%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU970^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% 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 13:33:27 EDT 2014

% Result   : Theorem 5.61s
% Output   : Proof 5.61s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU970^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % 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 11:46:46 CDT 2014
% % CPUTime  : 5.61 
% 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 0x1622cf8>, <kernel.DependentProduct object at 0x1803908>) of role type named s_type
% Using role type
% Declaring s:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1805170>, <kernel.DependentProduct object at 0x1803638>) of role type named cCKB_E2_type
% Using role type
% Declaring cCKB_E2:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) cCKB_E2) (fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy))))) of role definition named cCKB_E2_def
% A new definition: (((eq (fofType->(fofType->Prop))) cCKB_E2) (fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy)))))
% Defined: cCKB_E2:=(fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy))))
% FOF formula (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))) of role conjecture named cCKB_L34000_pme
% Conjecture to prove = (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz)))']
% Parameter fofType:Type.
% Parameter s:(fofType->fofType).
% Definition cCKB_E2:=(fun (Xx:fofType) (Xy:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy)))):(fofType->(fofType->Prop)).
% Trying to prove (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz)))
% Found x0:((cCKB_E2 Xx) Xy)
% Found x0 as proof of ((cCKB_E2 Xx) Xy)
% Found x00:=(x0 Xp):(((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy))
% Found (x0 Xp) as proof of (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy))
% Found (x0 Xp) as proof of (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xy))
% Found x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found x2 as proof of ((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found x0:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found x0 as proof of ((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found x000:=(x00 x2):(Xp Xy)
% Found (x00 x2) as proof of (Xp Xy)
% Found ((x0 Xp) x2) as proof of (Xp Xy)
% Found ((x0 Xp) x2) as proof of (Xp Xy)
% Found x100:=(x10 x0):(Xp Xy)
% Found (x10 x0) as proof of (Xp Xy)
% Found ((x1 Xp) x0) as proof of (Xp Xy)
% Found ((x1 Xp) x0) as proof of (Xp Xy)
% Found x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))
% Found x4 as proof of (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))
% Found x000:=(x00 x2):(Xp Xy)
% Found (x00 x2) as proof of (Xp Xy)
% Found ((x0 Xp) x2) as proof of (Xp Xy)
% Found ((x0 Xp) x2) as proof of (Xp Xy)
% Found ((conj00 ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found (((conj0 (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4) as proof of ((and (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))
% Found (x10 ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)) as proof of (Xp Xz)
% Found ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)) as proof of (Xp Xz)
% Found (fun (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))) as proof of (Xp Xz)
% Found (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))) as proof of ((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->(Xp Xz))
% Found (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))) as proof of ((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->(Xp Xz)))
% Found (and_rect10 (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))) as proof of (Xp Xz)
% Found ((and_rect1 (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))) as proof of (Xp Xz)
% Found (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))) as proof of (Xp Xz)
% Found (fun (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (Xp Xz)
% Found (fun (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))->(Xp Xz))
% Found (fun (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of ((cCKB_E2 Xx) Xz)
% Found (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (((cCKB_E2 Xy) Xz)->((cCKB_E2 Xx) Xz))
% Found (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))) as proof of (((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->((cCKB_E2 Xx) Xz)))
% Found (and_rect00 (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))) as proof of ((cCKB_E2 Xx) Xz)
% Found ((and_rect0 ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))) as proof of ((cCKB_E2 Xx) Xz)
% Found (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))) as proof of ((cCKB_E2 Xx) Xz)
% Found (fun (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of ((cCKB_E2 Xx) Xz)
% Found (fun (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz))
% Found (fun (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (forall (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz)))
% Found (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (forall (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz)))
% Found (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4))))))) as proof of (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz))->((cCKB_E2 Xx) Xz)))
% Got proof (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))))
% Time elapsed = 5.229947s
% node=926 cost=595.000000 depth=27
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (Xx:fofType) (Xy:fofType) (Xz:fofType) (x:((and ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)))=> (((fun (P:Type) (x0:(((cCKB_E2 Xx) Xy)->(((cCKB_E2 Xy) Xz)->P)))=> (((((and_rect ((cCKB_E2 Xx) Xy)) ((cCKB_E2 Xy) Xz)) P) x0) x)) ((cCKB_E2 Xx) Xz)) (fun (x0:((cCKB_E2 Xx) Xy)) (x1:((cCKB_E2 Xy) Xz)) (Xp:(fofType->Prop)) (x2:((and (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))))=> (((fun (P:Type) (x3:((Xp Xx)->((forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))->P)))=> (((((and_rect (Xp Xx)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) P) x3) x2)) (Xp Xz)) (fun (x3:(Xp Xx)) (x4:(forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu))))))=> ((x1 Xp) ((((conj (Xp Xy)) (forall (Xu:fofType), ((Xp Xu)->(Xp (s (s Xu)))))) ((x0 Xp) x2)) x4)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------