%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV264^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n095.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 13:33:58 EDT 2014

% Result   : Unknown 5.28s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV264^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n095.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 08:39:36 CDT 2014
% % CPUTime  : 5.28 
% 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 0x1ea76c8>, <kernel.Type object at 0x1ea7fc8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (T:((a->Prop)->Prop)), ((forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))->(T (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))->(forall (S:(a->Prop)), ((iff (T S)) (forall (Xx:a), ((S Xx)->((ex (a->Prop)) (fun (R:(a->Prop))=> ((and ((ex (a->Prop)) (fun (N:(a->Prop))=> ((and ((and (T N)) (forall (Xx0:a), ((N Xx0)->(R Xx0))))) (N Xx))))) (forall (Xx0:a), ((R Xx0)->(S Xx0)))))))))))) of role conjecture named cNBHD_THM2A_pme
% Conjecture to prove = (forall (T:((a->Prop)->Prop)), ((forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))->(T (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))->(forall (S:(a->Prop)), ((iff (T S)) (forall (Xx:a), ((S Xx)->((ex (a->Prop)) (fun (R:(a->Prop))=> ((and ((ex (a->Prop)) (fun (N:(a->Prop))=> ((and ((and (T N)) (forall (Xx0:a), ((N Xx0)->(R Xx0))))) (N Xx))))) (forall (Xx0:a), ((R Xx0)->(S Xx0)))))))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (T:((a->Prop)->Prop)), ((forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))->(T (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))->(forall (S:(a->Prop)), ((iff (T S)) (forall (Xx:a), ((S Xx)->((ex (a->Prop)) (fun (R:(a->Prop))=> ((and ((ex (a->Prop)) (fun (N:(a->Prop))=> ((and ((and (T N)) (forall (Xx0:a), ((N Xx0)->(R Xx0))))) (N Xx))))) (forall (Xx0:a), ((R Xx0)->(S Xx0))))))))))))']
% Parameter a:Type.
% Trying to prove (forall (T:((a->Prop)->Prop)), ((forall (K:((a->Prop)->Prop)), ((forall (Xx:(a->Prop)), ((K Xx)->(T Xx)))->(T (fun (Xx:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (K S)) (S Xx))))))))->(forall (S:(a->Prop)), ((iff (T S)) (forall (Xx:a), ((S Xx)->((ex (a->Prop)) (fun (R:(a->Prop))=> ((and ((ex (a->Prop)) (fun (N:(a->Prop))=> ((and ((and (T N)) (forall (Xx0:a), ((N Xx0)->(R Xx0))))) (N Xx))))) (forall (Xx0:a), ((R Xx0)->(S Xx0))))))))))))
% Found x00:(x2 Xx0)
% Found x00 as proof of (S Xx0)
% Found (fun (x00:(x2 Xx0))=> x00) as proof of (S Xx0)
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of ((x2 Xx0)->(S Xx0))
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of (forall (Xx0:a), ((x2 Xx0)->(S Xx0)))
% Found x00:(x2 Xx0)
% Found x00 as proof of (S Xx0)
% Found (fun (x00:(x2 Xx0))=> x00) as proof of (S Xx0)
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of ((x2 Xx0)->(S Xx0))
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of (forall (Xx0:a), ((x2 Xx0)->(S Xx0)))
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x00:(x3 Xx0)
% Instantiate: x2:=x3:(a->Prop)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x3 Xx0)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x00:(x3 Xx0)
% Instantiate: x2:=x3:(a->Prop)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x3 Xx0)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x2 Xx0)
% Found x00 as proof of (S Xx0)
% Found (fun (x00:(x2 Xx0))=> x00) as proof of (S Xx0)
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of ((x2 Xx0)->(S Xx0))
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of (forall (Xx0:a), ((x2 Xx0)->(S Xx0)))
% Found x00:(x2 Xx0)
% Found x00 as proof of (S Xx0)
% Found (fun (x00:(x2 Xx0))=> x00) as proof of (S Xx0)
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of ((x2 Xx0)->(S Xx0))
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of (forall (Xx0:a), ((x2 Xx0)->(S Xx0)))
% Found x00:(x2 Xx0)
% Found x00 as proof of (S Xx0)
% Found (fun (x00:(x2 Xx0))=> x00) as proof of (S Xx0)
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of ((x2 Xx0)->(S Xx0))
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of (forall (Xx0:a), ((x2 Xx0)->(S Xx0)))
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x00:(x3 Xx0)
% Instantiate: x2:=x3:(a->Prop)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x3 Xx0)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x00:(x3 Xx0)
% Instantiate: x2:=x3:(a->Prop)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x3 Xx0)
% Instantiate: x2:=x3:(a->Prop)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x3 Xx0)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x3 Xx0)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x2 Xx0)
% Found x00 as proof of (S Xx0)
% Found (fun (x00:(x2 Xx0))=> x00) as proof of (S Xx0)
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of ((x2 Xx0)->(S Xx0))
% Found (fun (Xx0:a) (x00:(x2 Xx0))=> x00) as proof of (forall (Xx0:a), ((x2 Xx0)->(S Xx0)))
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x0:(T S)
% Instantiate: x3:=S:(a->Prop)
% Found x0 as proof of (T x3)
% Found x00:(x3 Xx0)
% Instantiate: x2:=x3:(a->Prop)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found x00:(x3 Xx0)
% Found (fun (x00:(x3 Xx0))=> x00) as proof of (x2 Xx0)
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of ((x3 Xx0)->(x2 Xx0))
% Found (fun (Xx0:a) (x00:(x3 Xx0))=> x00) as proof of (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))
% Found ((conj30 x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found (((conj3 (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% Found ((((conj (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0)))) x0) (fun (Xx0:a) (x00:(x3 Xx0))=> x00)) as proof of ((and (T x3)) (forall (Xx0:a), ((x3 Xx0)->(x2 Xx0))))
% % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------