TSTP Solution File: SEU649^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU649^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n097.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 13:32:42 EDT 2014
% Result : Timeout 300.10s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU649^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n097.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 11:02:26 CDT 2014
% % CPUTime : 300.10
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x21b2710>, <kernel.DependentProduct object at 0x21b2b00>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x207ae18>, <kernel.Single object at 0x21b2bd8>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x21b2b00>, <kernel.DependentProduct object at 0x21b2c20>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x21b2950>, <kernel.Sort object at 0x207ce18>) of role type named setext_type
% Using role type
% Declaring setext:Prop
% FOF formula (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))) of role definition named setext
% A new definition: (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))))
% Defined: setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))
% FOF formula (<kernel.Constant object at 0x21b2b90>, <kernel.Sort object at 0x207ce18>) of role type named setadjoinIL_type
% Using role type
% Declaring setadjoinIL:Prop
% FOF formula (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))) of role definition named setadjoinIL
% A new definition: (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))))
% Defined: setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x21b2b00>, <kernel.Sort object at 0x207ce18>) of role type named uniqinunit_type
% Using role type
% Declaring uniqinunit:Prop
% FOF formula (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))) of role definition named uniqinunit
% A new definition: (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))))
% Defined: uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x21b2bd8>, <kernel.Sort object at 0x207ce18>) of role type named eqinunit_type
% Using role type
% Declaring eqinunit:Prop
% FOF formula (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))) of role definition named eqinunit
% A new definition: (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))))
% Defined: eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))
% FOF formula (<kernel.Constant object at 0x21b2dd0>, <kernel.Sort object at 0x207ce18>) of role type named upairset2E_type
% Using role type
% Declaring upairset2E:Prop
% FOF formula (((eq Prop) upairset2E) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy))))) of role definition named upairset2E
% A new definition: (((eq Prop) upairset2E) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy)))))
% Defined: upairset2E:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy))))
% FOF formula (setext->(setadjoinIL->(uniqinunit->(eqinunit->(upairset2E->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xx) emptyset))))))))) of role conjecture named setukpairinjR11
% Conjecture to prove = (setext->(setadjoinIL->(uniqinunit->(eqinunit->(upairset2E->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xx) emptyset))))))))):Prop
% We need to prove ['(setext->(setadjoinIL->(uniqinunit->(eqinunit->(upairset2E->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xx) emptyset)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Definition setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))):Prop.
% Definition setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))):Prop.
% Definition uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))):Prop.
% Definition eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition upairset2E:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy)))):Prop.
% Trying to prove (setext->(setadjoinIL->(uniqinunit->(eqinunit->(upairset2E->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xx) emptyset)))))))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) ((setadjoin Xy) emptyset)))->(P ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) ((setadjoin Xy) emptyset)))->(P ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) ((setadjoin Xy) emptyset)))->(P ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) ((setadjoin Xy) emptyset)))->(P ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) ((setadjoin Xy) emptyset)))->(P ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) P) as proof of (P0 ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))):(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) ((setadjoin Xx) emptyset))):(((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found (eq_ref0 ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (P emptyset)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (P emptyset)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (P emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) ((setadjoin Xx) emptyset))):(((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found (eq_ref0 ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found x40:=(x4 (fun (x5:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found x40:=(x4 (fun (x5:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found x40:=(x4 (fun (x5:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found x40:=(x4 (fun (x6:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x6:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x6:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P emptyset)
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P emptyset)
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P emptyset)
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P emptyset)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((in Xx0) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found ((eq_ref0 ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) (in Xx0)) as proof of (P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin Xx) emptyset))->(P ((setadjoin Xx) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) P) as proof of (P0 ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found x40:=(x4 (fun (x5:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found x40:=(x4 (fun (x5:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found x40:=(x4 (fun (x6:fofType)=> ((in Xx0) emptyset))):(((in Xx0) emptyset)->((in Xx0) emptyset))
% Found (x4 (fun (x6:fofType)=> ((in Xx0) emptyset))) as proof of (P emptyset)
% Found (x4 (fun (x6:fofType)=> ((in Xx0) emptyset))) as proof of (P emptyset)
% Found x5:(P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Instantiate: Xx0:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType
% Found x5 as proof of (P0 Xx0)
% Found x000:=(x00 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x00 emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found ((x0 Xx0) emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found ((x0 Xx0) emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found ((x0 Xx0) emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) ((setadjoin Xx) emptyset))):(((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Found (eq_ref0 ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found ((eq_ref fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xx) emptyset))) b)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found x5:(P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Instantiate: b:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx0)):(((in Xx0) ((setadjoin Xx) emptyset))->((in Xx0) ((setadjoin Xx) emptyset)))
% Found (eq_ref00 (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found ((eq_ref0 ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found (((eq_ref fofType) ((setadjoin Xx) emptyset)) (in Xx0)) as proof of (P ((setadjoin Xx) emptyset))
% Found x40:=(x4 (fun (x5:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x5:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found x40:=(x4 (fun (x6:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x6:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x6:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found x40:=(x4 (fun (x6:fofType)=> (P emptyset))):((P emptyset)->(P emptyset))
% Found (x4 (fun (x6:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found (x4 (fun (x6:fofType)=> (P emptyset))) as proof of (P0 emptyset)
% Found x5:(P ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Instantiate: A:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType
% Found x5 as proof of (P0 A)
% Found x5:(P ((setadjoin Xx) ((setadjoin Xx) emptyset)))
% Instantiate: Xx0:=((setadjoin Xx) ((setadjoin Xx) emptyset)):fofType
% Found x5 as proof of (P0 Xx0)
% Found x000:=(x00 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x00 emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found ((x0 Xx0) emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found ((x0 Xx0) emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found ((x0 Xx0) emptyset) as proof of ((in Xx0) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of ((
% EOF
%------------------------------------------------------------------------------