%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU793^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n111.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 13:33:08 EDT 2014

% Result   : Theorem 7.48s
% Output   : Proof 7.48s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU793^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n111.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 11:30:01 CDT 2014
% % CPUTime  : 7.48 
% 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 0x28a0560>, <kernel.DependentProduct object at 0x28bf878>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2b16a28>, <kernel.DependentProduct object at 0x28bf7e8>) of role type named exu_type
% Using role type
% Declaring exu:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))) of role definition named exu
% A new definition: (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))
% Defined: exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))
% FOF formula (<kernel.Constant object at 0x25abb90>, <kernel.Sort object at 0x25a5128>) of role type named replAx_type
% Using role type
% Declaring replAx:Prop
% FOF formula (((eq Prop) replAx) (forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx))))))))))) of role definition named replAx
% A new definition: (((eq Prop) replAx) (forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx)))))))))))
% Defined: replAx:=(forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx))))))))))
% FOF formula (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))) of role conjecture named image1Ex
% Conjecture to prove = (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Definition exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))):((fofType->Prop)->Prop).
% Definition replAx:=(forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx)))))))))):Prop.
% Trying to prove (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))))
% Found eq_ref00:=(eq_ref0 (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))):(((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (eq_ref0 (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) as proof of (((eq (fofType->Prop)) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Xx:fofType), ((iff ((in Xx) x)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (forall (Xx:fofType), ((iff ((in Xx) x0)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (Xx:fofType), ((iff ((in Xx) x)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found x1:((in Xx) x0)
% Instantiate: x2:=Xx:fofType;x0:=A:fofType
% Found x1 as proof of ((in x2) A)
% Found x1:((in Xx) x0)
% Instantiate: x2:=Xx:fofType;x0:=A:fofType
% Found x1 as proof of ((in x2) A)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found eq_ref00:=(eq_ref0 x2):(((eq fofType) x2) x2)
% Found (eq_ref0 x2) as proof of (((eq fofType) x2) (Xf Xx))
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) (Xf Xx))
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) (Xf Xx))
% Found ((eq_ref fofType) x2) as proof of (((eq fofType) x2) (Xf Xx))
% Found eq_sym000:=(eq_sym00 (Xf Xx)):((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy))
% Found (eq_sym00 (Xf Xx)) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))
% Found ((eq_sym0 Xy) (Xf Xx)) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))
% Found (((eq_sym fofType) Xy) (Xf Xx)) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))
% Found (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))) as proof of ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))
% Found (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))) as proof of (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))
% Found ((conj00 ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))))
% Found (((conj0 (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))))
% Found ((((conj (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))))
% Found ((((conj (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))) as proof of ((and (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy))))
% Found (ex_intro000 ((((conj (((eq fofType) x2) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) x2) Xy)))) ((eq_ref fofType) x2)) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy))))))
% Found ((ex_intro00 (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy))))))
% Found (((ex_intro0 (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy))))))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy))))))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))) as proof of ((ex fofType) (fun (Xx0:fofType)=> ((and ((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xx0)) (forall (Xy:fofType), (((fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))) Xy)->(((eq fofType) Xx0) Xy))))))
% Found (fun (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))) as proof of (exu (fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))))
% Found (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))) as proof of (((in Xx) A)->(exu (fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx)))))
% Found (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))) as proof of (forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> (((eq fofType) Xy) (Xf Xx))))))
% Found (x00 (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found ((x0 A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (fun (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))
% Found (fun (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of (forall (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))
% Found (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of (forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy))))))))))
% Found (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx)))))))) as proof of (replAx->(forall (A:fofType) (Xf:(fofType->fofType)), ((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) (((eq fofType) Xx) (Xf Xy)))))))))))
% Got proof (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))))
% Time elapsed = 7.109090s
% node=1171 cost=2340.000000 depth=23
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:replAx) (A:fofType) (Xf:(fofType->fofType))=> (((x (fun (x6:fofType) (x50:fofType)=> (((eq fofType) x50) (Xf x6)))) A) (fun (Xx:fofType) (x1:((in Xx) A))=> ((((ex_intro fofType) (fun (Xx0:fofType)=> ((and (((eq fofType) Xx0) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) Xx0) Xy)))))) (Xf Xx)) ((((conj (((eq fofType) (Xf Xx)) (Xf Xx))) (forall (Xy:fofType), ((((eq fofType) Xy) (Xf Xx))->(((eq fofType) (Xf Xx)) Xy)))) ((eq_ref fofType) (Xf Xx))) (fun (Xy:fofType)=> (((eq_sym fofType) Xy) (Xf Xx))))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------