TSTP Solution File: ALG286^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ALG286^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n106.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 13:18:23 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG286^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.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 09:08:36 CDT 2014
% % CPUTime : 300.03
% 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 0x1bf5830>, <kernel.Type object at 0x1bf5d40>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1fcd128>, <kernel.Constant object at 0x1bf59e0>) of role type named cZ
% Using role type
% Declaring cZ:a
% FOF formula (<kernel.Constant object at 0x1bf58c0>, <kernel.Constant object at 0x1bf59e0>) of role type named u
% Using role type
% Declaring u:a
% FOF formula (<kernel.Constant object at 0x1bf5830>, <kernel.Constant object at 0x1bf59e0>) of role type named y
% Using role type
% Declaring y:a
% FOF formula (<kernel.Constant object at 0x1bf5c20>, <kernel.Constant object at 0x1bf59e0>) of role type named x
% Using role type
% Declaring x:a
% FOF formula (<kernel.Constant object at 0x1bf58c0>, <kernel.DependentProduct object at 0x1bf5cb0>) of role type named cP
% Using role type
% Declaring cP:(a->(a->a))
% FOF formula (<kernel.Constant object at 0x1bf5560>, <kernel.DependentProduct object at 0x1bf5758>) of role type named cR
% Using role type
% Declaring cR:(a->a)
% FOF formula (<kernel.Constant object at 0x1bf59e0>, <kernel.DependentProduct object at 0x1bf5830>) 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 (Xx0:a) (Xy0:a), (((eq a) (cL ((cP Xx0) Xy0))) Xx0)))) (forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->((((eq a) u) ((cP x) y))->(not (((eq a) u) cZ)))) of role conjecture named cPU_PAIR_NOT_ZERO_pme
% Conjecture to prove = (((and ((and ((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx0:a) (Xy0:a), (((eq a) (cL ((cP Xx0) Xy0))) Xx0)))) (forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->((((eq a) u) ((cP x) y))->(not (((eq a) u) cZ)))):Prop
% We need to prove ['(((and ((and ((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx0:a) (Xy0:a), (((eq a) (cL ((cP Xx0) Xy0))) Xx0)))) (forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->((((eq a) u) ((cP x) y))->(not (((eq a) u) cZ))))']
% Parameter a:Type.
% Parameter cZ:a.
% Parameter u:a.
% Parameter y:a.
% Parameter x:a.
% Parameter cP:(a->(a->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 (Xx0:a) (Xy0:a), (((eq a) (cL ((cP Xx0) Xy0))) Xx0)))) (forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))) (forall (Xt:a), ((iff (not (((eq a) Xt) cZ))) (((eq a) Xt) ((cP (cL Xt)) (cR Xt))))))->((((eq a) u) ((cP x) y))->(not (((eq a) u) cZ))))
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x8:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x8 as proof of (((eq a) Xt) cZ)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x8:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x8 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x50:(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found x50 as proof of (not (((eq a) u) cZ))
% Found x10:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x10 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x8:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x8 as proof of (((eq a) Xt) cZ)
% Found x50:=(x5 x40):(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found x10:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x10 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x8:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x8 as proof of (((eq a) Xt) cZ)
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x50:=(x5 x40):(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x5 x40)) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x5 x40)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->(not (((eq a) u) cZ)))
% Found x10:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x10 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x8:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x8 as proof of (((eq a) Xt) cZ)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x50:=(x5 x40):(not (((eq a) Xt) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found x1:(((eq a) u) ((cP x) y))
% Found x1 as proof of (((eq a) Xt) ((cP x) y))
% Found x50:=(x5 x40):(not (((eq a) Xt) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x5 x40)) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x5 x40)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->(not (((eq a) u) cZ)))
% Found x40:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x40 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found x1:(((eq a) u) ((cP x) y))
% Found x1 as proof of (((eq a) Xt) ((cP x) y))
% Found x6:(((eq a) u) cZ)
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x4:(((eq a) u) cZ)
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x1:(((eq a) u) ((cP x) y))
% Found x1 as proof of (((eq a) Xt) ((cP x) y))
% Found x2:(((eq a) u) cZ)
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x1:(((eq a) u) ((cP x) y))
% Found x1 as proof of (((eq a) Xt) ((cP x) y))
% Found x40:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x40 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x5 x40)) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x5 x40)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->(not (((eq a) u) cZ)))
% Found x40:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x40 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found ((x5 x40) x6) as proof of False
% Found ((x5 x40) x6) as proof of False
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x50:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x50 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found ((x6 x50) x4) as proof of False
% Found ((x6 x50) x4) as proof of False
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found (x50 x6) as proof of False
% Found ((x5 x40) x6) as proof of False
% Found ((x5 x40) x6) as proof of False
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found (x60 x4) as proof of False
% Found ((x6 x50) x4) as proof of False
% Found ((x6 x50) x4) as proof of False
% Found x50:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x50 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found ((x6 x50) x2) as proof of False
% Found ((x6 x50) x2) as proof of False
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found (x60 x2) as proof of False
% Found ((x6 x50) x2) as proof of False
% Found ((x6 x50) x2) as proof of False
% Found x6:(((eq a) Xt) cZ)
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x50:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x50 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found ((x6 x50) x4) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x4)) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x4)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->False)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x40:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x40 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found ((x5 x40) x6) as proof of False
% Found (fun (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of False
% Found (fun (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of (not (((eq a) u) cZ))
% Found x70:(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found x70 as proof of (not (((eq a) u) cZ))
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found (x60 x4) as proof of False
% Found ((x6 x50) x4) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x4)) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x4)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->False)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x50:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x50 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found ((x6 x50) x2) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x2)) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x2)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->False)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found (x50 x6) as proof of False
% Found ((x5 x40) x6) as proof of False
% Found (fun (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of False
% Found (fun (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of (not (((eq a) u) cZ))
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found (x60 x2) as proof of False
% Found ((x6 x50) x2) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x2)) as proof of False
% Found (fun (x6:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> ((x6 x50) x2)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->False)
% Found x50:(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found x50 as proof of (not (((eq a) u) cZ))
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x40:(((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found x40 as proof of (((eq a) Xt) ((cP (cL Xt)) (cR Xt)))
% Found ((x5 x40) x6) as proof of False
% Found (fun (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of False
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))) (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))) (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->(not (((eq a) u) cZ)))
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found x6:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x6 as proof of (((eq a) Xt) cZ)
% Found (x50 x6) as proof of False
% Found ((x5 x40) x6) as proof of False
% Found (fun (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of False
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))) (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of (not (((eq a) u) cZ))
% Found (fun (x5:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))) (x6:(((eq a) u) cZ))=> ((x5 x40) x6)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->(not (((eq a) u) cZ)))
% Found x4:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x4 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x50:(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))=> x50) as proof of (not (((eq a) u) cZ))
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))=> x50) as proof of ((forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0))->(not (((eq a) u) cZ)))
% Found x11:(((eq a) (cR cZ)) cZ)
% Instantiate: Xt:=(cR cZ):a
% Found x11 as proof of (((eq a) Xt) cZ)
% Found x2:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x2 as proof of (((eq a) Xt) cZ)
% Found x11:(((eq a) (cL cZ)) cZ)
% Instantiate: Xt:=(cL cZ):a
% Found x11 as proof of (((eq a) Xt) cZ)
% Found x50:(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))=> x50) as proof of (not (((eq a) u) cZ))
% Found (fun (x6:((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx0:a) (Xy0:a), (((eq a) (cL ((cP Xx0) Xy0))) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))=> x50) as proof of ((forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0))->(not (((eq a) u) cZ)))
% Found (fun (x6:((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx0:a) (Xy0:a), (((eq a) (cL ((cP Xx0) Xy0))) Xx0)))) (x7:(forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0)))=> x50) as proof of (((and ((and (((eq a) (cL cZ)) cZ)) (((eq a) (cR cZ)) cZ))) (forall (Xx0:a) (Xy0:a), (((eq a) (cL ((cP Xx0) Xy0))) Xx0)))->((forall (Xx0:a) (Xy0:a), (((eq a) (cR ((cP Xx0) Xy0))) Xy0))->(not (((eq a) u) cZ))))
% Found x11:(((eq a) (cL cZ)) cZ)
% Instantiate: Xt:=(cL cZ):a
% Found x11 as proof of (((eq a) Xt) cZ)
% Found x70:=(x7 x60):(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (x7 x60) as proof of (not (((eq a) u) cZ))
% Found (x7 x60) as proof of (not (((eq a) u) cZ))
% Found x8:(((eq a) u) cZ)
% Instantiate: Xt:=u:a
% Found x8 as proof of (((eq a) Xt) cZ)
% Found x11:(((eq a) (cL cZ)) cZ)
% Instantiate: Xt:=(cL cZ):a
% Found x11 as proof of (((eq a) Xt) cZ)
% Found x50:=(x5 x40):(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found x70:=(x7 x60):(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (x7 x60) as proof of (not (((eq a) u) cZ))
% Found (fun (x7:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x7 x60)) as proof of (not (((eq a) u) cZ))
% Found (fun (x7:((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ))))=> (x7 x60)) as proof of (((((eq a) Xt) ((cP (cL Xt)) (cR Xt)))->(not (((eq a) Xt) cZ)))->(not (((eq a) u) cZ)))
% Found x7:(P Xt)
% Found x7 as proof of (P0 Xt)
% Found x7:(P Xt)
% Found x7 as proof of (P0 Xt)
% Found x7:(P Xt)
% Found x7 as proof of (P0 Xt)
% Found x50:=(x5 x40):(not (((eq a) Xt) cZ))
% Instantiate: Xt:=u:a
% Found (x5 x40) as proof of (not (((eq a) u) cZ))
% Found (fun (x7:(forall (Xx0:a) (Xy0:a), (((eq a) (cR ((c
% EOF
%------------------------------------------------------------------------------