TSTP Solution File: SEU971^5 by cocATP---0.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU971^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n098.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-504.8.1.el6.x86_64
% CPULimit : 300s
% DateTime : Wed May  6 14:27:22 EDT 2015

% Result   : Timeout 286.98s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU971^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.00/0.03  % Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/1.08  % Computer : n098.star.cs.uiowa.edu
% 0.02/1.08  % Model    : x86_64 x86_64
% 0.02/1.08  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/1.08  % Memory   : 32286.75MB
% 0.02/1.08  % OS       : Linux 2.6.32-504.8.1.el6.x86_64
% 0.02/1.08  % CPULimit : 300
% 0.02/1.08  % DateTime : Thu Apr 16 12:02:12 CDT 2015
% 0.02/1.08  % CPUTime  : 
% 0.02/1.10  Python 2.7.5
% 0.05/1.42  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.05/1.42  FOF formula (<kernel.Constant object at 0x15bf440>, <kernel.DependentProduct object at 0x15bfa28>) of role type named cCKB_INF_type
% 0.05/1.42  Using role type
% 0.05/1.42  Declaring cCKB_INF:((fofType->(fofType->Prop))->Prop)
% 0.05/1.42  FOF formula (<kernel.Constant object at 0x186a830>, <kernel.DependentProduct object at 0x15bfa70>) of role type named cCKB_INJ_type
% 0.05/1.42  Using role type
% 0.05/1.42  Declaring cCKB_INJ:((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)
% 0.05/1.42  FOF formula (<kernel.Constant object at 0x15bf6c8>, <kernel.DependentProduct object at 0x15bff80>) of role type named cCKB_XPL_type
% 0.05/1.42  Using role type
% 0.05/1.42  Declaring cCKB_XPL:((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.05/1.42  FOF formula (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)) cCKB_INJ) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))))) of role definition named cCKB_INJ_def
% 0.05/1.42  A new definition: (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)) cCKB_INJ) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))))
% 0.05/1.42  Defined: cCKB_INJ:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2)))))
% 0.05/1.42  FOF formula (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) cCKB_XPL) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False))))))))))) of role definition named cCKB_XPL_def
% 0.05/1.42  A new definition: (((eq ((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) cCKB_XPL) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False)))))))))))
% 0.05/1.42  Defined: cCKB_XPL:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False))))))))))
% 0.05/1.42  FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) cCKB_INF) (fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn)))))))))) of role definition named cCKB_INF_def
% 0.05/1.42  A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) cCKB_INF) (fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn))))))))))
% 15.40/16.52  Defined: cCKB_INF:=(fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn)))))))))
% 15.40/16.52  FOF formula (forall (Xx:fofType) (Xy:fofType) (Xr:(fofType->(fofType->Prop))), ((cCKB_INF (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy)))))->(cCKB_INF Xr))) of role conjecture named cCKB6_L80000_pme
% 15.40/16.52  Conjecture to prove = (forall (Xx:fofType) (Xy:fofType) (Xr:(fofType->(fofType->Prop))), ((cCKB_INF (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy)))))->(cCKB_INF Xr))):Prop
% 15.40/16.52  Parameter fofType_DUMMY:fofType.
% 15.40/16.52  We need to prove ['(forall (Xx:fofType) (Xy:fofType) (Xr:(fofType->(fofType->Prop))), ((cCKB_INF (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy)))))->(cCKB_INF Xr)))']
% 15.40/16.52  Parameter fofType:Type.
% 15.40/16.52  Definition cCKB_INF:=(fun (Xk:(fofType->(fofType->Prop)))=> ((ex (fofType->(fofType->(fofType->(fofType->Prop))))) (fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> ((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ Xh)) ((((cCKB_XPL Xh) Xk) Xm) Xn))))))))):((fofType->(fofType->Prop))->Prop).
% 15.40/16.52  Definition cCKB_INJ:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop)))))=> (forall (Xx1:fofType) (Xy1:fofType) (Xx2:fofType) (Xy2:fofType) (Xu:fofType) (Xv:fofType), (((and ((((Xh Xx1) Xy1) Xu) Xv)) ((((Xh Xx2) Xy2) Xu) Xv))->((and (((eq fofType) Xx1) Xx2)) (((eq fofType) Xy1) Xy2))))):((fofType->(fofType->(fofType->(fofType->Prop))))->Prop).
% 15.40/16.52  Definition cCKB_XPL:=(fun (Xh:(fofType->(fofType->(fofType->(fofType->Prop))))) (Xk:(fofType->(fofType->Prop))) (Xm:fofType) (Xn:fofType)=> ((and ((Xk Xm) Xn)) (forall (Xx:fofType) (Xy:fofType), (((Xk Xx) Xy)->((ex fofType) (fun (Xu:fofType)=> ((ex fofType) (fun (Xv:fofType)=> ((and ((and ((((Xh Xx) Xy) Xu) Xv)) ((Xk Xu) Xv))) (((and (((eq fofType) Xu) Xm)) (((eq fofType) Xv) Xn))->False)))))))))):((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 15.40/16.52  Trying to prove (forall (Xx:fofType) (Xy:fofType) (Xr:(fofType->(fofType->Prop))), ((cCKB_INF (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy)))))->(cCKB_INF Xr)))
% 15.40/16.52  Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))->((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))))
% 15.40/16.52  Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 15.40/16.52  Found ((eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 15.40/16.52  Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 15.40/16.52  Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found eta_expansion_dep0000:=(eta_expansion_dep000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x)))))
% 17.79/18.98  Found (eta_expansion_dep000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found ((eta_expansion_dep00 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found (((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found ((((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found ((((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found eta_expansion_dep0000:=(eta_expansion_dep000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x)))))
% 17.79/18.98  Found (eta_expansion_dep000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found ((eta_expansion_dep00 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 17.79/18.98  Found (((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 66.61/67.76  Found ((((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 66.61/67.76  Found ((((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 66.61/67.76  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 66.61/67.76  Instantiate: b:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 66.61/67.76  Found x1 as proof of (P b)
% 66.61/67.76  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 66.61/67.76  Found (eta_expansion_dep00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 66.61/67.76  Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 66.61/67.76  Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 66.61/67.76  Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 66.61/67.76  Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 66.61/67.76  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 66.61/67.76  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 66.61/67.76  Found x1 as proof of (P f)
% 66.61/67.76  Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 66.61/67.76  Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.25  Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.25  Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.25  Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.25  Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 76.11/77.25  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 76.11/77.26  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 76.11/77.26  Found x1 as proof of (P f)
% 76.11/77.26  Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 76.11/77.26  Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.26  Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.26  Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.26  Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x3) Xn)))))
% 76.11/77.26  Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 76.11/77.26  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 76.11/77.26  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 76.11/77.26  Found x3 as proof of (P b)
% 76.11/77.26  Found eq_ref00:=(eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn))))))
% 76.11/77.26  Found (eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 76.11/77.26  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 76.11/77.26  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 76.11/77.26  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 83.82/84.91  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 83.82/84.91  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 83.82/84.91  Found x3 as proof of (P f)
% 83.82/84.91  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 83.82/84.91  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 83.82/84.91  Found x3 as proof of (P f)
% 83.82/84.91  Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% 83.82/84.91  Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x) Xn))))))
% 83.82/84.91  Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% 83.82/84.91  Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x5) Xn)))))
% 83.82/84.91  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x) Xn))))))
% 83.82/84.91  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 83.82/84.91  Instantiate: b:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 83.82/84.91  Found x1 as proof of (P b)
% 83.82/84.91  Found eq_ref00:=(eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 83.82/84.91  Found (eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 83.82/84.91  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 83.82/84.91  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 91.12/92.25  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 91.12/92.25  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 91.12/92.25  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 91.12/92.25  Found x1 as proof of (P f)
% 91.12/92.25  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 91.12/92.25  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 91.12/92.25  Found x1 as proof of (P f)
% 91.12/92.25  Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% 91.12/92.25  Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 91.12/92.25  Found eq_ref00:=(eq_ref0 (f x5)):(((eq Prop) (f x5)) (f x5))
% 91.12/92.25  Found (eq_ref0 (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found ((eq_ref Prop) (f x5)) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (((eq Prop) (f x5)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x5) Xn)))))
% 91.12/92.25  Found (fun (x5:fofType)=> ((eq_ref Prop) (f x5))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 91.12/92.25  Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))->((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))))
% 91.12/92.25  Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 91.12/92.25  Found ((eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 93.02/94.14  Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 93.02/94.14  Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 93.02/94.14  Found eq_ref00:=(eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))):(((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 93.02/94.14  Found (eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 93.02/94.14  Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 93.02/94.14  Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 93.02/94.14  Found ((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 93.02/94.14  Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 93.02/94.14  Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 93.02/94.14  Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 93.02/94.14  Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 93.02/94.14  Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 107.42/108.50  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))):(((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) (fun (x:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x))))
% 107.42/108.50  Found (eta_expansion_dep00 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 107.42/108.50  Found ((eta_expansion_dep0 (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 107.42/108.50  Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 107.42/108.50  Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 107.42/108.50  Found (((eta_expansion_dep fofType) (fun (x5:fofType)=> Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) as proof of (((eq (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn)))) b)
% 107.42/108.50  Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% 107.42/108.50  Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 107.42/108.50  Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 107.42/108.50  Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 107.42/108.50  Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 107.42/108.50  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 107.42/108.50  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 107.42/108.50  Found x3 as proof of (P b)
% 107.42/108.50  Found eta_expansion000:=(eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x) Xn))))))
% 119.33/120.40  Found (eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 119.33/120.40  Found ((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 119.33/120.40  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 119.33/120.40  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 119.33/120.40  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 119.33/120.40  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 119.33/120.40  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 119.33/120.40  Found x1 as proof of (P f)
% 119.33/120.40  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 119.33/120.40  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 119.33/120.40  Found x1 as proof of (P f)
% 119.33/120.40  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 119.33/120.40  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 119.33/120.40  Found x3 as proof of (P b)
% 119.33/120.40  Found eta_expansion000:=(eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x) Xn))))))
% 119.33/120.40  Found (eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 119.33/120.40  Found ((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found x4:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 122.53/123.65  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))):(fofType->Prop)
% 122.53/123.65  Found x4 as proof of (P b)
% 122.53/123.65  Found eta_expansion000:=(eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 122.53/123.65  Found (eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found ((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 122.53/123.65  Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 122.53/123.65  Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 122.53/123.65  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 122.53/123.65  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 122.53/123.65  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 122.53/123.65  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x) Xn))))))
% 135.54/136.69  Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 135.54/136.69  Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 135.54/136.69  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 135.54/136.69  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 135.54/136.69  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x7) Xn)))))
% 135.54/136.69  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x) Xn))))))
% 135.54/136.69  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 135.54/136.69  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 135.54/136.69  Found x1 as proof of (P f)
% 135.54/136.69  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 135.54/136.69  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 135.54/136.69  Found x1 as proof of (P f)
% 135.54/136.69  Found x4:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 135.54/136.69  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))):(fofType->Prop)
% 135.54/136.69  Found x4 as proof of (P f)
% 135.54/136.69  Found x4:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 135.54/136.69  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))):(fofType->Prop)
% 135.54/136.69  Found x4 as proof of (P f)
% 135.54/136.69  Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) x)))))
% 135.54/136.69  Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 135.54/136.69  Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 135.54/136.69  Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 141.34/142.43  Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 141.34/142.43  Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 141.34/142.43  Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 141.34/142.43  Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x) Xn))))))
% 141.34/142.43  Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 141.34/142.43  Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x7) Xn)))))
% 141.34/142.43  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x) Xn))))))
% 141.34/142.43  Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 141.34/142.43  Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 141.34/142.43  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 141.34/142.43  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 141.34/142.43  Found eq_ref00:=(eq_ref0 (f x7)):(((eq Prop) (f x7)) (f x7))
% 141.34/142.43  Found (eq_ref0 (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 141.34/142.43  Found ((eq_ref Prop) (f x7)) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 154.64/155.77  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (((eq Prop) (f x7)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x7) Xn)))))
% 154.64/155.77  Found (fun (x7:fofType)=> ((eq_ref Prop) (f x7))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 154.64/155.77  Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))->(P0 (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn)))))))
% 154.64/155.77  Found (eta_expansion000 P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found ((eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found (((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))->(P0 (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn)))))))
% 154.64/155.77  Found (eta_expansion000 P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found ((eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found (((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 154.64/155.77  Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) x)))))
% 154.64/155.77  Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 154.64/155.77  Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))->((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))))
% 163.15/164.26  Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found ((eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x4) Xn))))
% 163.15/164.26  Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 163.15/164.26  Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 163.15/164.26  Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 164.05/165.18  Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 164.05/165.18  Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 164.05/165.18  Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 164.05/165.18  Found eta_expansion000:=(eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 164.05/165.18  Found (eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found ((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found eta_expansion000:=(eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn))))))
% 164.05/165.18  Found (eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found ((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 164.05/165.18  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 185.15/186.23  Found (((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 185.15/186.23  Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% 185.15/186.23  Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 185.15/186.23  Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 185.15/186.23  Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 185.15/186.23  Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 185.15/186.23  Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 185.15/186.23  Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))->(P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))))
% 185.15/186.23  Found (eq_ref00 P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 185.15/186.23  Found ((eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 185.15/186.23  Found (((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 185.15/186.23  Found (((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 185.15/186.23  Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))->(P0 (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn)))))))
% 185.15/186.23  Found (eta_expansion000 P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 185.15/186.23  Found ((eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 185.15/186.23  Found (((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 185.15/186.23  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))->(P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))))
% 197.75/198.86  Found (eq_ref00 P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found ((eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found (((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found (((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))->(P0 (fun (x:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x) Xn)))))))
% 197.75/198.86  Found (eta_expansion000 P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found ((eta_expansion00 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found (((eta_expansion0 Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found ((((eta_expansion fofType) Prop) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) P0) as proof of (P1 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 197.75/198.86  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 197.75/198.86  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 197.75/198.86  Found x3 as proof of (P b)
% 197.75/198.86  Found eq_ref00:=(eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn))))))
% 197.75/198.86  Found (eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) b)
% 200.46/201.58  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) b)
% 200.46/201.58  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) b)
% 200.46/201.58  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) Xm) Xn)))))) b)
% 200.46/201.58  Found eq_ref00:=(eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))):(((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 200.46/201.58  Found (eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 200.46/201.58  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 200.46/201.58  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 200.46/201.58  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 200.46/201.58  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 200.46/201.58  Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 200.46/201.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 200.46/201.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 200.46/201.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 200.46/201.58  Found eq_ref00:=(eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))):(((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 200.46/201.58  Found (eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 201.06/202.19  Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 201.06/202.19  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 201.06/202.19  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 201.06/202.19  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 201.06/202.19  Found eq_ref00:=(eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))):(((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 201.06/202.19  Found (eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 201.06/202.19  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 201.06/202.19  Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 201.06/202.19  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 202.36/203.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 202.36/203.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 202.36/203.47  Found eq_ref00:=(eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))):(((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 202.36/203.47  Found (eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 202.36/203.47  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 202.36/203.47  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 202.36/203.47  Found ((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) as proof of (((eq Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) b)
% 202.36/203.47  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 202.36/203.47  Found (eq_ref0 b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 202.36/203.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 202.36/203.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 202.36/203.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x4) Xn)))))
% 202.36/203.47  Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))->(P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))))
% 202.36/203.47  Found (eq_ref00 P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 202.36/203.47  Found ((eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 202.36/203.47  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))->(P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))))
% 204.16/205.24  Found (eq_ref00 P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found ((eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))->(P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))))
% 204.16/205.24  Found (eq_ref00 P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found ((eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 204.16/205.24  Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))->(P0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))))
% 204.16/205.24  Found (eq_ref00 P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 227.97/229.05  Found ((eq_ref0 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 227.97/229.05  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 227.97/229.05  Found (((eq_ref Prop) ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4))) P0) as proof of (P1 ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) x4)))
% 227.97/229.05  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 227.97/229.05  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 227.97/229.05  Found x3 as proof of (P b)
% 227.97/229.05  Found eq_ref00:=(eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn))))))
% 227.97/229.05  Found (eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 227.97/229.05  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 227.97/229.05  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 227.97/229.05  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) Xm) Xn)))))) b)
% 227.97/229.05  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 227.97/229.05  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 227.97/229.05  Found x3 as proof of (P f)
% 227.97/229.05  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 227.97/229.05  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 227.97/229.05  Found x3 as proof of (P f)
% 227.97/229.05  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 248.69/249.73  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 248.69/249.73  Found x3 as proof of (P b)
% 248.69/249.73  Found eq_ref00:=(eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn))))))
% 248.69/249.73  Found (eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found x4:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))))
% 248.69/249.73  Instantiate: b:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x3) Xn))):(fofType->Prop)
% 248.69/249.73  Found x4 as proof of (P b)
% 248.69/249.73  Found eq_ref00:=(eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))):(((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn))))))
% 248.69/249.73  Found (eq_ref0 (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found ((eq_ref (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) as proof of (((eq (fofType->Prop)) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) Xm) Xn)))))) b)
% 248.69/249.73  Found eq_ref00:=(eq_ref0 (f x9)):(((eq Prop) (f x9)) (f x9))
% 248.69/249.73  Found (eq_ref0 (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 248.69/249.73  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 262.88/263.92  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 262.88/263.92  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 262.88/263.92  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x) Xn))))))
% 262.88/263.92  Found eq_ref00:=(eq_ref0 (f x9)):(((eq Prop) (f x9)) (f x9))
% 262.88/263.92  Found (eq_ref0 (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 262.88/263.92  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 262.88/263.92  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 262.88/263.92  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x9) Xn)))))
% 262.88/263.92  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x8)) ((((cCKB_XPL x8) Xr) x) Xn))))))
% 262.88/263.92  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 262.88/263.92  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 262.88/263.92  Found x3 as proof of (P f)
% 262.88/263.92  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 262.88/263.92  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 262.88/263.92  Found x3 as proof of (P f)
% 262.88/263.92  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 262.88/263.92  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 262.88/263.92  Found x3 as proof of (P f)
% 262.88/263.92  Found x3:((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))))
% 262.88/263.92  Instantiate: f:=(fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) x2) Xn))):(fofType->Prop)
% 262.88/263.92  Found x3 as proof of (P f)
% 262.88/263.92  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 262.88/263.92  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 262.88/263.92  Found x1 as proof of (P f)
% 262.88/263.92  Found x1:((ex fofType) (fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))))
% 262.88/263.92  Instantiate: f:=(fun (Xm:fofType)=> ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x0)) ((((cCKB_XPL x0) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xr Xu) Xv)) ((and (((eq fofType) Xu) Xx)) (((eq fofType) Xv) Xy))))) Xm) Xn))))):(fofType->Prop)
% 286.98/288.00  Found x1 as proof of (P f)
% 286.98/288.00  Found eq_ref00:=(eq_ref0 (f x9)):(((eq Prop) (f x9)) (f x9))
% 286.98/288.00  Found (eq_ref0 (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x) Xn))))))
% 286.98/288.00  Found eq_ref00:=(eq_ref0 (f x9)):(((eq Prop) (f x9)) (f x9))
% 286.98/288.00  Found (eq_ref0 (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x6)) ((((cCKB_XPL x6) Xr) x) Xn))))))
% 286.98/288.00  Found eq_ref00:=(eq_ref0 (f x9)):(((eq Prop) (f x9)) (f x9))
% 286.98/288.00  Found (eq_ref0 (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x) Xn))))))
% 286.98/288.00  Found eq_ref00:=(eq_ref0 (f x9)):(((eq Prop) (f x9)) (f x9))
% 286.98/288.00  Found (eq_ref0 (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x4)) ((((cCKB_XPL x4) Xr) x) Xn))))))
% 286.98/288.00  Found eq_ref00:=(eq_ref0 (f x9)):(((eq Prop) (f x9)) (f x9))
% 286.98/288.00  Found (eq_ref0 (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x9) Xn)))))
% 286.98/288.00  Found ((eq_ref Prop) (f x9)) as proof of (((eq Prop) (f x9)) ((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x2)) ((((cCKB_XPL x2) Xr) x9) Xn)))))
% 286.98/288.00  Found (fun (x9:fofType)=> ((eq_ref Prop) (f x9))) as proof o
%------------------------------------------------------------------------------