%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : PUZ123^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n185.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 13:29:00 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : PUZ123^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n185.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 08:25:16 CDT 2014
% % CPUTime  : 300.09 
% 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 0x1b5d560>, <kernel.Constant object at 0x1b5d320>) of role type named c1_type
% Using role type
% Declaring c1:fofType
% FOF formula (<kernel.Constant object at 0x1b5d3b0>, <kernel.Single object at 0x1b5d248>) of role type named c8_type
% Using role type
% Declaring c8:fofType
% FOF formula (<kernel.Constant object at 0x1b5d2d8>, <kernel.DependentProduct object at 0x1b7cab8>) of role type named s_type
% Using role type
% Declaring s:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1b5d488>, <kernel.DependentProduct object at 0x1b7cab8>) of role type named cCKB6_BLACK_type
% Using role type
% Declaring cCKB6_BLACK:(fofType->(fofType->Prop))
% FOF formula (((eq (fofType->(fofType->Prop))) cCKB6_BLACK) (fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv))))) of role definition named cCKB6_BLACK_def
% A new definition: (((eq (fofType->(fofType->Prop))) cCKB6_BLACK) (fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv)))))
% Defined: cCKB6_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv))))
% FOF formula (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->(((or ((and (((eq fofType) (s (s Xx))) c1)) (((eq fofType) (s Xy)) c1))) ((and (((eq fofType) (s (s Xx))) c8)) (((eq fofType) (s Xy)) c8)))->False))) of role conjecture named cCKB_L39000
% Conjecture to prove = (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->(((or ((and (((eq fofType) (s (s Xx))) c1)) (((eq fofType) (s Xy)) c1))) ((and (((eq fofType) (s (s Xx))) c8)) (((eq fofType) (s Xy)) c8)))->False))):Prop
% We need to prove ['(forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->(((or ((and (((eq fofType) (s (s Xx))) c1)) (((eq fofType) (s Xy)) c1))) ((and (((eq fofType) (s (s Xx))) c8)) (((eq fofType) (s Xy)) c8)))->False)))']
% Parameter fofType:Type.
% Parameter c1:fofType.
% Parameter c8:fofType.
% Parameter s:(fofType->fofType).
% Definition cCKB6_BLACK:=(fun (Xu:fofType) (Xv:fofType)=> (forall (Xw:(fofType->(fofType->Prop))), (((and ((Xw c1) c1)) (forall (Xj:fofType) (Xk:fofType), (((Xw Xj) Xk)->((and ((Xw (s (s Xj))) Xk)) ((Xw (s Xj)) (s Xk))))))->((Xw Xu) Xv)))):(fofType->(fofType->Prop)).
% Trying to prove (forall (Xx:fofType) (Xy:fofType), (((cCKB6_BLACK Xx) Xy)->(((or ((and (((eq fofType) (s (s Xx))) c1)) (((eq fofType) (s Xy)) c1))) ((and (((eq fofType) (s (s Xx))) c8)) (((eq fofType) (s Xy)) c8)))->False)))
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))):(((eq Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))))))
% Found (eq_ref0 (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) b)
% Found ((eq_ref Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) as proof of (((eq Prop) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))):(((eq Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))
% Found (eq_ref0 (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) as proof of (((eq Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) b)
% Found ((eq_ref Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) as proof of (((eq Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) b)
% Found ((eq_ref Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) as proof of (((eq Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) b)
% Found ((eq_ref Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) as proof of (((eq Prop) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: b:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of b
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xj:fofType) (Xk:fofType), ((not ((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8))))))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c8))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not ((or ((and (((eq fofType) (s (s (s Xj)))) c1)) (((eq fofType) (s (s Xk))) c1))) ((and (((eq fofType) (s (s (s Xj)))) c8)) (((eq fofType) (s (s Xk))) c8)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% Found iff_sym as proof of b
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(fofType->(False->((and False) False))))):(((eq Prop) (fofType->(fofType->(False->((and False) False))))) (fofType->(fofType->(False->((and False) False)))))
% Found (eq_ref0 (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found ((eq_ref Prop) (fofType->(fofType->(False->((and False) False))))) as proof of (((eq Prop) (fofType->(fofType->(False->((and False) False))))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):((or ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) (not ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):((or ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) (not ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) b)
% Found conj1:=(conj (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))):(forall (B:Prop), ((not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))->(B->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) B))))
% Instantiate: a:=(forall (B:Prop), ((not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))->(B->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) B)))):Prop
% Found conj1 as proof of a
% Found eq_ref00:=(eq_ref0 (((eq fofType) (s Xk)) c8)):(((eq Prop) (((eq fofType) (s Xk)) c8)) (((eq fofType) (s Xk)) c8))
% Found (eq_ref0 (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (s Xk)) c8)):(((eq Prop) (((eq fofType) (s Xk)) c8)) (((eq fofType) (s Xk)) c8))
% Found (eq_ref0 (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c8)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c8)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (s Xk)) c1)):(((eq Prop) (((eq fofType) (s Xk)) c1)) (((eq fofType) (s Xk)) c1))
% Found (eq_ref0 (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) (s Xk)) c1)):(((eq Prop) (((eq fofType) (s Xk)) c1)) (((eq fofType) (s Xk)) c1))
% Found (eq_ref0 (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found ((eq_ref Prop) (((eq fofType) (s Xk)) c1)) as proof of (((eq Prop) (((eq fofType) (s Xk)) c1)) b)
% Found conj1:=(conj (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))):(forall (B:Prop), ((not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))->(B->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) B))))
% Instantiate: a:=(forall (B:Prop), ((not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))->(B->((and (not ((or ((and (((eq fofType) (s (s (s (s Xj))))) c1)) (((eq fofType) (s Xk)) c1))) ((and (((eq fofType) (s (s (s (s Xj))))) c8)) (((eq fofType) (s Xk)) c8))))) B)))):Prop
% Found conj1 as proof of a
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found eq_ref00:=(eq_ref0 (s (s Xj))):(((eq fofType) (s (s Xj))) (s (s Xj)))
% Found (eq_ref0 (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found eq_ref00:=(eq_ref0 (s Xk)):(((eq fofType) (s Xk)) (s Xk))
% Found (eq_ref0 (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found eq_ref00:=(eq_ref0 (s (s Xj))):(((eq fofType) (s (s Xj))) (s (s Xj)))
% Found (eq_ref0 (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found eq_ref00:=(eq_ref0 (s Xk)):(((eq fofType) (s Xk)) (s Xk))
% Found (eq_ref0 (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found eq_ref00:=(eq_ref0 (s Xk)):(((eq fofType) (s Xk)) (s Xk))
% Found (eq_ref0 (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found eq_ref00:=(eq_ref0 (s (s Xj))):(((eq fofType) (s (s Xj))) (s (s Xj)))
% Found (eq_ref0 (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found eq_ref00:=(eq_ref0 (s Xk)):(((eq fofType) (s Xk)) (s Xk))
% Found (eq_ref0 (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found ((eq_ref fofType) (s Xk)) as proof of (((eq fofType) (s Xk)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c8)
% Found eq_ref00:=(eq_ref0 (s (s Xj))):(((eq fofType) (s (s Xj))) (s (s Xj)))
% Found (eq_ref0 (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found ((eq_ref fofType) (s (s Xj))) as proof of (((eq fofType) (s (s Xj))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (fofType->(fofType->(False->((and False) False)))))
% Found x30:(P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P0 (s Xk))
% Found x30:(P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P0 (s Xk))
% Found x30:(P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P0 (s Xk))
% Found x30:(P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P0 (s (s Xj)))
% Found x30:(P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P (s Xk))
% Found (fun (x30:(P (s Xk)))=> x30) as proof of (P0 (s Xk))
% Found x30:(P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P0 (s (s Xj)))
% Found x30:(P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P0 (s (s Xj)))
% Found x30:(P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P (s (s Xj)))
% Found (fun (x30:(P (s (s Xj))))=> x30) as proof of (P0 (s (s Xj)))
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: b:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of b
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) (s Xk)) c1))
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found x5:(((eq fofType) (s Xk)) c8)
% Found x5 as proof of (((eq fofType) (s Xk)) c8)
% Found x5:(((eq fofType) (s Xk)) c1)
% Found x5 as proof of (((eq fofType) (s Xk)) c1)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) (not ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))))
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found (classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))):(((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8)))
% Found (eq_ref0 ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found ((eq_ref Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) as proof of (((eq Prop) ((and (((eq fofType) (s (s Xj))) c8)) (((eq fofType) (s Xk)) c8))) b)
% Found classic0:=(classic ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofType) (s Xk)) c1))):((or ((and (((eq fofType) (s (s Xj))) c1)) (((eq fofT
% EOF
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