%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV137^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n116.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 13:33:47 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  : SEV137^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n116.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 08:12:36 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 0x120b6c8>, <kernel.Type object at 0x1202b00>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))) of role conjecture named cTHM204_pme
% Conjecture to prove = (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))))']
% Parameter a:Type.
% Trying to prove (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))))
% Found x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))
% Found x0 as proof of (forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))
% Found x2000:=(x200 x1):(Xx0 Xy)
% Found (x200 x1) as proof of (Xx0 Xy)
% Found ((x20 x0) x1) as proof of (Xx0 Xy)
% Found (((x2 Xx0) x0) x1) as proof of (Xx0 Xy)
% Found (((x2 Xx0) x0) x1) as proof of (Xx0 Xy)
% Found ((x30 x0) (((x2 Xx0) x0) x1)) as proof of (Xx0 Xz)
% Found (((x3 Xx0) x0) (((x2 Xx0) x0) x1)) as proof of (Xx0 Xz)
% Found (fun (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))) as proof of (Xx0 Xz)
% Found (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))) as proof of ((forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz))))->(Xx0 Xz))
% Found (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))) as proof of ((forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))->((forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz))))->(Xx0 Xz)))
% Found (and_rect00 (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))) as proof of (Xx0 Xz)
% Found ((and_rect0 (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))) as proof of (Xx0 Xz)
% Found (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))) as proof of (Xx0 Xz)
% Found (fun (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (Xx0 Xz)
% Found (fun (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of ((Xx0 Xx)->(Xx0 Xz))
% Found (fun (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))
% Found (fun (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))
% Found (fun (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz)))))
% Found (fun (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))))
% Found (fun (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))))
% Found (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))))
% Found (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1))))) as proof of (forall (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a), (((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))->(forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xz))))))
% Got proof (fun (Xr:(a->(a->Prop))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))))
% Time elapsed = 0.288848s
% node=40 cost=345.000000 depth=20
% ::::::::::::::::::::::
% % 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))) (Xx:a) (Xy:a) (Xz:a) (x:((and (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz)))))) (Xx0:(a->Prop)) (x0:(forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))) (x1:(Xx0 Xx))=> (((fun (P:Type) (x2:((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))->((forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))->P)))=> (((((and_rect (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xx)->(Xx0 Xy))))) (forall (Xx0:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx0 Xy0))->(Xx0 Xz0)))->((Xx0 Xy)->(Xx0 Xz))))) P) x2) x)) (Xx0 Xz)) (fun (x2:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xx)->(Xx00 Xy))))) (x3:(forall (Xx00:(a->Prop)), ((forall (Xy0:a) (Xz0:a), (((and ((Xr Xy0) Xz0)) (Xx00 Xy0))->(Xx00 Xz0)))->((Xx00 Xy)->(Xx00 Xz)))))=> (((x3 Xx0) x0) (((x2 Xx0) x0) x1)))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------