 249.98/250.33 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 249.98/250.33 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))))
% 249.98/250.33 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))):(fofType->Prop)
% 249.98/250.33 Found x3 as proof of (P f)
% 249.98/250.33 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))))
% 249.98/250.33 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))):(fofType->Prop)
% 249.98/250.33 Found x3 as proof of (P f)
% 249.98/250.33 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 249.98/250.33 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 249.98/250.33 Found eq_ref00:=(eq_ref0 (fun (y:fofType)=> ((r x3) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) (fun (y:fofType)=> ((r x3) y)))
% 249.98/250.33 Found (eq_ref0 (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 249.98/250.33 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 252.26/252.62 Found ((eq_ref (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b0)
% 252.26/252.62 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 252.26/252.62 Found (eq_ref0 x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 252.26/252.62 Found x30:=(x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))):((P0 (fun (y:fofType)=> ((r x0) y)))->(P0 (fun (y:fofType)=> ((r x0) y))))
% 252.26/252.62 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 252.26/252.62 Found (eq_ref0 x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 252.26/252.62 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 252.26/252.62 Found eta_expansion_dep000:=(eta_expansion_dep00 (r X)):(((eq (fofType->Prop)) (r X)) (fun (x:fofType)=> ((r X) x)))
% 252.26/252.62 Found (eta_expansion_dep00 (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (r X)) as proof of (((eq (fofType->Prop)) (r X)) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found (x30 (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (r X))) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found ((x3 (fun (x5:(fofType->Prop))=> (((eq (fofType->Prop)) x5) (fun (y:fofType)=> ((r x0) y))))) (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (r X))) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found ((x3 (fun (x5:(fofType->Prop))=> (((eq (fofType->Prop)) x5) (fun (y:fofType)=> ((r x0) y))))) (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (r X))) as proof of (((eq (fofType->Prop)) b) (fun (y:fofType)=> ((r x0) y)))
% 252.26/252.62 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))))
% 252.26/252.62 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))):(fofType->Prop)
% 252.26/252.62 Found x4 as proof of (P b)
% 252.26/252.62 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) (fun (x:fofType)=> ((r x3) x)))
% 252.26/252.62 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 252.26/252.62 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 252.26/252.62 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 252.26/252.62 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 252.26/252.62 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x3) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x3) y))) b)
% 254.18/254.52 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 254.18/254.52 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x6) x)))
% 254.18/254.52 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 254.18/254.52 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x6) x7))
% 254.18/254.52 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x6) x)))
% 254.18/254.52 Found x30:=(x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))):((P0 (fun (y:fofType)=> ((r x0) y)))->(P0 (fun (y:fofType)=> ((r x0) y))))
% 254.18/254.52 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 254.18/254.52 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 254.18/254.52 Found x30:=(x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))):((P0 (fun (y:fofType)=> ((r x0) y)))->(P0 (fun (y:fofType)=> ((r x0) y))))
% 254.18/254.52 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 254.18/254.52 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 254.18/254.52 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 254.18/254.52 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 254.18/254.52 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 254.18/254.52 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 254.18/254.52 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 254.18/254.52 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 254.18/254.52 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 254.18/254.52 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 254.18/254.52 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 254.18/254.52 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 254.18/254.52 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 254.18/254.52 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 257.58/257.92 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 257.58/257.92 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 257.58/257.92 Found x1 as proof of (P f)
% 257.58/257.92 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 257.58/257.92 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 257.58/257.92 Found x1 as proof of (P f)
% 257.58/257.92 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 257.58/257.92 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 257.58/257.92 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 257.58/257.92 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 263.11/263.44 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 263.11/263.44 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 263.11/263.44 Found x1 as proof of (P a)
% 263.11/263.44 Found x3:(((eq (fofType->Prop)) (r X)) ((eq fofType) x2))
% 263.11/263.44 Instantiate: a:=(r X):(fofType->Prop);b:=((eq fofType) x2):(fofType->Prop)
% 263.11/263.44 Found x3 as proof of (((eq (fofType->Prop)) a) b)
% 263.11/263.44 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 263.11/263.44 Instantiate: a:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 263.11/263.44 Found x1 as proof of (P a)
% 263.11/263.44 Found x3:(((eq (fofType->Prop)) (r X)) ((eq fofType) x2))
% 263.11/263.44 Instantiate: a:=(r X):(fofType->Prop);b:=((eq fofType) x2):(fofType->Prop)
% 263.11/263.44 Found x3 as proof of (((eq (fofType->Prop)) a) b)
% 263.11/263.44 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 263.11/263.44 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 263.11/263.44 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 263.11/263.44 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 263.11/263.44 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 263.11/263.44 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 263.11/263.44 Found (eq_ref0 x1) as proof of (((eq fofType) x1) b)
% 263.11/263.44 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 263.11/263.44 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 263.11/263.44 Found ((eq_ref fofType) x1) as proof of (((eq fofType) x1) b)
% 263.11/263.44 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 263.11/263.44 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 263.11/263.44 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 263.11/263.44 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 263.11/263.44 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 263.77/264.13 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 263.77/264.13 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 263.77/264.13 Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 263.77/264.13 Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 263.77/264.13 Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 263.77/264.13 Found eta_expansion000:=(eta_expansion00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% 263.77/264.13 Found (eta_expansion00 a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found ((eta_expansion0 Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found (((eta_expansion fofType) Prop) a) as proof of (((eq (fofType->Prop)) a) b)
% 263.77/264.13 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 263.77/264.13 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 263.77/264.13 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 263.77/264.13 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x0) x7))
% 263.77/264.13 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x0) x)))
% 263.77/264.13 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 263.77/264.13 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 263.77/264.13 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 263.77/264.13 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 263.77/264.13 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 265.74/266.15 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 265.74/266.15 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 265.74/266.15 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 265.74/266.15 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 265.74/266.15 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 265.74/266.15 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 265.74/266.15 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 265.74/266.15 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 265.74/266.15 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 265.74/266.15 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 265.74/266.15 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 265.74/266.15 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 265.74/266.15 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 265.74/266.15 Found x20:=(x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))):((P0 (fun (y:fofType)=> ((r x3) y)))->(P0 (fun (y:fofType)=> ((r x3) y))))
% 265.74/266.15 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 269.83/270.19 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 269.83/270.19 Found x20:=(x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))):((P0 (fun (y:fofType)=> ((r x3) y)))->(P0 (fun (y:fofType)=> ((r x3) y))))
% 269.83/270.19 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 269.83/270.19 Found (x2 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x3) y))))) as proof of (P1 (fun (y:fofType)=> ((r x3) y)))
% 269.83/270.19 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 269.83/270.19 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 269.83/270.19 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 269.83/270.19 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 269.83/270.19 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 269.83/270.19 Found x30:=(x3 (fun (x5:(fofType->Prop))=> (P0 (f x4)))):((P0 (f x4))->(P0 (f x4)))
% 269.83/270.19 Found (x3 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 269.83/270.19 Found (x3 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 269.83/270.19 Found x30:=(x3 (fun (x5:(fofType->Prop))=> (P0 (f x4)))):((P0 (f x4))->(P0 (f x4)))
% 269.83/270.19 Found (x3 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 269.83/270.19 Found (x3 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 269.83/270.19 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 269.83/270.19 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 269.83/270.19 Found (eq_ref0 b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 269.83/270.19 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 269.83/270.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 269.83/270.19 Found (eq_ref0 b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x0) x4))
% 269.83/270.19 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 269.83/270.19 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 269.83/270.19 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 269.83/270.19 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 269.83/270.19 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 269.83/270.19 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 269.83/270.19 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 269.83/270.19 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 269.83/270.19 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 269.83/270.19 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 270.57/270.95 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 270.57/270.95 Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% 270.57/270.95 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 270.57/270.95 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 270.57/270.95 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 270.57/270.95 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 270.57/270.95 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 274.68/275.05 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 274.68/275.05 Found eta_expansion000:=(eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 274.68/275.05 Found (eta_expansion00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 274.68/275.05 Found ((eta_expansion0 Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 274.68/275.05 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 274.68/275.05 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 274.68/275.05 Found (((eta_expansion fofType) Prop) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b)
% 274.68/275.05 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))))
% 274.68/275.05 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))):(fofType->Prop)
% 274.68/275.05 Found x4 as proof of (P f)
% 274.68/275.05 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))))
% 274.68/275.05 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))):(fofType->Prop)
% 274.68/275.05 Found x4 as proof of (P f)
% 274.68/275.05 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 274.68/275.05 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 274.68/275.05 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 274.68/275.05 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 274.68/275.05 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 274.68/275.05 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 274.68/275.05 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) b)
% 274.68/275.05 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 274.68/275.05 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 274.68/275.05 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 274.68/275.05 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) b)
% 274.68/275.05 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 274.68/275.05 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 274.68/275.05 Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 274.68/275.05 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 274.68/275.05 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 277.63/278.02 Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b0)
% 277.63/278.02 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 277.63/278.02 Found (eq_ref0 x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 277.63/278.02 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 277.63/278.02 Found (eq_ref0 x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 277.63/278.02 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 277.63/278.02 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))):((P0 (f x4))->(P0 (f x4)))
% 277.63/278.02 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 277.63/278.02 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 277.63/278.02 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))):((P0 (f x4))->(P0 (f x4)))
% 277.63/278.02 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 277.63/278.02 Found (x2 (fun (x5:(fofType->Prop))=> (P0 (f x4)))) as proof of (P1 (f x4))
% 277.63/278.02 Found x4:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))))
% 277.63/278.02 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) ((eq fofType) Y))):(fofType->Prop)
% 277.63/278.02 Found x4 as proof of (P b)
% 277.63/278.02 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))):(((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) (fun (x:fofType)=> ((r x0) x)))
% 277.63/278.02 Found (eta_expansion_dep00 (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 277.63/278.02 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 277.63/278.02 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 277.63/278.02 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 277.63/278.02 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) (fun (y:fofType)=> ((r x0) y))) as proof of (((eq (fofType->Prop)) (fun (y:fofType)=> ((r x0) y))) b)
% 277.63/278.02 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 277.63/278.02 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 277.63/278.02 Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 277.63/278.02 Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((r x3) x7))
% 277.63/278.02 Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((r x3) x)))
% 277.63/278.02 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 277.63/278.02 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 277.63/278.02 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 278.16/278.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 278.16/278.57 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 278.16/278.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 278.16/278.57 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 278.16/278.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 278.16/278.57 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 278.16/278.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 278.16/278.57 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 278.16/278.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 278.16/278.57 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 278.16/278.57 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 278.16/278.57 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 279.17/279.61 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 279.17/279.61 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 279.17/279.61 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 279.17/279.61 Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 279.17/279.61 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 279.17/279.61 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 279.17/279.61 Found (eq_ref0 b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found x5:(P x4)
% 279.17/279.61 Instantiate: x4:=x':fofType
% 279.17/279.61 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 279.17/279.61 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 279.17/279.61 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 279.17/279.61 Found (fun (x00:((r x3) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 279.17/279.61 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 279.17/279.61 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 279.17/279.61 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 279.17/279.61 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 279.17/279.61 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 279.17/279.61 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 279.17/279.61 Found x5:(P x4)
% 279.17/279.61 Instantiate: x4:=x':fofType
% 279.17/279.61 Found (fun (x5:(P x4))=> x5) as proof of (P x')
% 279.17/279.61 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of ((P x4)->(P x'))
% 279.17/279.61 Found (fun (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 279.17/279.61 Found (fun (x00:((r x3) x')) (P:(fofType->Prop)) (x5:(P x4))=> x5) as proof of (((eq fofType) x4) x')
% 279.17/279.61 Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% 279.17/279.61 Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) b)
% 279.17/279.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 279.17/279.61 Found (eq_ref0 b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((r x3) x4))
% 279.17/279.61 Found x20:=(x2 (fun (x5:(fofType->Prop))=> (P x4))):((P x4)->(P x4))
% 279.17/279.61 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 279.17/279.61 Found (x2 (fun (x5:(fofType->Prop))=> (P x4))) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (fun (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 283.92/284.28 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (x2 (fun (x5:(fofType->Prop))=> (P x4)))) as proof of (((eq fofType) x4) x')
% 283.92/284.28 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 283.92/284.28 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 283.92/284.28 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 283.92/284.28 Found eq_ref000:=(eq_ref00 P):((P x4)->(P x4))
% 283.92/284.28 Found (eq_ref00 P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found ((eq_ref0 x4) P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (((eq_ref fofType) x4) P) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of ((P x4)->(P x'))
% 283.92/284.28 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 283.92/284.28 Found (fun (x00:((r x3) x')) (P:(fofType->Prop))=> (((eq_ref fofType) x4) P)) as proof of (((eq fofType) x4) x')
% 283.92/284.28 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 283.92/284.28 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 283.92/284.28 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 283.92/284.28 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 283.92/284.28 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 283.92/284.28 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 283.92/284.28 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 283.92/284.28 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 283.92/284.28 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 283.92/284.28 Found eq_ref00:=(eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) ((unique fofType) (fun (y:fofType)=> ((r x0) y))))
% 283.92/284.28 Found (eq_ref0 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 283.92/284.28 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 283.92/284.28 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 288.76/289.17 Found ((eq_ref (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 288.76/289.17 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 288.76/289.17 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 288.76/289.17 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 288.76/289.17 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 288.76/289.17 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 288.76/289.17 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x0) y)))) b0)
% 288.76/289.17 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 288.76/289.17 Found (eq_ref0 x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 288.76/289.17 Found eq_ref00:=(eq_ref0 x4):(((eq fofType) x4) x4)
% 288.76/289.17 Found (eq_ref0 x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found ((eq_ref fofType) x4) as proof of (forall (P:(fofType->Prop)), ((P x4)->(P x')))
% 288.76/289.17 Found (fun (x00:((r x3) x'))=> ((eq_ref fofType) x4)) as proof of (((eq fofType) x4) x')
% 288.76/289.17 Found x30:=(x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))):((P0 (fun (y:fofType)=> ((r x0) y)))->(P0 (fun (y:fofType)=> ((r x0) y))))
% 288.76/289.17 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 288.76/289.17 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 288.76/289.17 Found x30:=(x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))):((P0 (fun (y:fofType)=> ((r x0) y)))->(P0 (fun (y:fofType)=> ((r x0) y))))
% 288.76/289.17 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 288.76/289.17 Found (x3 (fun (x4:(fofType->Prop))=> (P0 (fun (y:fofType)=> ((r x0) y))))) as proof of (P1 (fun (y:fofType)=> ((r x0) y)))
% 288.76/289.17 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 288.76/289.17 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 288.76/289.17 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 288.76/289.17 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 288.76/289.17 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 290.62/291.01 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 290.62/291.01 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 290.62/291.01 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 290.62/291.01 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% 290.62/291.01 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 290.62/291.01 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 290.62/291.01 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 290.62/291.01 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 290.62/291.01 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 290.62/291.01 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 290.62/291.01 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 290.62/291.01 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x1))
% 290.62/291.01 Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((unique fofType) (fun (y:fofType)=> ((r x0) y))) x)))
% 290.62/291.01 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 290.62/291.01 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 290.62/291.01 Found x3 as proof of (P b)
% 290.62/291.01 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x6) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x6) y))) x)))
% 293.36/293.77 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found x3:=(x X0):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))))
% 293.36/293.77 Instantiate: b:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X0)) (fun (Z:fofType)=> (((eq fofType) Y) Z)))):(fofType->Prop)
% 293.36/293.77 Found x3 as proof of (P b)
% 293.36/293.77 Found eta_expansion_dep000:=(eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x6) y)))):(((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) (fun (x:fofType)=> (((unique fofType) (fun (y:fofType)=> ((r x6) y))) x)))
% 293.36/293.77 Found (eta_expansion_dep00 ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found ((eta_expansion_dep0 (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found (((eta_expansion_dep fofType) (fun (x8:fofType)=> Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) as proof of (((eq (fofType->Prop)) ((unique fofType) (fun (y:fofType)=> ((r x6) y)))) b)
% 293.36/293.77 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 293.36/293.77 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 293.36/293.77 Found x1 as proof of (P f)
% 293.36/293.77 Found x1:=(x X):((ex fofType) (fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))))
% 293.36/293.77 Instantiate: f:=(fun (Y:fofType)=> (((eq (fofType->Prop)) (r X)) ((eq fofType) Y))):(fofType->Prop)
% 293.36/293.77 Found x1 as proof of (P f)
% 293.36/293.77 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 293.36/293.77 Found (eq_ref0 x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x1) x')
% 293.36/293.77 Found eq_ref00:=(eq_ref0 x1):(((eq fofType) x1) x1)
% 293.36/293.77 Found (eq_ref0 x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found ((eq_ref fofType) x1) as proof of (forall (P:(fofType->Prop)), ((P x1)->(P x')))
% 293.36/293.77 Found (fun (x00:((r x0) x'))=> ((eq_ref fofType) x1)) as proof of (((eq fofType) x
%------------------------------------------------------------------------------