cocATP---0.2.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SET626^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n094.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 13:30:53 EDT 2014

% Result   : Theorem 0.80s
% Output   : Proof 0.80s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET626^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n094.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 10:26:06 CDT 2014
% % CPUTime  : 0.80 
% 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 0x2590908>, <kernel.Type object at 0x2590ab8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x227afc8>, <kernel.DependentProduct object at 0x2590878>) of role type named cZ
% Using role type
% Declaring cZ:(a->Prop)
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))))) of role conjecture named cBOOL_PROP_102_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))']
% Parameter a:Type.
% Parameter cZ:(a->Prop).
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Found x3:((and (X x1)) (Y x1))
% Instantiate: x0:=x1:a
% Found (fun (x4:(cZ x1))=> x3) as proof of ((and (X x0)) (Y x0))
% Found (fun (x3:((and (X x1)) (Y x1))) (x4:(cZ x1))=> x3) as proof of ((cZ x1)->((and (X x0)) (Y x0)))
% Found (fun (x3:((and (X x1)) (Y x1))) (x4:(cZ x1))=> x3) as proof of (((and (X x1)) (Y x1))->((cZ x1)->((and (X x0)) (Y x0))))
% Found (and_rect00 (fun (x3:((and (X x1)) (Y x1))) (x4:(cZ x1))=> x3)) as proof of ((and (X x0)) (Y x0))
% Found ((and_rect0 ((and (X x0)) (Y x0))) (fun (x3:((and (X x1)) (Y x1))) (x4:(cZ x1))=> x3)) as proof of ((and (X x0)) (Y x0))
% Found (((fun (P:Type) (x3:(((and (X x1)) (Y x1))->((cZ x1)->P)))=> (((((and_rect ((and (X x1)) (Y x1))) (cZ x1)) P) x3) x2)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x1)) (Y x1))) (x4:(cZ x1))=> x3)) as proof of ((and (X x0)) (Y x0))
% Found (fun (x2:((and ((and (X x1)) (Y x1))) (cZ x1)))=> (((fun (P:Type) (x3:(((and (X x1)) (Y x1))->((cZ x1)->P)))=> (((((and_rect ((and (X x1)) (Y x1))) (cZ x1)) P) x3) x2)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x1)) (Y x1))) (x4:(cZ x1))=> x3))) as proof of ((and (X x0)) (Y x0))
% Found x3:((and (X x0)) (Y x0))
% Instantiate: x2:=x0:a
% Found (fun (x4:(cZ x0))=> x3) as proof of ((and (X x2)) (Y x2))
% Found (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3) as proof of ((cZ x0)->((and (X x2)) (Y x2)))
% Found (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3) as proof of (((and (X x0)) (Y x0))->((cZ x0)->((and (X x2)) (Y x2))))
% Found (and_rect00 (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)) as proof of ((and (X x2)) (Y x2))
% Found ((and_rect0 ((and (X x2)) (Y x2))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)) as proof of ((and (X x2)) (Y x2))
% Found (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x2)) (Y x2))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)) as proof of ((and (X x2)) (Y x2))
% Found (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x2)) (Y x2))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)) as proof of ((and (X x2)) (Y x2))
% Found (ex_intro000 (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x2)) (Y x2))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found ((ex_intro00 x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (((ex_intro0 (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (fun (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)))) as proof of (((and ((and (X x0)) (Y x0))) (cZ x0))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))))
% Found (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)))) as proof of (forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Found (ex_ind00 (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found ((ex_ind0 ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (fun (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (fun (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)))))) as proof of (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)))))) as proof of (forall (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3)))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))))))
% Time elapsed = 0.481864s
% node=67 cost=517.000000 depth=20
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) (cZ x))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) (cZ Xx)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) (cZ x0)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->((cZ x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (cZ x0)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:(cZ x0))=> x3))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------