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