cocATP---0.2.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV224^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n115.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 13:33:54 EDT 2014

% Result   : Theorem 1.41s
% Output   : Proof 1.41s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV224^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.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 08:32:41 CDT 2014
% % CPUTime  : 1.41 
% 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 0x1df1950>, <kernel.Type object at 0x1df1f80>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1cb9cb0>, <kernel.Type object at 0x1df1518>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)), ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))))) of role conjecture named cTHM142_1_pme
% Conjecture to prove = (forall (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)), ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))))):Prop
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)), ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))))']
% Parameter b:Type.
% Parameter a:Type.
% Trying to prove (forall (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)), ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))))
% Found x1:((x0 Xr) Xs)
% Found x1 as proof of (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))
% Found (fun (x1:((x0 Xr) Xs))=> x1) as proof of (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))
% Found (fun (x1:((x0 Xr) Xs))=> x1) as proof of (((x0 Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))
% Found x1:=(x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))):((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))
% Found (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) as proof of ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->((x0 Xr) Xs))
% Found (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) as proof of ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->((x0 Xr) Xs))
% Found ((conj00 (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:((x0 Xr) Xs))=> x1)) as proof of ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((x0 Xr) Xs))
% Found (((conj0 (((x0 Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:((x0 Xr) Xs))=> x1)) as proof of ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((x0 Xr) Xs))
% Found ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->((x0 Xr) Xs))) (((x0 Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:((x0 Xr) Xs))=> x1)) as proof of ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((x0 Xr) Xs))
% Found (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->((x0 Xr) Xs))) (((x0 Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:((x0 Xr) Xs))=> x1))) as proof of ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((x0 Xr) Xs))
% Found (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->((x0 Xr) Xs))) (((x0 Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:((x0 Xr) Xs))=> x1))) as proof of (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((x0 Xr) Xs)))
% Found (ex_intro000 (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->((x0 Xr) Xs))) (((x0 Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:((x0 Xr) Xs))=> x1)))) as proof of ((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))
% Found ((ex_intro00 (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1)))) as proof of ((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))
% Found (((ex_intro0 (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1)))) as proof of ((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))
% Found ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1)))) as proof of ((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))
% Found (fun (x:(((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy))))=> ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1))))) as proof of ((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))
% Found (fun (Xr:(b->Prop)) (x:(((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy))))=> ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1))))) as proof of ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))))
% Found (fun (Xy:a) (Xr:(b->Prop)) (x:(((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy))))=> ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1))))) as proof of (forall (Xr:(b->Prop)), ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))))
% Found (fun (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)) (x:(((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy))))=> ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1))))) as proof of (forall (Xy:a) (Xr:(b->Prop)), ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))))
% Found (fun (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)) (x:(((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy))))=> ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1))))) as proof of (forall (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)), ((((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy)))->((ex ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs)))))))
% Got proof (fun (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)) (x:(((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy))))=> ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1)))))
% Time elapsed = 1.083457s
% node=93 cost=341.000000 depth=15
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (Xa:(b->(a->Prop))) (Xy:a) (Xr:(b->Prop)) (x:(((eq (b->Prop)) Xr) (fun (Xj:b)=> ((Xa Xj) Xy))))=> ((((ex_intro ((b->Prop)->((b->Prop)->Prop))) (fun (Xp:((b->Prop)->((b->Prop)->Prop)))=> (forall (Xs:(b->Prop)), ((iff (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) ((Xp Xr) Xs))))) (fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (fun (Xs:(b->Prop))=> ((((conj ((forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))->(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))) ((((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs)->(forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy))))) (x (fun (x1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (Xs Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))))) (fun (x1:(((fun (a0:(b->Prop)) (a1:(b->Prop))=> (forall (S:(a->Prop)), (((ex b) (fun (Xt:b)=> ((and (a1 Xt)) (((eq (a->Prop)) S) (Xa Xt)))))->(S Xy)))) Xr) Xs))=> x1)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------