%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV311^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n114.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 13:34:02 EDT 2014

% Result   : Theorem 0.61s
% Output   : Proof 0.61s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV311^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n114.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 08:48:26 CDT 2014
% % CPUTime  : 0.61 
% 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 0x275c830>, <kernel.Type object at 0x275cc68>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x275c9e0>, <kernel.DependentProduct object at 0x275bf80>) of role type named cF
% Using role type
% Declaring cF:((a->Prop)->(a->Prop))
% FOF formula ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))))) of role conjecture named cTHM521_pme
% Conjecture to prove = ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))))))']
% Parameter a:Type.
% Parameter cF:((a->Prop)->(a->Prop)).
% Trying to prove ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))))))
% Found x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))
% Instantiate: X:=(cF S):(a->Prop)
% Found x1 as proof of (forall (Xx:a), ((X Xx)->(S Xx)))
% Found x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)
% Instantiate: X:=(fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))):(a->Prop)
% Found x0 as proof of ((cF X) Xx)
% Found x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)
% Instantiate: X0:=(fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))):(a->Prop)
% Found x0 as proof of ((cF X0) Xx)
% Found x3:(X0 Xx0)
% Found x3 as proof of (X Xx0)
% Found (fun (x3:(X0 Xx0))=> x3) as proof of (X Xx0)
% Found (fun (Xx0:a) (x3:(X0 Xx0))=> x3) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x3:(X0 Xx0))=> x3) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found x400:=(x40 x1):(forall (Xx:a), (((cF X) Xx)->((cF S) Xx)))
% Found (x40 x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1)))
% Found ((x4 S) x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1)))
% Found (((x X) S) x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1)))
% Found (((x X) S) x1) as proof of (forall (Xx1:a), (((cF X) Xx1)->(X Xx1)))
% Found (x30 (((x X) S) x1)) as proof of (X Xx0)
% Found ((x3 X) (((x X) S) x1)) as proof of (X Xx0)
% Found (fun (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1))) as proof of (X Xx0)
% Found (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1))) as proof of ((X0 Xx0)->(X Xx0))
% Found (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1))) as proof of (forall (Xx:a), ((X0 Xx)->(X Xx)))
% Found ((x210 (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx)
% Found (((x21 X) (fun (Xx0:a) (x3:(X0 Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx)
% Found ((((x2 (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx)
% Found ((((x2 (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0) as proof of ((cF X) Xx)
% Found ((x200 x1) ((((x2 (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0)) as proof of ((cF S) Xx)
% Found (((x20 S) x1) ((((x2 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) X) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 X) (((x X) S) x1)))) x0)) as proof of ((cF S) Xx)
% Found ((((x2 (cF S)) S) x1) ((((x2 (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)) as proof of ((cF S) Xx)
% Found (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)) as proof of ((cF S) Xx)
% Found (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)) as proof of ((cF S) Xx)
% Found (x10 (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx:a), ((X Xx)->(Y Xx))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0))) as proof of (S Xx)
% Found ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0))) as proof of (S Xx)
% Found (fun (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (S Xx)
% Found (fun (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))
% Found (fun (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))
% Found (fun (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))))
% Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of (forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx)))))
% Found (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0)))) as proof of ((forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))->(forall (Xx:a), (((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)->(forall (S:(a->Prop)), ((forall (Xx0:a), (((cF S) Xx0)->(S Xx0)))->(S Xx))))))
% Got proof (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0))))
% Time elapsed = 0.296557s
% node=66 cost=1449.000000 depth=25
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:(forall (X:(a->Prop)) (Y:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cF X) Xx)->((cF Y) Xx)))))) (Xx:a) (x0:((cF (fun (Xx0:a)=> (forall (S:(a->Prop)), ((forall (Xx1:a), (((cF S) Xx1)->(S Xx1)))->(S Xx0))))) Xx)) (S:(a->Prop)) (x1:(forall (Xx0:a), (((cF S) Xx0)->(S Xx0))))=> ((x1 Xx) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (cF S)) S) x1) (((((fun (X:(a->Prop)) (Y:(a->Prop)) (x2:(forall (Xx0:a), ((X Xx0)->(Y Xx0))))=> ((((x X) Y) x2) Xx)) (fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0))))) (cF S)) (fun (Xx0:a) (x3:((fun (Xx0:a)=> (forall (S0:(a->Prop)), ((forall (Xx1:a), (((cF S0) Xx1)->(S0 Xx1)))->(S0 Xx0)))) Xx0))=> ((x3 (cF S)) (((x (cF S)) S) x1)))) x0))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------