TSTP Solution File: SEV164^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV164^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n117.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 13:33:49 EDT 2014
% Result : Unknown 2.77s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEV164^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n117.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 08:17:36 CDT 2014
% % CPUTime : 2.77
% 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 0x146e1b8>, <kernel.Type object at 0x144e200>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))), ((iff ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) ((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))) of role conjecture named cTHM185_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))), ((iff ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) ((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))), ((iff ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) ((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy)))))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))), ((iff ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) ((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy)))))))
% Found x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy)))
% Instantiate: x2:=(x0 (fun (Xx:a) (Xy:a)=> Xx)):a;x3:=(x0 (fun (Xx:a) (Xy:a)=> Xy)):a
% Found x1 as proof of ((Xr x2) x3)
% Found (ex_intro010 x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found ((ex_intro01 (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (ex_intro000 (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((ex_intro00 (x0 (fun (Xx:a) (Xy:a)=> Xx))) (((ex_intro0 (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (((ex_intro0 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) (((ex_intro0 (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of (((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy)))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))))
% Found (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of (forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))))
% Found (ex_ind00 (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((ex_ind0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x:((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))=> (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x:((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))=> (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))))) as proof of (((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy)))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))))
% Found x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy)))
% Instantiate: x2:=(x0 (fun (Xx:a) (Xy:a)=> Xx)):a;x3:=(x0 (fun (Xx:a) (Xy:a)=> Xy)):a
% Found x1 as proof of ((Xr x2) x3)
% Found (ex_intro010 x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found ((ex_intro01 (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (ex_intro000 (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((ex_intro00 (x0 (fun (Xx:a) (Xy:a)=> Xx))) (((ex_intro0 (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (((ex_intro0 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) (((ex_intro0 (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of (((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy)))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))))
% Found (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of (forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))))
% Found (ex_ind00 (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((ex_ind0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x:((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))=> (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x:((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))=> (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))))) as proof of (((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy)))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))))
% Found x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy)))
% Instantiate: x2:=(x0 (fun (Xx:a) (Xy:a)=> Xx)):a;x3:=(x0 (fun (Xx:a) (Xy:a)=> Xy)):a
% Found x1 as proof of ((Xr x2) x3)
% Found (ex_intro010 x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found ((ex_intro01 (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1) as proof of ((ex a) (fun (Xy:a)=> ((Xr x2) Xy)))
% Found (ex_intro000 (((ex_intro0 (fun (Xy:a)=> ((Xr x2) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((ex_intro00 (x0 (fun (Xx:a) (Xy:a)=> Xx))) (((ex_intro0 (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (((ex_intro0 (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) (((ex_intro0 (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of (((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy)))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))))
% Found (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))) as proof of (forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))))
% Found (ex_ind00 (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found ((ex_ind0 ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1)))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x:((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))=> (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))))) as proof of ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))
% Found (fun (x:((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))))=> (((fun (P:Prop) (x0:(forall (x:((a->(a->a))->a)), (((Xr (x (fun (Xx:a) (Xy:a)=> Xx))) (x (fun (Xx:a) (Xy:a)=> Xy)))->P)))=> (((((ex_ind ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy))))) P) x0) x)) ((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy)))))) (fun (x0:((a->(a->a))->a)) (x1:((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) (x0 (fun (Xx:a) (Xy:a)=> Xy))))=> ((((ex_intro a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))) (x0 (fun (Xx:a) (Xy:a)=> Xx))) ((((ex_intro a) (fun (Xy:a)=> ((Xr (x0 (fun (Xx:a) (Xy:a)=> Xx))) Xy))) (x0 (fun (Xx:a) (Xy:a)=> Xy))) x1))))) as proof of (((ex ((a->(a->a))->a)) (fun (Xp:((a->(a->a))->a))=> ((Xr (Xp (fun (Xx:a) (Xy:a)=> Xx))) (Xp (fun (Xx:a) (Xy:a)=> Xy)))))->((ex a) (fun (Xx:a)=> ((ex a) (fun (Xy:a)=> ((Xr Xx) Xy))))))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------