TSTP Solution File: PUZ122^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : PUZ122^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n059.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 14:22:31 EDT 2015
% Result : Unknown 153.34s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.02 % Problem : PUZ122^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.01/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/1.08 % Computer : n059.star.cs.uiowa.edu
% 0.03/1.08 % Model : x86_64 x86_64
% 0.03/1.08 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/1.08 % Memory : 32286.75MB
% 0.03/1.08 % OS : Linux 2.6.32-504.8.1.el6.x86_64
% 0.03/1.08 % CPULimit : 300
% 0.03/1.08 % DateTime : Thu Apr 16 11:49:12 CDT 2015
% 0.03/1.08 % CPUTime :
% 0.03/1.09 Python 2.7.5
% 0.05/1.44 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.05/1.44 FOF formula (<kernel.Constant object at 0x2942878>, <kernel.DependentProduct object at 0x2942998>) of role type named cCKB_FIN_type
% 0.05/1.44 Using role type
% 0.05/1.44 Declaring cCKB_FIN:((fofType->(fofType->Prop))->Prop)
% 0.05/1.44 FOF formula (<kernel.Constant object at 0x2923248>, <kernel.DependentProduct object at 0x2942878>) of role type named cCKB_INF_type
% 0.05/1.44 Using role type
% 0.05/1.44 Declaring cCKB_INF:((fofType->(fofType->Prop))->Prop)
% 0.05/1.44 FOF formula (<kernel.Constant object at 0x2942128>, <kernel.DependentProduct object at 0x2942bd8>) of role type named cCKB_INJ_type
% 0.05/1.44 Using role type
% 0.05/1.44 Declaring cCKB_INJ:((fofType->(fofType->(fofType->(fofType->Prop))))->Prop)
% 0.05/1.44 FOF formula (<kernel.Constant object at 0x2942998>, <kernel.DependentProduct object at 0x2942f38>) of role type named cCKB_XPL_type
% 0.05/1.44 Using role type
% 0.05/1.44 Declaring cCKB_XPL:((fofType->(fofType->(fofType->(fofType->Prop))))->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.05/1.44 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
% 0.05/1.44 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))))))
% 0.05/1.44 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)))))
% 0.05/1.44 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
% 0.05/1.44 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)))))))))))
% 0.05/1.44 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))))))))))
% 0.05/1.44 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
% 0.05/1.44 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))))))))))
% 106.51/107.67 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)))))))))
% 106.51/107.67 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) cCKB_FIN) (fun (Xk:(fofType->(fofType->Prop)))=> ((cCKB_INF Xk)->False))) of role definition named cCKB_FIN_def
% 106.51/107.67 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) cCKB_FIN) (fun (Xk:(fofType->(fofType->Prop)))=> ((cCKB_INF Xk)->False)))
% 106.51/107.67 Defined: cCKB_FIN:=(fun (Xk:(fofType->(fofType->Prop)))=> ((cCKB_INF Xk)->False))
% 106.51/107.67 FOF formula (forall (Xk:(fofType->(fofType->Prop))) (Xz:fofType) (Xw:fofType), ((cCKB_FIN Xk)->(cCKB_FIN (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))))) of role conjecture named cL2000_pme
% 106.51/107.67 Conjecture to prove = (forall (Xk:(fofType->(fofType->Prop))) (Xz:fofType) (Xw:fofType), ((cCKB_FIN Xk)->(cCKB_FIN (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))))):Prop
% 106.51/107.67 Parameter fofType_DUMMY:fofType.
% 106.51/107.67 We need to prove ['(forall (Xk:(fofType->(fofType->Prop))) (Xz:fofType) (Xw:fofType), ((cCKB_FIN Xk)->(cCKB_FIN (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw)))))))']
% 106.51/107.67 Parameter fofType:Type.
% 106.51/107.67 Definition cCKB_FIN:=(fun (Xk:(fofType->(fofType->Prop)))=> ((cCKB_INF Xk)->False)):((fofType->(fofType->Prop))->Prop).
% 106.51/107.67 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).
% 106.51/107.67 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).
% 106.51/107.67 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)))).
% 106.51/107.67 Trying to prove (forall (Xk:(fofType->(fofType->Prop))) (Xz:fofType) (Xw:fofType), ((cCKB_FIN Xk)->(cCKB_FIN (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw)))))))
% 106.51/107.67 Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))->((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))))
% 106.51/107.67 Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 106.51/107.67 Found ((eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))->((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))))
% 117.12/118.23 Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found ((eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) x)))))
% 117.12/118.23 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 117.12/118.23 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) x)))))
% 118.02/119.15 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 118.02/119.15 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) x)))))
% 118.02/119.15 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) x)))))
% 136.23/137.37 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (Xu:fofType) (Xv:fofType)=> ((or ((Xk Xu) Xv)) ((and (((eq fofType) Xu) Xz)) (((eq fofType) Xv) Xw))))) x4) Xn))))
% 136.23/137.37 Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))->((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))))
% 151.63/152.77 Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found ((eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))->((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))))
% 151.63/152.77 Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found ((eq_ref0 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found (((eq_ref (fofType->Prop)) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 151.63/152.77 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) x)))))
% 152.33/153.41 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) x)))))
% 152.33/153.41 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 152.33/153.41 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) x)))))
% 153.34/154.45 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found ((((eta_expansion fofType) Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))->((ex fofType) (fun (x:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) x)))))
% 153.34/154.45 Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found ((eta_expansion00 (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn)))) (ex fofType)) as proof of (P (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1) (fun (x40:fofType) (x30:fofType)=> ((or ((Xk x40) x30)) ((and (((eq fofType) x40) Xz)) (((eq fofType) x30) Xw))))) x4) Xn))))
% 153.34/154.45 Found (((eta_expansion0 Prop) (fun (Xn:fofType)=> ((and (cCKB_INJ x1)) ((((cCKB_XPL x1)
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