%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV198^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n112.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 13:33:52 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV198^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n112.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 08:27:21 CDT 2014
% % CPUTime  : 300.10 
% 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 0x1f86710>, <kernel.Type object at 0x1f86ef0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x23d9d40>, <kernel.Constant object at 0x1f86cb0>) of role type named c0
% Using role type
% Declaring c0:a
% FOF formula (<kernel.Constant object at 0x1f86dd0>, <kernel.Constant object at 0x1f86cb0>) of role type named x
% Using role type
% Declaring x:a
% FOF formula (<kernel.Constant object at 0x1f86710>, <kernel.DependentProduct object at 0x1f86488>) of role type named cP
% Using role type
% Declaring cP:(a->(a->a))
% FOF formula (((and (forall (Xx0:a) (Xy:a) (Xu:a) (Xv:a), ((((eq a) ((cP Xx0) Xu)) ((cP Xy) Xv))->((and (((eq a) Xx0) Xy)) (((eq a) Xu) Xv))))) (forall (Xx0:a) (Xy:a), (not (((eq a) ((cP Xx0) Xy)) c0))))->((forall (R:(a->(a->(a->Prop)))), (((and True) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((R Xx1) Xy1) Xz1))) (((R Xx2) Xy2) Xz2)))))))))))))))->(((R Xa) Xb) Xc))))->(((R x) c0) c0)))->(((eq a) x) c0))) of role conjecture named cS_INCL_LEM6_pme
% Conjecture to prove = (((and (forall (Xx0:a) (Xy:a) (Xu:a) (Xv:a), ((((eq a) ((cP Xx0) Xu)) ((cP Xy) Xv))->((and (((eq a) Xx0) Xy)) (((eq a) Xu) Xv))))) (forall (Xx0:a) (Xy:a), (not (((eq a) ((cP Xx0) Xy)) c0))))->((forall (R:(a->(a->(a->Prop)))), (((and True) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((R Xx1) Xy1) Xz1))) (((R Xx2) Xy2) Xz2)))))))))))))))->(((R Xa) Xb) Xc))))->(((R x) c0) c0)))->(((eq a) x) c0))):Prop
% We need to prove ['(((and (forall (Xx0:a) (Xy:a) (Xu:a) (Xv:a), ((((eq a) ((cP Xx0) Xu)) ((cP Xy) Xv))->((and (((eq a) Xx0) Xy)) (((eq a) Xu) Xv))))) (forall (Xx0:a) (Xy:a), (not (((eq a) ((cP Xx0) Xy)) c0))))->((forall (R:(a->(a->(a->Prop)))), (((and True) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((R Xx1) Xy1) Xz1))) (((R Xx2) Xy2) Xz2)))))))))))))))->(((R Xa) Xb) Xc))))->(((R x) c0) c0)))->(((eq a) x) c0)))']
% Parameter a:Type.
% Parameter c0:a.
% Parameter x:a.
% Parameter cP:(a->(a->a)).
% Trying to prove (((and (forall (Xx0:a) (Xy:a) (Xu:a) (Xv:a), ((((eq a) ((cP Xx0) Xu)) ((cP Xy) Xv))->((and (((eq a) Xx0) Xy)) (((eq a) Xu) Xv))))) (forall (Xx0:a) (Xy:a), (not (((eq a) ((cP Xx0) Xy)) c0))))->((forall (R:(a->(a->(a->Prop)))), (((and True) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((R Xx1) Xy1) Xz1))) (((R Xx2) Xy2) Xz2)))))))))))))))->(((R Xa) Xb) Xc))))->(((R x) c0) c0)))->(((eq a) x) c0)))
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% Found (eq_ref00 P) as proof of (P0 x)
% Found ((eq_ref0 x) P) as proof of (P0 x)
% Found (((eq_ref a) x) P) as proof of (P0 x)
% Found (((eq_ref a) x) P) as proof of (P0 x)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 x):(((eq a) x) x)
% Found (eq_ref0 x) as proof of (((eq a) x) b)
% Found ((eq_ref a) x) as proof of (((eq a) x) b)
% Found ((eq_ref a) x) as proof of (((eq a) x) b)
% Found ((eq_ref a) x) as proof of (((eq a) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) c0)
% Found ((eq_ref a) b) as proof of (((eq a) b) c0)
% Found ((eq_ref a) b) as proof of (((eq a) b) c0)
% Found ((eq_ref a) b) as proof of (((eq a) b) c0)
% Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% Found (eq_ref00 P) as proof of (P0 x)
% Found ((eq_ref0 x) P) as proof of (P0 x)
% Found (((eq_ref a) x) P) as proof of (P0 x)
% Found (((eq_ref a) x) P) as proof of (P0 x)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 x):(((eq a) x) x)
% Found (eq_ref0 x) as proof of (((eq a) x) b)
% Found ((eq_ref a) x) as proof of (((eq a) x) b)
% Found ((eq_ref a) x) as proof of (((eq a) x) b)
% Found ((eq_ref a) x) as proof of (((eq a) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) c0)
% Found ((eq_ref a) b) as proof of (((eq a) b) c0)
% Found ((eq_ref a) b) as proof of (((eq a) b) c0)
% Found ((eq_ref a) b) as proof of (((eq a) b) c0)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 c0):(((eq a) c0) c0)
% Found (eq_ref0 c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref00:=(eq_ref0 c0):(((eq a) c0) c0)
% Found (eq_ref0 c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 c0):(((eq a) c0) c0)
% Found (eq_ref0 c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found ((eq_ref a) b) as proof of (((eq a) b) x)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xc)->(P Xc))
% Found (eq_ref00 P) as proof of (P0 Xc)
% Found ((eq_ref0 Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xc)->(P Xc))
% Found (eq_ref00 P) as proof of (P0 Xc)
% Found ((eq_ref0 Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found eq_ref000:=(eq_ref00 P):((P Xc)->(P Xc))
% Found (eq_ref00 P) as proof of (P0 Xc)
% Found ((eq_ref0 Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found x01:(P x)
% Instantiate: b:=x:a
% Found x01 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 c0):(((eq a) c0) c0)
% Found (eq_ref0 c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found ((eq_ref a) c0) as proof of (((eq a) c0) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref00:=(eq_ref0 Xc):(((eq a) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq a) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref a) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq a) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq a) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq a) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xa)
% Found eq_ref00:=(eq_ref0 Xc):(((eq a) Xc) Xc)
% Found (eq_ref0 Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found ((eq_ref a) Xc) as proof of (((eq a) Xc) b)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))):(((eq Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc))))
% Found (eq_ref0 (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) as proof of (((eq Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) b)
% Found ((eq_ref Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) as proof of (((eq Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) b)
% Found ((eq_ref Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) as proof of (((eq Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) b)
% Found ((eq_ref Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) as proof of (((eq Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (((eq a) Xx1) Xz1))) (((eq a) Xx2) Xz2)))))))))))))))->(((eq a) Xa) Xc)))) b)
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found I:True
% Found I as proof of True
% Found eq_ref00:=(eq_ref0 Xa):(((eq a) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found ((eq_ref a) Xa) as proof of (((eq a) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xc)
% Found I:True
% Found I as proof of True
% Found eq_ref000:=(eq_ref00 P):((P Xc)->(P Xc))
% Found (eq_ref00 P) as proof of (P0 Xc)
% Found ((eq_ref0 Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found (((eq_ref a) Xc) P) as proof of (P0 Xc)
% Found eq_ref00:=(eq_ref0 (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (P Xz1))) (P Xz2)))))))))))))))->(P Xc)))):(((eq Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (P Xz1))) (P Xz2)))))))))))))))->(P Xc)))) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (P Xz1))) (P Xz2)))))))))))))))->(P Xc))))
% Found (eq_ref0 (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (P Xz1))) (P Xz2)))))))))))))))->(P Xc)))) as proof of (((eq Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (P Xz1))) (P Xz2)))))))))))))))->(P Xc)))) b)
% Found ((eq_ref Prop) (forall (Xa:a) (Xb:a) (Xc:a), (((or ((or ((and (((eq a) Xa) c0)) (((eq a) Xb) Xc))) ((and (((eq a) Xb) c0)) (((eq a) Xa) Xc)))) ((ex a) (fun (Xx1:a)=> ((ex a) (fun (Xx2:a)=> ((ex a) (fun (Xy1:a)=> ((ex a) (fun (Xy2:a)=> ((ex a) (fun (Xz1:a)=> ((ex a) (fun (Xz2:a)=> ((and ((and ((and ((and (((eq a) Xa) ((cP Xx1) Xx2))) (((eq a) Xb) ((cP Xy1) Xy2)))) (((eq a) Xc) ((cP Xz1) Xz2)))) (P Xz1))) (P Xz2)))))))))))))))->(P Xc)))
% EOF
%------------------------------------------------------------------------------