TSTP Solution File: SET631^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET631^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n179.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 13:30:54 EDT 2014
% Result : Theorem 1.15s
% Output : Proof 1.15s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET631^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n179.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 10:27:31 CDT 2014
% % CPUTime : 1.15
% 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 0x21f4830>, <kernel.Type object at 0x21f4ef0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))))) of role conjecture named cBOOL_PROP_113_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((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)) (Z:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Found x3:((and (X x0)) (Y x0))
% Instantiate: x2:=x0:a
% Found (fun (x4:((Z x0)->False))=> x3) as proof of ((and (X x2)) (Y x2))
% Found (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3) as proof of (((Z x0)->False)->((and (X x2)) (Y x2)))
% Found (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3) as proof of (((and (X x0)) (Y x0))->(((Z x0)->False)->((and (X x2)) (Y x2))))
% Found (and_rect00 (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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:((Z x0)->False))=> x3)) as proof of ((and (X x2)) (Y x2))
% Found (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x2)) (Y x2))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)) as proof of ((and (X x2)) (Y x2))
% Found (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x2)) (Y x2))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)) as proof of ((and (X x2)) (Y x2))
% Found (ex_intro000 (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x2)) (Y x2))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (fun (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)))) as proof of (((and ((and (X x0)) (Y x0))) ((Z x0)->False))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))))
% Found (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)))) as proof of (forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Found (ex_ind00 (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> 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))) ((Z Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)))))) as proof of ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))
% Found (fun (Z:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)))))) as proof of (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))))
% Found (fun (Y:(a->Prop)) (Z:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)))))) as proof of (forall (Z:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)))))) as proof of (forall (Y:(a->Prop)) (Z:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3)))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False))))->((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3))))))
% Time elapsed = 0.826717s
% node=130 cost=540.000000 depth=21
% ::::::::::::::::::::::
% % 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)) (Z:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and (X x)) (Y x))) ((Z x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and (X Xx)) (Y Xx))) ((Z Xx)->False)))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx))))) (fun (x0:a) (x1:((and ((and (X x0)) (Y x0))) ((Z x0)->False)))=> ((((ex_intro a) (fun (Xx:a)=> ((and (X Xx)) (Y Xx)))) x0) (((fun (P:Type) (x3:(((and (X x0)) (Y x0))->(((Z x0)->False)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) ((Z x0)->False)) P) x3) x1)) ((and (X x0)) (Y x0))) (fun (x3:((and (X x0)) (Y x0))) (x4:((Z x0)->False))=> x3))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------