TSTP Solution File: SYO243^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO243^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 00:51:00 EDT 2022
% Result : Timeout 300.04s 300.60s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO243^5 : TPTP v7.5.0. Released v4.0.0.
% 0.00/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Fri Mar 11 21:23:11 EST 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.33 Python 2.7.5
% 0.85/1.07 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.85/1.07 FOF formula (<kernel.Constant object at 0x936200>, <kernel.DependentProduct object at 0x935200>) of role type named f
% 0.85/1.07 Using role type
% 0.85/1.07 Declaring f:(fofType->fofType)
% 0.85/1.07 FOF formula (<kernel.Constant object at 0x2ba29a67dcf8>, <kernel.DependentProduct object at 0x935290>) of role type named g
% 0.85/1.07 Using role type
% 0.85/1.07 Declaring g:(fofType->fofType)
% 0.85/1.07 FOF formula ((forall (Xr:(fofType->(fofType->Prop))), ((forall (Xx:fofType), ((ex fofType) (fun (Xy:fofType)=> ((Xr Xx) Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType), ((Xr Xx) (Xh Xx)))))))->((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) (f Xx)) (f Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))))) of role conjecture named cTHM588LEM1
% 0.85/1.07 Conjecture to prove = ((forall (Xr:(fofType->(fofType->Prop))), ((forall (Xx:fofType), ((ex fofType) (fun (Xy:fofType)=> ((Xr Xx) Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType), ((Xr Xx) (Xh Xx)))))))->((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) (f Xx)) (f Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))))):Prop
% 0.85/1.07 Parameter fofType_DUMMY:fofType.
% 0.85/1.07 We need to prove ['((forall (Xr:(fofType->(fofType->Prop))), ((forall (Xx:fofType), ((ex fofType) (fun (Xy:fofType)=> ((Xr Xx) Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType), ((Xr Xx) (Xh Xx)))))))->((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) (f Xx)) (f Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx))))))))']
% 0.85/1.07 Parameter fofType:Type.
% 0.85/1.07 Parameter f:(fofType->fofType).
% 0.85/1.07 Parameter g:(fofType->fofType).
% 0.85/1.07 Trying to prove ((forall (Xr:(fofType->(fofType->Prop))), ((forall (Xx:fofType), ((ex fofType) (fun (Xy:fofType)=> ((Xr Xx) Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType), ((Xr Xx) (Xh Xx)))))))->((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) (g Xy))->(((eq fofType) (f Xx)) (f Xy))))->((ex (fofType->fofType)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx))))))))
% 0.85/1.07 Found eq_ref00:=(eq_ref0 (x1 Xy)):(((eq fofType) (x1 Xy)) (x1 Xy))
% 0.85/1.07 Found (eq_ref0 (x1 Xy)) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 0.85/1.07 Found ((eq_ref fofType) (x1 Xy)) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 0.85/1.07 Found ((eq_ref fofType) (x1 Xy)) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 0.85/1.07 Found (fun (x00:(((eq fofType) (g Xx)) Xy))=> ((eq_ref fofType) (x1 Xy))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 0.85/1.07 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy))=> ((eq_ref fofType) (x1 Xy))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 0.85/1.07 Found eq_ref000:=(eq_ref00 P):((P (x1 Xy))->(P (x1 Xy)))
% 0.85/1.07 Found (eq_ref00 P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 0.85/1.07 Found ((eq_ref0 (x1 Xy)) P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 0.85/1.07 Found (((eq_ref fofType) (x1 Xy)) P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 0.85/1.07 Found (((eq_ref fofType) (x1 Xy)) P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 0.85/1.07 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x1 Xy)) P)) as proof of ((P (x1 Xy))->(P (f Xx)))
% 0.85/1.07 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (((eq_ref fofType) (x1 Xy)) P)) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 0.85/1.07 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (((eq_ref fofType) (x1 Xy)) P)) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 0.85/1.07 Found x000:=(x00 (fun (x2:fofType)=> (P (x1 Xy)))):((P (x1 Xy))->(P (x1 Xy)))
% 0.85/1.07 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 6.46/6.65 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 6.46/6.65 Found (fun (P:(fofType->Prop))=> (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 6.46/6.65 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 6.46/6.65 Found eq_ref00:=(eq_ref0 (x1 (g Xx))):(((eq fofType) (x1 (g Xx))) (x1 (g Xx)))
% 6.46/6.65 Found (eq_ref0 (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found (x000 ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (x1 x3)) (f Xx)))) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found (fun (x00:(((eq fofType) (g Xx)) Xy))=> ((x00 (fun (x3:fofType)=> (((eq fofType) (x1 x3)) (f Xx)))) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy))=> ((x00 (fun (x3:fofType)=> (((eq fofType) (x1 x3)) (f Xx)))) ((eq_ref fofType) (x1 (g Xx))))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 6.46/6.65 Found eq_ref00:=(eq_ref0 (x1 (g Xx))):(((eq fofType) (x1 (g Xx))) (x1 (g Xx)))
% 6.46/6.65 Found (eq_ref0 (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 6.46/6.65 Found (eq_sym010 ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 6.46/6.65 Found ((eq_sym01 (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 6.46/6.65 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 6.46/6.65 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 6.46/6.65 Found (x000 (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 6.46/6.65 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 6.46/6.65 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 6.46/6.65 Found (eq_sym000 ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found ((eq_sym00 (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found (((eq_sym0 (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found ((((eq_sym fofType) (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found (fun (x00:(((eq fofType) (g Xx)) Xy))=> ((((eq_sym fofType) (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 6.46/6.65 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy))=> ((((eq_sym fofType) (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 18.46/18.68 Found eq_ref00:=(eq_ref0 (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))):(((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx))))))
% 18.46/18.68 Found (eq_ref0 (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) b)
% 18.46/18.68 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) b)
% 18.46/18.68 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) b)
% 18.46/18.68 Found ((eq_ref ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) as proof of (((eq ((fofType->fofType)->Prop)) (fun (Xh:(fofType->fofType))=> (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (Xh Xy)) (f Xx)))))) b)
% 18.46/18.68 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 18.46/18.68 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found (fun (x1:(fofType->fofType))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found (fun (x1:(fofType->fofType))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x Xy)) (f Xx))))))
% 18.46/18.68 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 18.46/18.68 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found (fun (x1:(fofType->fofType))=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))))
% 18.46/18.68 Found (fun (x1:(fofType->fofType))=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:(fofType->fofType)), (((eq Prop) (f0 x)) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x Xy)) (f Xx))))))
% 18.46/18.68 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 18.46/18.68 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.46/18.68 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 18.54/18.76 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 18.54/18.76 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 18.54/18.76 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 18.54/18.76 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 18.54/18.76 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 18.54/18.76 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 23.47/23.66 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 23.47/23.66 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 23.47/23.66 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((x0 Xx) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 23.47/23.66 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.47/23.66 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.47/23.66 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 23.47/23.66 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 23.62/23.79 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 23.62/23.79 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 23.62/23.79 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 23.62/23.79 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 23.62/23.79 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) P)) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 23.62/23.79 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found (eq_ref0 (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 23.62/23.79 Found ((eq_ref fofType) (g Xx)) as proof of (((eq fofType) (g Xx)) (g Xx))
% 36.24/36.42 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 36.24/36.42 Found (x0100 ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 36.24/36.42 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((x010 x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 36.24/36.42 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 36.24/36.42 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> (((x01 Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 36.24/36.42 Found ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 36.24/36.42 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 36.24/36.42 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 36.24/36.42 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (g Xx)) (g Xx)))=> ((((fun (Xx0:fofType)=> ((x0 Xx0) Xx)) Xx) x2) (fun (x3:fofType)=> (P (x1 Xy))))) ((eq_ref fofType) (g Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 36.24/36.42 Found x000:=(x00 (fun (x2:fofType)=> (P (x1 Xy)))):((P (x1 Xy))->(P (x1 Xy)))
% 36.24/36.42 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 (x1 Xy))
% 36.24/36.42 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 (x1 Xy))
% 36.24/36.42 Found x00:(((eq fofType) (g Xx)) Xy)
% 36.24/36.42 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 36.24/36.42 Found x00:(((eq fofType) (g Xx)) Xy)
% 36.24/36.42 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 36.24/36.42 Found eq_ref00:=(eq_ref0 (x1 Xy)):(((eq fofType) (x1 Xy)) (x1 Xy))
% 36.24/36.42 Found (eq_ref0 (x1 Xy)) as proof of (((eq fofType) (x1 Xy)) b)
% 36.24/36.42 Found ((eq_ref fofType) (x1 Xy)) as proof of (((eq fofType) (x1 Xy)) b)
% 36.24/36.42 Found ((eq_ref fofType) (x1 Xy)) as proof of (((eq fofType) (x1 Xy)) b)
% 36.24/36.42 Found ((eq_ref fofType) (x1 Xy)) as proof of (((eq fofType) (x1 Xy)) b)
% 36.24/36.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 36.24/36.42 Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% 36.24/36.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% 36.24/36.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% 36.24/36.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% 36.24/36.42 Found ((eq_trans0000 ((eq_ref fofType) (x1 Xy))) ((eq_ref fofType) b)) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 36.24/36.42 Found (((eq_trans000 (f Xx)) ((eq_ref fofType) (x1 Xy))) ((eq_ref fofType) (f Xx))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 36.24/36.42 Found ((((fun (b:fofType)=> ((eq_trans00 b) (f Xx))) (f Xx)) ((eq_ref fofType) (x1 Xy))) ((eq_ref fofType) (f Xx))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 36.24/36.42 Found ((((fun (b:fofType)=> (((eq_trans0 (x1 Xy)) b) (f Xx))) (f Xx)) ((eq_ref fofType) (x1 Xy))) ((eq_ref fofType) (f Xx))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 36.24/36.42 Found ((((fun (b:fofType)=> ((((eq_trans fofType) (x1 Xy)) b) (f Xx))) (f Xx)) ((eq_ref fofType) (x1 Xy))) ((eq_ref fofType) (f Xx))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 36.24/36.42 Found (fun (x00:(((eq fofType) (g Xx)) Xy))=> ((((fun (b:fofType)=> ((((eq_trans fofType) (x1 Xy)) b) (f Xx))) (f Xx)) ((eq_ref fofType) (x1 Xy))) ((eq_ref fofType) (f Xx)))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 36.24/36.42 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy))=> ((((fun (b:fofType)=> ((((eq_trans fofType) (x1 Xy)) b) (f Xx))) (f Xx)) ((eq_ref fofType) (x1 Xy))) ((eq_ref fofType) (f Xx)))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 36.24/36.42 Found x000:=(x00 (fun (x2:fofType)=> (P (x1 Xy)))):((P (x1 Xy))->(P (x1 Xy)))
% 36.24/36.42 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 Xy)
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 Xy)
% 46.73/46.96 Found x000:=(x00 (fun (x2:fofType)=> (P (x1 Xy)))):((P (x1 Xy))->(P (x1 Xy)))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 (x1 Xy))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 (x1 Xy))
% 46.73/46.96 Found x000:=(x00 (fun (x2:fofType)=> (P (x1 Xy)))):((P (x1 Xy))->(P (x1 Xy)))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 (f Xy))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of (P0 (f Xy))
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (x1 Xy)):(((eq fofType) (x1 Xy)) (x1 Xy))
% 46.73/46.96 Found (eq_ref0 (x1 Xy)) as proof of (P Xy)
% 46.73/46.96 Found ((eq_ref fofType) (x1 Xy)) as proof of (P Xy)
% 46.73/46.96 Found ((eq_ref fofType) (x1 Xy)) as proof of (P Xy)
% 46.73/46.96 Found x00:(((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00:(((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (x1 Xy)):(((eq fofType) (x1 Xy)) (x1 Xy))
% 46.73/46.96 Found (eq_ref0 (x1 Xy)) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 46.73/46.96 Found ((eq_ref fofType) (x1 Xy)) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 46.73/46.96 Found ((eq_ref fofType) (x1 Xy)) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 46.73/46.96 Found ((eq_ref fofType) (x1 Xy)) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 46.73/46.96 Found (fun (x00:(((eq fofType) (g Xx)) Xy))=> ((eq_ref fofType) (x1 Xy))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 46.73/46.96 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy))=> ((eq_ref fofType) (x1 Xy))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 46.73/46.96 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 46.73/46.96 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 46.73/46.96 Found eq_ref000:=(eq_ref00 P):((P (x1 Xy))->(P (x1 Xy)))
% 46.73/46.96 Found (eq_ref00 P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found ((eq_ref0 (x1 Xy)) P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found (((eq_ref fofType) (x1 Xy)) P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found (((eq_ref fofType) (x1 Xy)) P) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x1 Xy)) P)) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found (fun (P:(fofType->Prop))=> (((eq_ref fofType) (x1 Xy)) P)) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 46.73/46.96 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (((eq_ref fofType) (x1 Xy)) P)) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 46.73/46.96 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (((eq_ref fofType) (x1 Xy)) P)) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 46.73/46.96 Found x000:=(x00 (fun (x2:fofType)=> (P (x1 Xy)))):((P (x1 Xy))->(P (x1 Xy)))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found (x00 (fun (x2:fofType)=> (P (x1 Xy)))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found (fun (P:(fofType->Prop))=> (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 46.73/46.96 Found (fun (P:(fofType->Prop))=> (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 46.73/46.96 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 46.73/46.96 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 46.73/46.96 Found x00:(((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00:(((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00:(((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00:(((eq fofType) (g Xx)) Xy)
% 46.73/46.96 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00:(((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 61.67/61.90 Found (eq_ref0 (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 61.67/61.90 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found x00:(((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00:(((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 61.67/61.90 Found (eq_ref0 (g Xy)) as proof of (P Xy)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 61.67/61.90 Found x00:(((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00:(((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00:(((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 61.67/61.90 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 61.67/61.90 Found (eq_ref0 (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 61.67/61.90 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 61.67/61.90 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 61.67/61.90 Found x00:(((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 61.67/61.90 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 61.67/61.90 Found (eq_ref0 (g Xy)) as proof of (P Xy)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 61.67/61.90 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 61.67/61.90 Found eq_ref00:=(eq_ref0 (x1 (g Xx))):(((eq fofType) (x1 (g Xx))) (x1 (g Xx)))
% 61.67/61.90 Found (eq_ref0 (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 61.74/61.92 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 61.74/61.92 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 61.74/61.92 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 61.74/61.92 Found (eq_sym010 ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 61.74/61.92 Found ((eq_sym01 (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 61.74/61.92 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 61.74/61.92 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 61.74/61.92 Found (x000 (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 61.74/61.92 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 61.74/61.92 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 61.74/61.92 Found ((eq_sym0000 ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 61.74/61.92 Found ((eq_sym0000 ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 61.74/61.92 Found (((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> ((eq_sym000 x2) (fun (x4:fofType)=> ((P (x1 Xy))->(P x4))))) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 61.74/61.92 Found (((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((eq_sym00 (x1 Xy)) x2) (fun (x4:fofType)=> ((P (x1 Xy))->(P x4))))) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 61.74/61.92 Found (((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> ((((eq_sym0 (f Xx)) (x1 Xy)) x2) (fun (x4:fofType)=> ((P (x1 Xy))->(P x4))))) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 61.74/61.92 Found (((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) (fun (x4:fofType)=> ((P (x1 Xy))->(P x4))))) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 61.74/61.92 Found (fun (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) (fun (x4:fofType)=> ((P (x1 Xy))->(P x4))))) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy)))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 61.74/61.92 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) (fun (x4:fofType)=> ((P (x1 Xy))->(P x4))))) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy)))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 61.74/61.92 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> (((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) (fun (x4:fofType)=> ((P (x1 Xy))->(P x4))))) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) (x00 (fun (x2:fofType)=> (P (x1 Xy)))))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 69.92/70.09 Found eq_ref00:=(eq_ref0 (x1 (g Xx))):(((eq fofType) (x1 (g Xx))) (x1 (g Xx)))
% 69.92/70.09 Found (eq_ref0 (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 69.92/70.09 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 69.92/70.09 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 69.92/70.09 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 69.92/70.09 Found (eq_sym010 ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 69.92/70.09 Found ((eq_sym01 (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 69.92/70.09 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 69.92/70.09 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 69.92/70.09 Found (x000 (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 69.92/70.09 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 69.92/70.09 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 69.92/70.09 Found (eq_sym0000 ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 69.92/70.09 Found (eq_sym0000 ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 69.92/70.09 Found ((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> ((eq_sym000 x2) P)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 69.92/70.09 Found ((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((eq_sym00 (x1 Xy)) x2) P)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 69.92/70.09 Found ((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> ((((eq_sym0 (f Xx)) (x1 Xy)) x2) P)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 69.92/70.09 Found ((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) P)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 69.92/70.09 Found (fun (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) P)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))))) as proof of ((P (x1 Xy))->(P (f Xx)))
% 69.92/70.09 Found (fun (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) P)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 69.92/70.09 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy)) (P:(fofType->Prop))=> ((fun (x2:(((eq fofType) (f Xx)) (x1 Xy)))=> (((((eq_sym fofType) (f Xx)) (x1 Xy)) x2) P)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 69.92/70.09 Found x00:(((eq fofType) (g Xx)) Xy)
% 69.92/70.09 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 69.92/70.09 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 69.92/70.09 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 69.92/70.09 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 79.83/80.05 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 79.83/80.05 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 79.83/80.05 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 79.83/80.05 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 Xy)
% 79.83/80.05 Found x000:=(x00 (fun (x2:fofType)=> (P (g Xy)))):((P (g Xy))->(P (g Xy)))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P (g Xy)))) as proof of (P0 (g Xy))
% 79.83/80.05 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 79.83/80.05 Found (eq_ref0 (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 79.83/80.05 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 79.83/80.05 Found (eq_ref0 (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (((eq fofType) (g Xy)) b)
% 79.83/80.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 79.83/80.05 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 79.83/80.05 Found (eq_ref0 (g Xy)) as proof of (P Xy)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 79.83/80.05 Found eq_ref00:=(eq_ref0 (g Xy)):(((eq fofType) (g Xy)) (g Xy))
% 79.83/80.05 Found (eq_ref0 (g Xy)) as proof of (P Xy)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 79.83/80.05 Found ((eq_ref fofType) (g Xy)) as proof of (P Xy)
% 79.83/80.05 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 79.83/80.05 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 79.83/80.05 Found x00:(((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found x00:(((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found x00:(((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% 79.83/80.05 Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 79.83/80.05 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 79.83/80.05 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 79.83/80.05 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 79.83/80.05 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 79.83/80.05 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 79.83/80.05 Found x00:(((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 79.83/80.05 Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% 79.83/80.05 Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 109.61/109.85 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 109.61/109.85 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 109.61/109.85 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% 109.61/109.85 Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 109.61/109.85 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% 109.61/109.85 Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% 109.61/109.85 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 109.61/109.85 Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% 109.61/109.85 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 109.61/109.85 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 109.61/109.85 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 109.61/109.85 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 109.61/109.85 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 109.61/109.85 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 109.61/109.85 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 109.61/109.85 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00:(((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 109.61/109.85 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 109.61/109.85 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 109.61/109.85 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 109.61/109.85 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 128.48/128.76 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 128.48/128.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 128.48/128.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 128.48/128.76 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 128.48/128.76 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 128.48/128.76 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 128.48/128.76 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 128.48/128.76 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 128.48/128.76 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 128.48/128.76 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 128.48/128.76 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 Xx)
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 Xx)
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found x00:(((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found x00:(((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found x00:(((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found x00:(((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 128.48/128.76 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 128.48/128.76 Found (eq_ref0 (g Xx)) as proof of (P Xx)
% 128.48/128.76 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 128.48/128.76 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 128.48/128.76 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 128.48/128.76 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 128.48/128.76 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 Xx)
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 Xx)
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 128.48/128.76 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 128.48/128.76 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 128.48/128.76 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 128.48/128.76 Found (eq_ref0 (g Xx)) as proof of (P Xx)
% 128.48/128.76 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 155.18/155.42 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 155.18/155.42 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 Xx)
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 Xx)
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 Xx)
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 Xx)
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 Xx)
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 155.18/155.42 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 155.18/155.42 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 155.18/155.42 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 155.18/155.42 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 155.18/155.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 155.18/155.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 155.18/155.42 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 155.18/155.42 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 155.18/155.42 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 155.18/155.42 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 155.18/155.42 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 155.18/155.42 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 155.18/155.42 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 155.18/155.42 Found (eq_ref0 (g Xx)) as proof of (P Xx)
% 174.93/175.20 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 174.93/175.20 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 174.93/175.20 Found eq_ref00:=(eq_ref0 (g Xx)):(((eq fofType) (g Xx)) (g Xx))
% 174.93/175.20 Found (eq_ref0 (g Xx)) as proof of (P Xx)
% 174.93/175.20 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 174.93/175.20 Found ((eq_ref fofType) (g Xx)) as proof of (P Xx)
% 174.93/175.20 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 174.93/175.20 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 174.93/175.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 174.93/175.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 174.93/175.20 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 174.93/175.20 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 174.93/175.20 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 174.93/175.20 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 174.93/175.20 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 174.93/175.20 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 174.93/175.20 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 174.93/175.20 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 174.93/175.20 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 174.93/175.20 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 174.93/175.20 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 174.93/175.20 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found x000:=(x00 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% 174.93/175.20 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 174.93/175.20 Found (x00 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% 174.93/175.20 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 174.93/175.20 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 174.93/175.20 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 174.93/175.20 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 174.93/175.20 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 174.93/175.20 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 174.93/175.20 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 174.93/175.20 Found eq_ref00:=(eq_ref0 (x1 (g Xx))):(((eq fofType) (x1 (g Xx))) (x1 (g Xx)))
% 174.93/175.20 Found (eq_ref0 (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 174.93/175.20 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 174.93/175.20 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 174.93/175.20 Found ((eq_ref fofType) (x1 (g Xx))) as proof of (((eq fofType) (x1 (g Xx))) (f Xx))
% 174.93/175.20 Found (eq_sym010 ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 174.93/175.20 Found ((eq_sym01 (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 174.93/175.20 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 174.93/175.20 Found (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))) as proof of (((eq fofType) (f Xx)) (x1 (g Xx)))
% 174.93/175.20 Found (x000 (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 174.93/175.20 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 174.93/175.20 Found ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))) as proof of (((eq fofType) (f Xx)) (x1 Xy))
% 174.93/175.20 Found (eq_sym000 ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 174.93/175.20 Found ((eq_sym00 (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 193.04/193.39 Found (((eq_sym0 (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) (((eq_sym0 (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 193.04/193.39 Found ((((eq_sym fofType) (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 193.04/193.39 Found ((((eq_sym fofType) (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx)))))) as proof of (forall (P:(fofType->Prop)), ((P (x1 Xy))->(P (f Xx))))
% 193.04/193.39 Found (fun (x00:(((eq fofType) (g Xx)) Xy))=> ((((eq_sym fofType) (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))))) as proof of (((eq fofType) (x1 Xy)) (f Xx))
% 193.04/193.39 Found (fun (Xy:fofType) (x00:(((eq fofType) (g Xx)) Xy))=> ((((eq_sym fofType) (f Xx)) (x1 Xy)) ((x00 (fun (x3:fofType)=> (((eq fofType) (f Xx)) (x1 x3)))) ((((eq_sym fofType) (x1 (g Xx))) (f Xx)) ((eq_ref fofType) (x1 (g Xx))))))) as proof of ((((eq fofType) (g Xx)) Xy)->(((eq fofType) (x1 Xy)) (f Xx)))
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 193.04/193.39 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 193.04/193.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 193.04/193.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 193.04/193.39 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 193.04/193.39 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 193.04/193.39 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 193.04/193.39 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 193.04/193.39 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 193.04/193.39 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 193.04/193.39 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 193.04/193.39 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 193.04/193.39 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 193.04/193.39 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 229.32/229.62 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 229.32/229.62 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 229.32/229.62 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 229.32/229.62 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 229.32/229.62 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 229.32/229.62 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 Xx)
% 229.32/229.62 Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% 229.32/229.62 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 229.32/229.62 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 Xx)
% 229.32/229.62 Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% 229.32/229.62 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 229.32/229.62 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 229.32/229.62 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 229.32/229.62 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 229.32/229.62 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 229.32/229.62 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 229.32/229.62 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 229.32/229.62 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 229.32/229.62 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 229.32/229.62 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 229.32/229.62 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 273.14/273.48 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 273.14/273.48 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 273.14/273.48 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 273.14/273.48 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 273.14/273.48 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 273.14/273.48 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 273.14/273.48 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found eq_ref000:=(eq_ref00 P):((P (g Xx))->(P (g Xx)))
% 273.14/273.48 Found (eq_ref00 P) as proof of (P0 (g Xx))
% 273.14/273.48 Found ((eq_ref0 (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found (((eq_ref fofType) (g Xx)) P) as proof of (P0 (g Xx))
% 273.14/273.48 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 273.14/273.48 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 273.14/273.48 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 273.14/273.48 Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 273.14/273.48 Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% 273.14/273.48 Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% 273.14/273.48 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 273.14/273.48 Found (eq_ref00 P) as proof of (P0 Xx)
% 273.14/273.48 Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% 273.14/273.48 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 273.14/273.48 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 273.14/273.48 Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% 273.14/273.48 Found (eq_ref00 P) as proof of (P0 Xx)
% 273.14/273.48 Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% 273.14/273.48 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 273.14/273.48 Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% 273.14/273.48 Found x000:=(x00 (fun (x2:fofType)=> (P Xx))):((P Xx)->(P Xx))
% 273.14/273.48 Found (x00 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% 273.14/273.48 Found (x00 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x000:=(x00 (fun (x2:fofType)=> (P Xx))):((P Xx)->(P Xx))
% 273.14/273.48 Found (x00 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% 273.14/273.48 Found (x00 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00:(((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x00 as proof of (((eq fofType) (g Xx)) Xy)
% 273.14/273.48 Found x000:=(x00 (fun (x2:fofType)=> (P Xx))):((P Xx)->(P Xx))
% 273.14/273.48 Found (x00 (
%------------------------------------------------------------------------------