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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV272^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n118.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 13:33:58 EDT 2014

% Result   : Theorem 0.59s
% Output   : Proof 0.59s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV272^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n118.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 08:41:26 CDT 2014
% % CPUTime  : 0.59 
% 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 0x27d4cf8>, <kernel.DependentProduct object at 0x27d4a70>) of role type named cSUCC_type
% Using role type
% Declaring cSUCC:(((fofType->Prop)->Prop)->((fofType->Prop)->Prop))
% FOF formula (<kernel.Constant object at 0x23f9dd0>, <kernel.DependentProduct object at 0x27d4b00>) of role type named cZERO_type
% Using role type
% Declaring cZERO:((fofType->Prop)->Prop)
% FOF formula (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))) of role definition named cSUCC_def
% A new definition: (((eq (((fofType->Prop)->Prop)->((fofType->Prop)->Prop))) cSUCC) (fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))))
% Defined: cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt))))))))
% FOF formula (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))) of role definition named cZERO_def
% A new definition: (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)))
% Defined: cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))
% FOF formula (((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx))))) of role conjecture named cX6007A_pme
% Conjecture to prove = (((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx)))))']
% Parameter fofType:Type.
% Definition cSUCC:=(fun (Xn:((fofType->Prop)->Prop)) (Xp:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xp Xx)) (Xn (fun (Xt:fofType)=> ((and (not (((eq fofType) Xt) Xx))) (Xp Xt)))))))):(((fofType->Prop)->Prop)->((fofType->Prop)->Prop)).
% Definition cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)):((fofType->Prop)->Prop).
% Trying to prove (((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx)))))
% Found eta_expansion000:=(eta_expansion00 (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))):(((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (x:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P x)))))
% Found (eta_expansion00 (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) as proof of (((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx)))))
% Found ((eta_expansion0 Prop) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) as proof of (((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx)))))
% Found (((eta_expansion ((fofType->Prop)->Prop)) Prop) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) as proof of (((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx)))))
% Found (((eta_expansion ((fofType->Prop)->Prop)) Prop) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) as proof of (((eq (((fofType->Prop)->Prop)->Prop)) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N))))) (fun (Xx:((fofType->Prop)->Prop))=> (forall (S:(((fofType->Prop)->Prop)->Prop)), (((and (S cZERO)) (forall (X:((fofType->Prop)->Prop)), ((S X)->(S (cSUCC X)))))->(S Xx)))))
% Got proof (((eta_expansion ((fofType->Prop)->Prop)) Prop) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N)))))
% Time elapsed = 0.259090s
% node=11 cost=-282.000000 depth=3
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (((eta_expansion ((fofType->Prop)->Prop)) Prop) (fun (N:((fofType->Prop)->Prop))=> (forall (P:(((fofType->Prop)->Prop)->Prop)), (((and (P cZERO)) (forall (X:((fofType->Prop)->Prop)), ((P X)->(P (cSUCC X)))))->(P N)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------