TSTP Solution File: SEV219^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV219^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n104.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 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:53 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV219^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n104.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 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:31:36 CDT 2014
% % CPUTime : 300.02
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x23bb1b8>, <kernel.Type object at 0x23bb560>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1ffe320>, <kernel.DependentProduct object at 0x23bb2d8>) of role type named cP
% Using role type
% Declaring cP:(a->(a->a))
% FOF formula (<kernel.Constant object at 0x23bb128>, <kernel.Constant object at 0x23bb2d8>) of role type named cZ
% Using role type
% Declaring cZ:a
% FOF formula (<kernel.Constant object at 0x23bb1b8>, <kernel.DependentProduct object at 0x23db488>) of role type named cR
% Using role type
% Declaring cR:(a->a)
% FOF formula (<kernel.Constant object at 0x23bb0e0>, <kernel.DependentProduct object at 0x23db4d0>) of role type named cL
% Using role type
% Declaring cL:(a->a)
% FOF formula (((and ((and ((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx:a) (Xy:a), (((eq a) (cL ((cP Xx) Xy))) Xx)))) (forall (Xx:a) (Xy:a), (((eq a) (cR ((cP Xx) Xy))) Xy)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->(forall (Xb:a), ((forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx:a), ((X Xx)->((and (X ((cP Xx) cZ))) (X ((cP Xx) ((cP cZ) cZ)))))))->(X Xb)))->(forall (D:(a->Prop)), (((and ((and ((and (forall (Xx:a), ((D Xx)->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) (D cZ))) (forall (Xx:a), ((D Xx)->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->(D Xy))))))) (forall (Xx:a) (Xy:a), (((and (D Xx)) (D Xy))->((ex a) (fun (Xz:a)=> ((D Xz)->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))->((and ((and ((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_2:a)=> ((ex a) (fun (Xu_1:a)=> ((and (((eq a) ((cP Xb) cZ)) ((cP Xb_2) Xu_1))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_2) Xu_1))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_3:a)=> ((ex a) (fun (Xu_2:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_3) Xu_2))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_3) Xu_2))))))))))))->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_4:a)=> ((ex a) (fun (Xu_6:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_4) Xu_6))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_4) Xu_6)))))))))))))))))) (forall (Xx:a) (Xy:a), (((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_5:a)=> ((ex a) (fun (Xu_7:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_5) Xu_7))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_5) Xu_7))))))))))))) ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_6:a)=> ((ex a) (fun (Xu_8:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_6) Xu_8))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_6) Xu_8)))))))))))))->((ex a) (fun (Xz:a)=> (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_7:a)=> ((ex a) (fun (Xu_9:a)=> ((and (((eq a) ((cP Xb) Xz)) ((cP Xb_7) Xu_9))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_7) Xu_9))))))))))))->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx))))))))))) of role conjecture named cPU_LEM9_pme
% Conjecture to prove = (((and ((and ((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx:a) (Xy:a), (((eq a) (cL ((cP Xx) Xy))) Xx)))) (forall (Xx:a) (Xy:a), (((eq a) (cR ((cP Xx) Xy))) Xy)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->(forall (Xb:a), ((forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx:a), ((X Xx)->((and (X ((cP Xx) cZ))) (X ((cP Xx) ((cP cZ) cZ)))))))->(X Xb)))->(forall (D:(a->Prop)), (((and ((and ((and (forall (Xx:a), ((D Xx)->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) (D cZ))) (forall (Xx:a), ((D Xx)->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->(D Xy))))))) (forall (Xx:a) (Xy:a), (((and (D Xx)) (D Xy))->((ex a) (fun (Xz:a)=> ((D Xz)->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))->((and ((and ((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_2:a)=> ((ex a) (fun (Xu_1:a)=> ((and (((eq a) ((cP Xb) cZ)) ((cP Xb_2) Xu_1))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_2) Xu_1))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_3:a)=> ((ex a) (fun (Xu_2:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_3) Xu_2))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_3) Xu_2))))))))))))->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_4:a)=> ((ex a) (fun (Xu_6:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_4) Xu_6))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_4) Xu_6)))))))))))))))))) (forall (Xx:a) (Xy:a), (((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_5:a)=> ((ex a) (fun (Xu_7:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_5) Xu_7))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_5) Xu_7))))))))))))) ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_6:a)=> ((ex a) (fun (Xu_8:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_6) Xu_8))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_6) Xu_8)))))))))))))->((ex a) (fun (Xz:a)=> (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_7:a)=> ((ex a) (fun (Xu_9:a)=> ((and (((eq a) ((cP Xb) Xz)) ((cP Xb_7) Xu_9))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_7) Xu_9))))))))))))->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx))))))))))):Prop
% We need to prove ['(((and ((and ((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx:a) (Xy:a), (((eq a) (cL ((cP Xx) Xy))) Xx)))) (forall (Xx:a) (Xy:a), (((eq a) (cR ((cP Xx) Xy))) Xy)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->(forall (Xb:a), ((forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx:a), ((X Xx)->((and (X ((cP Xx) cZ))) (X ((cP Xx) ((cP cZ) cZ)))))))->(X Xb)))->(forall (D:(a->Prop)), (((and ((and ((and (forall (Xx:a), ((D Xx)->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) (D cZ))) (forall (Xx:a), ((D Xx)->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->(D Xy))))))) (forall (Xx:a) (Xy:a), (((and (D Xx)) (D Xy))->((ex a) (fun (Xz:a)=> ((D Xz)->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))->((and ((and ((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_2:a)=> ((ex a) (fun (Xu_1:a)=> ((and (((eq a) ((cP Xb) cZ)) ((cP Xb_2) Xu_1))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_2) Xu_1))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_3:a)=> ((ex a) (fun (Xu_2:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_3) Xu_2))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_3) Xu_2))))))))))))->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_4:a)=> ((ex a) (fun (Xu_6:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_4) Xu_6))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_4) Xu_6)))))))))))))))))) (forall (Xx:a) (Xy:a), (((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_5:a)=> ((ex a) (fun (Xu_7:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_5) Xu_7))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_5) Xu_7))))))))))))) ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_6:a)=> ((ex a) (fun (Xu_8:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_6) Xu_8))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_6) Xu_8)))))))))))))->((ex a) (fun (Xz:a)=> (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_7:a)=> ((ex a) (fun (Xu_9:a)=> ((and (((eq a) ((cP Xb) Xz)) ((cP Xb_7) Xu_9))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_7) Xu_9))))))))))))->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))))))))']
% Parameter a:Type.
% Parameter cP:(a->(a->a)).
% Parameter cZ:a.
% Parameter cR:(a->a).
% Parameter cL:(a->a).
% Trying to prove (((and ((and ((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx:a) (Xy:a), (((eq a) (cL ((cP Xx) Xy))) Xx)))) (forall (Xx:a) (Xy:a), (((eq a) (cR ((cP Xx) Xy))) Xy)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->(forall (Xb:a), ((forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx:a), ((X Xx)->((and (X ((cP Xx) cZ))) (X ((cP Xx) ((cP cZ) cZ)))))))->(X Xb)))->(forall (D:(a->Prop)), (((and ((and ((and (forall (Xx:a), ((D Xx)->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) (D cZ))) (forall (Xx:a), ((D Xx)->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->(D Xy))))))) (forall (Xx:a) (Xy:a), (((and (D Xx)) (D Xy))->((ex a) (fun (Xz:a)=> ((D Xz)->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))->((and ((and ((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_2:a)=> ((ex a) (fun (Xu_1:a)=> ((and (((eq a) ((cP Xb) cZ)) ((cP Xb_2) Xu_1))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_2) Xu_1))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_3:a)=> ((ex a) (fun (Xu_2:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_3) Xu_2))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_3) Xu_2))))))))))))->(forall (Xy:a), (((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xx))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))->((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_4:a)=> ((ex a) (fun (Xu_6:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_4) Xu_6))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_4) Xu_6)))))))))))))))))) (forall (Xx:a) (Xy:a), (((and ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_5:a)=> ((ex a) (fun (Xu_7:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_5) Xu_7))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_5) Xu_7))))))))))))) ((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_6:a)=> ((ex a) (fun (Xu_8:a)=> ((and (((eq a) ((cP Xb) Xy)) ((cP Xb_6) Xu_8))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_6) Xu_8)))))))))))))->((ex a) (fun (Xz:a)=> (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_7:a)=> ((ex a) (fun (Xu_9:a)=> ((and (((eq a) ((cP Xb) Xz)) ((cP Xb_7) Xu_9))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_7) Xu_9))))))))))))->((and ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xx) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu)))))))))) ((ex (a->Prop)) (fun (X:(a->Prop))=> ((and (X ((cP Xy) Xz))) (forall (Xt:a) (Xu:a), ((X ((cP Xt) Xu))->((and ((and ((((eq a) Xu) cZ)->(((eq a) Xt) cZ))) (X ((cP (cL Xt)) (cL Xu))))) (X ((cP (cR Xt)) (cR Xu))))))))))))))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))))))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))):(((eq Prop) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx))))))
% Found (eq_ref0 (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) as proof of (((eq Prop) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) as proof of (((eq Prop) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) as proof of (((eq Prop) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=> ((and (((eq a) ((cP Xb) Xx)) ((cP Xb_8) Xu_10))) (forall (X:(a->Prop)), (((and (X ((cP cZ) Xt))) (forall (Xc:a) (Xv:a), ((X ((cP Xc) Xv))->((and (X ((cP ((cP Xc) cZ)) (cL Xv)))) (X ((cP ((cP Xc) ((cP cZ) cZ))) (cR Xv)))))))->(X ((cP Xb_8) Xu_10))))))))))))->(forall (X:(a->Prop)), (((and (X cZ)) (forall (Xx0:a) (Xy:a), (((and (X Xx0)) (X Xy))->(X ((cP Xx0) Xy)))))->(X Xx)))))) b)
% Found ((eq_ref Prop) (forall (Xx:a), (((ex a) (fun (Xt:a)=> ((and (D Xt)) ((ex a) (fun (Xb_8:a)=> ((ex a) (fun (Xu_10:a)=>
% EOF
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