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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV289^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n053.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 : Tue Apr 21 16:51:41 EDT 2015

% Result   : Theorem 0.06s
% Output   : Proof 0.06s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEV289^5 : TPTP v6.2.0. Bugfixed v6.2.0.
% 0.00/0.03  % Command  : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/1.07  % Computer : n053.star.cs.uiowa.edu
% 0.03/1.07  % Model    : x86_64 x86_64
% 0.03/1.07  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/1.07  % Memory   : 32286.75MB
% 0.03/1.07  % OS       : Linux 2.6.32-504.8.1.el6.x86_64
% 0.03/1.07  % CPULimit : 300
% 0.03/1.07  % DateTime : Thu Apr 16 12:05:47 CDT 2015
% 0.03/1.07  % CPUTime  : 
% 0.03/1.09  Python 2.7.5
% 0.06/1.71  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.06/1.71  FOF formula (<kernel.Constant object at 0xb8ac20>, <kernel.DependentProduct object at 0xb8acf8>) of role type named cNAT_type
% 0.06/1.71  Using role type
% 0.06/1.71  Declaring cNAT:(((fofType->Prop)->Prop)->Prop)
% 0.06/1.71  FOF formula (<kernel.Constant object at 0xe523b0>, <kernel.DependentProduct object at 0xb8a440>) of role type named cSUCC_type
% 0.06/1.71  Using role type
% 0.06/1.71  Declaring cSUCC:(((fofType->Prop)->Prop)->((fofType->Prop)->Prop))
% 0.06/1.71  FOF formula (<kernel.Constant object at 0xb8abd8>, <kernel.DependentProduct object at 0xb8ac20>) of role type named cZERO_type
% 0.06/1.71  Using role type
% 0.06/1.71  Declaring cZERO:((fofType->Prop)->Prop)
% 0.06/1.71  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
% 0.06/1.71  A new definition: (((eq ((fofType->Prop)->Prop)) cZERO) (fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)))
% 0.06/1.71  Defined: cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False))
% 0.06/1.71  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
% 0.06/1.71  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)))))))))
% 0.06/1.71  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))))))))
% 0.06/1.71  FOF formula (((eq (((fofType->Prop)->Prop)->Prop)) cNAT) (fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn))))) of role definition named cNAT_def
% 0.06/1.71  A new definition: (((eq (((fofType->Prop)->Prop)->Prop)) cNAT) (fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn)))))
% 0.06/1.71  Defined: cNAT:=(fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn))))
% 0.06/1.71  FOF formula (forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->(cNAT (cSUCC Xx)))) of role conjecture named cTTTP6101
% 0.06/1.71  Conjecture to prove = (forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->(cNAT (cSUCC Xx)))):Prop
% 0.06/1.71  Parameter fofType_DUMMY:fofType.
% 0.06/1.71  We need to prove ['(forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->(cNAT (cSUCC Xx))))']
% 0.06/1.71  Parameter fofType:Type.
% 0.06/1.71  Definition cNAT:=(fun (Xn:((fofType->Prop)->Prop))=> (forall (Xp:(((fofType->Prop)->Prop)->Prop)), (((and (Xp cZERO)) (forall (Xx:((fofType->Prop)->Prop)), ((Xp Xx)->(Xp (cSUCC Xx)))))->(Xp Xn)))):(((fofType->Prop)->Prop)->Prop).
% 0.06/1.71  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)).
% 0.06/1.71  Definition cZERO:=(fun (Xp:(fofType->Prop))=> (((ex fofType) (fun (Xx:fofType)=> (Xp Xx)))->False)):((fofType->Prop)->Prop).
% 0.06/1.71  Trying to prove (forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->(cNAT (cSUCC Xx))))
% 0.06/1.71  Found x30:=(x3 x0):(Xp Xx)
% 0.06/1.71  Found (x3 x0) as proof of (Xp Xx)
% 0.06/1.71  Found ((x Xp) x0) as proof of (Xp Xx)
% 0.06/1.71  Found ((x Xp) x0) as proof of (Xp Xx)
% 0.06/1.71  Found (x20 ((x Xp) x0)) as proof of (Xp (cSUCC Xx))
% 0.06/1.71  Found ((x2 Xx) ((x Xp) x0)) as proof of (Xp (cSUCC Xx))
% 0.06/1.71  Found (fun (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))) as proof of (Xp (cSUCC Xx))
% 0.06/1.71  Found (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))) as proof of ((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->(Xp (cSUCC Xx)))
% 0.06/1.72  Found (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))) as proof of ((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->(Xp (cSUCC Xx))))
% 0.06/1.72  Found (and_rect00 (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0)))) as proof of (Xp (cSUCC Xx))
% 0.06/1.72  Found ((and_rect0 (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0)))) as proof of (Xp (cSUCC Xx))
% 0.06/1.72  Found (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0)))) as proof of (Xp (cSUCC Xx))
% 0.06/1.72  Found (fun (x0:((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))))=> (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))))) as proof of (Xp (cSUCC Xx))
% 0.06/1.72  Found (fun (Xp:(((fofType->Prop)->Prop)->Prop)) (x0:((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))))=> (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))))) as proof of (((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))->(Xp (cSUCC Xx)))
% 0.06/1.72  Found (fun (x:(cNAT Xx)) (Xp:(((fofType->Prop)->Prop)->Prop)) (x0:((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))))=> (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))))) as proof of (cNAT (cSUCC Xx))
% 0.06/1.72  Found (fun (Xx:((fofType->Prop)->Prop)) (x:(cNAT Xx)) (Xp:(((fofType->Prop)->Prop)->Prop)) (x0:((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))))=> (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))))) as proof of ((cNAT Xx)->(cNAT (cSUCC Xx)))
% 0.06/1.72  Found (fun (Xx:((fofType->Prop)->Prop)) (x:(cNAT Xx)) (Xp:(((fofType->Prop)->Prop)->Prop)) (x0:((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))))=> (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0))))) as proof of (forall (Xx:((fofType->Prop)->Prop)), ((cNAT Xx)->(cNAT (cSUCC Xx))))
% 0.06/1.72  Got proof (fun (Xx:((fofType->Prop)->Prop)) (x:(cNAT Xx)) (Xp:(((fofType->Prop)->Prop)->Prop)) (x0:((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))))=> (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0)))))
% 0.06/1.72  Time elapsed = 0.293779s
% 0.06/1.72  node=53 cost=207.000000 depth=15
% 0.06/1.72::::::::::::::::::::::
% 0.06/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/1.72  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/1.72  (fun (Xx:((fofType->Prop)->Prop)) (x:(cNAT Xx)) (Xp:(((fofType->Prop)->Prop)->Prop)) (x0:((and (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))))=> (((fun (P:Type) (x1:((Xp cZERO)->((forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))->P)))=> (((((and_rect (Xp cZERO)) (forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0))))) P) x1) x0)) (Xp (cSUCC Xx))) (fun (x1:(Xp cZERO)) (x2:(forall (Xx0:((fofType->Prop)->Prop)), ((Xp Xx0)->(Xp (cSUCC Xx0)))))=> ((x2 Xx) ((x Xp) x0)))))
% 0.06/1.72  % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------