%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV014^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n099.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 13:33:34 EDT 2014

% Result   : Theorem 0.48s
% Output   : Proof 0.48s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV014^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n099.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 07:29:31 CDT 2014
% % CPUTime  : 0.48 
% 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 0x1725710>, <kernel.Type object at 0x17257a0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx)))) of role conjecture named cTHM513_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx))))
% Found x20:=(x2 Xx):((Xr Xx) Xx)
% Found (x2 Xx) as proof of ((Xr Xx) Xx)
% Found (fun (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)) as proof of ((Xr Xx) Xx)
% Found (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)) as proof of ((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->((Xr Xx) Xx))
% Found (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)) as proof of ((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->((Xr Xx) Xx)))
% Found (and_rect10 (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))) as proof of ((Xr Xx) Xx)
% Found ((and_rect1 ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))) as proof of ((Xr Xx) Xx)
% Found (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))) as proof of ((Xr Xx) Xx)
% Found (fun (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))) as proof of ((Xr Xx) Xx)
% Found (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))) as proof of ((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz)))->((Xr Xx) Xx))
% Found (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))) as proof of (((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))->((forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz)))->((Xr Xx) Xx)))
% Found (and_rect00 (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))) as proof of ((Xr Xx) Xx)
% Found ((and_rect0 ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))) as proof of ((Xr Xx) Xx)
% Found (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))) as proof of ((Xr Xx) Xx)
% Found (fun (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of ((Xr Xx) Xx)
% Found (fun (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of (forall (Xx:a), ((Xr Xx) Xx))
% Found (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx)))
% Found (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx)))))) as proof of (forall (Xr:(a->(a->Prop))), (((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))->(forall (Xx:a), ((Xr Xx) Xx))))
% Got proof (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))))
% Time elapsed = 0.165021s
% node=19 cost=123.000000 depth=16
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (Xr:(a->(a->Prop))) (x:((and ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz))))) (Xx:a)=> (((fun (P:Type) (x0:(((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))->((forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))->P)))=> (((((and_rect ((and (forall (Xx:a), ((Xr Xx) Xx))) (forall (Xx:a) (Xy:a), (((Xr Xx) Xy)->((Xr Xy) Xx))))) (forall (Xx:a) (Xy:a) (Xz:a), (((and ((Xr Xx) Xy)) ((Xr Xy) Xz))->((Xr Xx) Xz)))) P) x0) x)) ((Xr Xx) Xx)) (fun (x0:((and (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))) (x1:(forall (Xx0:a) (Xy:a) (Xz:a), (((and ((Xr Xx0) Xy)) ((Xr Xy) Xz))->((Xr Xx0) Xz))))=> (((fun (P:Type) (x2:((forall (Xx0:a), ((Xr Xx0) Xx0))->((forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))->P)))=> (((((and_rect (forall (Xx0:a), ((Xr Xx0) Xx0))) (forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0)))) P) x2) x0)) ((Xr Xx) Xx)) (fun (x2:(forall (Xx0:a), ((Xr Xx0) Xx0))) (x3:(forall (Xx0:a) (Xy:a), (((Xr Xx0) Xy)->((Xr Xy) Xx0))))=> (x2 Xx))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------