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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU692^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n116.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 13:32:50 EDT 2014

% Result   : Theorem 1.94s
% Output   : Proof 1.94s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU692^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n116.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 11:13:06 CDT 2014
% % CPUTime  : 1.94 
% 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 0xfaa5a8>, <kernel.DependentProduct object at 0xfaa950>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x11881b8>, <kernel.DependentProduct object at 0xfaa950>) of role type named func_type
% Using role type
% Declaring func:(fofType->(fofType->(fofType->Prop)))
% FOF formula (<kernel.Constant object at 0xfaacf8>, <kernel.DependentProduct object at 0xfaa9e0>) of role type named funcSet_type
% Using role type
% Declaring funcSet:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xfaa6c8>, <kernel.DependentProduct object at 0xfaaf38>) of role type named ap_type
% Using role type
% Declaring ap:(fofType->(fofType->(fofType->(fofType->fofType))))
% FOF formula (<kernel.Constant object at 0xfaaf80>, <kernel.Sort object at 0x1258fc8>) of role type named infuncsetfunc_type
% Using role type
% Declaring infuncsetfunc:Prop
% FOF formula (((eq Prop) infuncsetfunc) (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))) of role definition named infuncsetfunc
% A new definition: (((eq Prop) infuncsetfunc) (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))))
% Defined: infuncsetfunc:=(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf)))
% FOF formula (<kernel.Constant object at 0xfaa488>, <kernel.Sort object at 0x1258fc8>) of role type named funcext_type
% Using role type
% Declaring funcext:Prop
% FOF formula (((eq Prop) funcext) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))) of role definition named funcext
% A new definition: (((eq Prop) funcext) (forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))))
% Defined: funcext:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))
% FOF formula (infuncsetfunc->(funcext->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))))) of role conjecture named funcext2
% Conjecture to prove = (infuncsetfunc->(funcext->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(infuncsetfunc->(funcext->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter func:(fofType->(fofType->(fofType->Prop))).
% Parameter funcSet:(fofType->(fofType->fofType)).
% Parameter ap:(fofType->(fofType->(fofType->(fofType->fofType)))).
% Definition infuncsetfunc:=(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(((func A) B) Xf))):Prop.
% Definition funcext:=(forall (A:fofType) (B:fofType) (Xf:fofType), ((((func A) B) Xf)->(forall (Xg:fofType), ((((func A) B) Xg)->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))):Prop.
% Trying to prove (infuncsetfunc->(funcext->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))))
% Found eq_ref000:=(eq_ref00 P):((P Xf)->(P Xf))
% Found (eq_ref00 P) as proof of (P0 Xf)
% Found ((eq_ref0 Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found (((eq_ref fofType) Xf) P) as proof of (P0 Xf)
% Found eq_ref00:=(eq_ref0 Xf):(((eq fofType) Xf) Xf)
% Found (eq_ref0 Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found ((eq_ref fofType) Xf) as proof of (((eq fofType) Xf) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xg)
% Found x3000:=(x300 x2):(((func A) B) Xg)
% Found (x300 x2) as proof of (((func A) B) Xg)
% Found ((x30 Xg) x2) as proof of (((func A) B) Xg)
% Found (((x3 B) Xg) x2) as proof of (((func A) B) Xg)
% Found ((((x A) B) Xg) x2) as proof of (((func A) B) Xg)
% Found ((((x A) B) Xg) x2) as proof of (((func A) B) Xg)
% Found x3000:=(x300 x1):(((func A) B) Xf)
% Found (x300 x1) as proof of (((func A) B) Xf)
% Found ((x30 Xf) x1) as proof of (((func A) B) Xf)
% Found (((x3 B) Xf) x1) as proof of (((func A) B) Xf)
% Found ((((x A) B) Xf) x1) as proof of (((func A) B) Xf)
% Found ((((x A) B) Xf) x1) as proof of (((func A) B) Xf)
% Found ((x00000 ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2)) as proof of ((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))
% Found (((fun (x3:(((func A) B) Xf))=> ((x0000 x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2)) as proof of ((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))
% Found (((fun (x3:(((func A) B) Xf))=> (((x000 Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2)) as proof of ((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))
% Found (((fun (x3:(((func A) B) Xf))=> ((((x00 B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2)) as proof of ((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))
% Found (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2)) as proof of ((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))
% Found (fun (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of ((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))
% Found (fun (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))
% Found (fun (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))
% Found (fun (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))
% Found (fun (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (forall (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))
% Found (fun (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (forall (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))
% Found (fun (x0:funcext) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))
% Found (fun (x:infuncsetfunc) (x0:funcext) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (funcext->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg)))))))
% Found (fun (x:infuncsetfunc) (x0:funcext) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2))) as proof of (infuncsetfunc->(funcext->(forall (A:fofType) (B:fofType) (Xf:fofType), (((in Xf) ((funcSet A) B))->(forall (Xg:fofType), (((in Xg) ((funcSet A) B))->((forall (Xx:fofType), (((in Xx) A)->(((eq fofType) ((((ap A) B) Xf) Xx)) ((((ap A) B) Xg) Xx))))->(((eq fofType) Xf) Xg))))))))
% Got proof (fun (x:infuncsetfunc) (x0:funcext) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2)))
% Time elapsed = 1.602534s
% node=218 cost=373.000000 depth=18
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:infuncsetfunc) (x0:funcext) (A:fofType) (B:fofType) (Xf:fofType) (x1:((in Xf) ((funcSet A) B))) (Xg:fofType) (x2:((in Xg) ((funcSet A) B)))=> (((fun (x3:(((func A) B) Xf))=> (((((x0 A) B) Xf) x3) Xg)) ((((x A) B) Xf) x1)) ((((x A) B) Xg) x2)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------