TSTP Solution File: SET629^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET629^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n105.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 0.87s
% Output : Proof 0.87s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET629^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n105.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 10:26:56 CDT 2014
% % CPUTime : 0.87
% 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 0x1f08bd8>, <kernel.Type object at 0x1f08e60>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False))))->False)) of role conjecture named cBOOL_PROP_111_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False))))->False)):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False))))->False))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False))))->False))
% Found x3:((Y x0)->False)
% Found (fun (x6:(X x0))=> x3) as proof of ((Y x0)->False)
% Found (fun (x6:(X x0))=> x3) as proof of ((X x0)->((Y x0)->False))
% Found (and_rect20 (fun (x6:(X x0))=> x3)) as proof of False
% Found ((and_rect2 False) (fun (x6:(X x0))=> x3)) as proof of False
% Found (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)) as proof of False
% Found (fun (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))) as proof of False
% Found (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))) as proof of ((X x0)->False)
% Found (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))) as proof of (((and (X x0)) (Y x0))->((X x0)->False))
% Found (and_rect10 (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))) as proof of False
% Found ((and_rect1 False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))) as proof of False
% Found (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))) as proof of False
% Found (fun (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))) as proof of False
% Found (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))) as proof of (((Y x0)->False)->False)
% Found (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))) as proof of (((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->False))
% Found (and_rect00 (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))) as proof of False
% Found ((and_rect0 False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))) as proof of False
% Found (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))) as proof of False
% Found (fun (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))))) as proof of False
% Found (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))))) as proof of (((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False))->False)
% Found (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))))) as proof of (forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->False))
% Found (ex_ind00 (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))))) as proof of False
% Found ((ex_ind0 False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))))) as proof of False
% Found (((fun (P:Prop) (x0:(forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))))) as proof of False
% Found (fun (x:((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))))))) as proof of False
% Found (fun (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))))))) as proof of (((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False))))->False)
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))))))) as proof of (forall (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False))))->False))
% Found (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3))))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)), (((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False))))->False))
% Got proof (fun (X:(a->Prop)) (Y:(a->Prop)) (x:((ex a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))))))
% Time elapsed = 0.556456s
% node=78 cost=499.000000 depth=26
% ::::::::::::::::::::::
% % 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 ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))))=> (((fun (P:Prop) (x0:(forall (x:a), (((and ((and ((and (X x)) (Y x))) (X x))) ((Y x)->False))->P)))=> (((((ex_ind a) (fun (Xx:a)=> ((and ((and ((and (X Xx)) (Y Xx))) (X Xx))) ((Y Xx)->False)))) P) x0) x)) False) (fun (x0:a) (x1:((and ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)))=> (((fun (P:Type) (x2:(((and ((and (X x0)) (Y x0))) (X x0))->(((Y x0)->False)->P)))=> (((((and_rect ((and ((and (X x0)) (Y x0))) (X x0))) ((Y x0)->False)) P) x2) x1)) False) (fun (x2:((and ((and (X x0)) (Y x0))) (X x0))) (x3:((Y x0)->False))=> (((fun (P:Type) (x4:(((and (X x0)) (Y x0))->((X x0)->P)))=> (((((and_rect ((and (X x0)) (Y x0))) (X x0)) P) x4) x2)) False) (fun (x4:((and (X x0)) (Y x0))) (x5:(X x0))=> (((fun (P:Type) (x6:((X x0)->((Y x0)->P)))=> (((((and_rect (X x0)) (Y x0)) P) x6) x4)) False) (fun (x6:(X x0))=> x3)))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------