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)���=��a��is�deriv��X�able,�then��a����=��a��is�deriv�able.����Eac��rh��of�these�form�ulas�is�in�fact�equiv��X�alen�t�to��a�UR�#�.��6ۍ����Cor���ollar��32y���10.2:���}k�src:618LambdaLogic.tex�If��/the�system�Otter2�(�5��)�r��ffefutes�the�clausal�form�of�the�ne�ga-����tion��{of��P����,�using�the�clauses��x����=��x�j�2i��E���(�x�)��{�and���E��(�x�)�j�x����=��x�,and��{some�other����axioms��z��,�but�with�the�option�to�gener��ffate���cases��%6?�terms�in�unic�ation�o,�then��P�����is�35pr��ffovable�fr�om�the�c�onjunction�of����in�p�artial�lamb�da�lo�gic�plus�A��2C.��!�����References���ۍ����1.���%��src:627LambdaLogic.texBarendregt,�&�H.,��The�jHL��ffamb�da�Calculus:�Its�Syntax�and�Semantics�,�&�Studies�in����%�Logic��and�the�F��Voundations�of�Mathematics��103�,�Elsevier�Science�Ltd.�Revised����%�edition��(Octob�S�er�1984).������2.���%��src:637LambdaLogic.texBarendregt,�ŎH.,�Bunder,�M.,�and�Dekk��rers,�W.,�Completeness�of�t�w�o�systems�of����%�illativ��re�
�com�binatory�logic�for�rst�order�prop�S�ositional�and�predicate�calculus����%��A��2r��ffchive�35f�&g��ٖur�Mathematische�L�o�gik���37�,�327{341,�1998.������3.���%��src:642LambdaLogic.texBeeson,��M.,��F���oundations�cof�Constructive�Mathematics�,��Springer-V��Verlag,����%�Berlin��Heidelb�S�erg�New�Y��Vork�(1985).������4.���%��src:644LambdaLogic.texBeeson,�p�M.,�Pro��rving�programs�and�programming�pro�S�ofs,�in:�Barcan,�Mar-����%�cus,�~�Dorn,�and�W��Veingartner�(eds.),��L��ffo�gic,���Metho�dolo�gy,�and�Philosophy�of����%�Scienc��ffe�;�VII,�pr�o�c�e�e�dings�of�the�International�Congr�ess,�Salzbur�g,�1983�,�
�pp.����%�51-81,��North-Holland,�Amsterdam�(1986).������5.���%��src:647LambdaLogic.texBeeson,��M.,�Otter�Tw��ro�System�Description,�submitted�to�IJCAR�2004.������6.���%��src:649LambdaLogic.texS.��oF��Veferman,�Constructiv��re�theories�of�functions�and�classes,�pp.�159-224�in:�M.����%�Boa,��D.�v��X�an�Dalen,�and�K.�McAlo�S�on�(eds.),��L��ffo�gic�/�Col���lo�quium�'78:�Pr�o�c�e�e�d-����%�ings�35of�the�L��ffo�gic�35Col���lo�quium�at�Mons�,��North-Holland,�Amsterdam�(1979).������7.���%��src:655LambdaLogic.texE.��pMoggi.�The�P��rartial�Lam�b�S�da-Calculus.�PhD��thesis,�Univ�ersit�y�of�Edin�burgh,����%�1988.��h��rttp://citeseer.nj.nec.com/moggi88partial.h�tml������8.���%��src:659LambdaLogic.texScott,���D.,�Iden��rtit�y���and�existence�in�in��rtuitionistic�logic,�in:�F��Vourman,�M.�P�.,����%�Mulv��rey��V,��C.�J.,�and�Scott,�D.�S.�(eds.),��Applic��ffations���of�She�aves�,��Lecture�Notes����%�in��QMathematics��753��660-696,�Springer{V��Verlag,�Berlin�Heidelb�S�erg�New�Y�ork����%�(1979).������9.���%��src:663LambdaLogic.texSho�S�eneld,��CJ.�R.,��Mathematic��ffal���L�o�gic�,��CAddison-W��Vesley�,�Reading,�Mass.����%�(1967).������=���;����
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