%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV076^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n110.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 13:33:42 EDT 2014

% Result   : Theorem 0.78s
% Output   : Proof 0.78s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV076^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n110.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 07:56:26 CDT 2014
% % CPUTime  : 0.78 
% 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 0x212c170>, <kernel.Type object at 0x214a5a8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (RRR:(a->(a->Prop))) (U:((a->Prop)->a)), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))->(forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))))) of role conjecture named cTHM401B_pme
% Conjecture to prove = (forall (RRR:(a->(a->Prop))) (U:((a->Prop)->a)), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))->(forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (RRR:(a->(a->Prop))) (U:((a->Prop)->a)), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))->(forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))))))']
% Parameter a:Type.
% Trying to prove (forall (RRR:(a->(a->Prop))) (U:((a->Prop)->a)), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))->(forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))))))
% Found x2:(forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))
% Instantiate: Xs0:=Xs:(a->Prop);x4:=(U Xs0):a
% Found x2 as proof of (forall (Xz:a), ((Xs Xz)->((RRR Xz) x4)))
% Found (ex_intro000 x2) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found ((ex_intro00 (U Xs0)) x2) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (((ex_intro0 (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (fun (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2)) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (fun (x2:(forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2)) as proof of ((forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj)))->((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))))
% Found (fun (x2:(forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2)) as proof of ((forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))->((forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj)))->((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))))
% Found (and_rect10 (fun (x2:(forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found ((and_rect1 ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (((fun (P:Type) (x2:((forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))->((forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj)))) P) x2) x10)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs0)) x2))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (fun (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))) as proof of ((forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj)))))->((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))))
% Found (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))) as proof of ((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj)))))->((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))))
% Found (and_rect00 (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2))))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found ((and_rect0 ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2))))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2))))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (fun (Xs:(a->Prop))=> (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))))) as proof of ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))
% Found (fun (x:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))) (Xs:(a->Prop))=> (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))))) as proof of (forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))))
% Found (fun (U:((a->Prop)->a)) (x:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))) (Xs:(a->Prop))=> (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))))) as proof of (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))->(forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))))
% Found (fun (RRR:(a->(a->Prop))) (U:((a->Prop)->a)) (x:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))) (Xs:(a->Prop))=> (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))))) as proof of (forall (U:((a->Prop)->a)), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))->(forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))))))
% Found (fun (RRR:(a->(a->Prop))) (U:((a->Prop)->a)) (x:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))) (Xs:(a->Prop))=> (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2)))))) as proof of (forall (RRR:(a->(a->Prop))) (U:((a->Prop)->a)), (((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))->(forall (Xs:(a->Prop)), ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))))))
% Got proof (fun (RRR:(a->(a->Prop))) (U:((a->Prop)->a)) (x:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))) (Xs:(a->Prop))=> (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2))))))
% Time elapsed = 0.457851s
% node=56 cost=1222.000000 depth=22
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (RRR:(a->(a->Prop))) (U:((a->Prop)->a)) (x:((and (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))))) (Xs:(a->Prop))=> (((fun (P:Type) (x0:((forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))->((forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))->P)))=> (((((and_rect (forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (forall (Xs:(a->Prop)), ((and (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))))) P) x0) x)) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x0:(forall (Xx:a) (Xy:a) (Xz:a), (((and ((RRR Xx) Xy)) ((RRR Xy) Xz))->((RRR Xx) Xz)))) (x1:(forall (Xs0:(a->Prop)), ((and (forall (Xz:a), ((Xs0 Xz)->((RRR Xz) (U Xs0))))) (forall (Xj:a), ((forall (Xk:a), ((Xs0 Xk)->((RRR Xk) Xj)))->((RRR (U Xs0)) Xj))))))=> (((fun (P:Type) (x2:((forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))->((forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))->P)))=> (((((and_rect (forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj)))) P) x2) (x1 Xs))) ((ex a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb)))))) (fun (x2:(forall (Xz:a), ((Xs Xz)->((RRR Xz) (U Xs))))) (x3:(forall (Xj:a), ((forall (Xk:a), ((Xs Xk)->((RRR Xk) Xj)))->((RRR (U Xs)) Xj))))=> ((((ex_intro a) (fun (Xb:a)=> (forall (Xz:a), ((Xs Xz)->((RRR Xz) Xb))))) (U Xs)) x2))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------