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Towards Finding Longer Proofs [article]

Zsolt Zombori, Adrián Csiszárik, Henryk Michalewski, Cezary Kaliszyk, Josef Urban
2021 arXiv   pre-print
We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP).  ...  We use several simple, structured datasets with very long proofs to show that FLoP can successfully generalise a single training proof to a large class of related problems.  ...  We find that providing some of the harder problems (having longer proofs) helps to avoid misleading shortcuts.  ... 
arXiv:1905.13100v2 fatcat:ynksh52rrrc2hjuywsnr7pbtam

Page 289 of The Christian Observer. From the London Ed Vol. 17, Issue 197 [page]

1818 The Christian Observer. From the London Ed  
Or do we imagine Wwe no longer need iis assistance ? I have lived, sir, a long time; and the longer [ live, the more convincing proofs | see of this truth, that God governs in the uffairs of men!  ...  diligence towards those by whom we are employed, kindness znd love towards one another, and sincere Charity towards all men ; that we, adorning the Gospel of cur Lord and Savfour in all things, these  ... 

Page 160 of Journal of Geography Vol. 6, Issue 5 [page]

1907 Journal of Geography  
be south; the compass points towards the north magnetic pole and not towards the true north pole.  ...  The explanation of why the days are longer and the sun’s  ... 

The Middlesex Hospital Appeal

1910 The Hospital  
never fear that it will be unable to stand the shocks of those who clamour for the abolition of a system which finds a proof of its success in the fact that our hospitals can still secure such supporters  ...  Allegations have been made to the effect that the nation is growing apathetic, that it is no longer responsive to the argument of humanity, no longer capable of exercising a just and fair discretion in  ... 
pmid:29840487 pmcid:PMC5276047 fatcat:nm35xaejubdrrf3afgo3nshmgm

Page 25 of Hartford Seminary Record; Issued Under the Auspices of the Faculty of Hartford Theological Seminary Vol. 5, Issue 1 [page]

1894 Hartford Seminary Record; Issued Under the Auspices of the Faculty of Hartford Theological Seminary  
with increasing purpose and steadily pressing towards a full revelation of God’s goodness, we find the argument strengthened by as mueh as we have enlarged the field of illustration.”  ...  But there is further proof in the agents having been brought into relation by long processes all tending to the one end.  ... 

Page 76 of The Journal of Sacred Literature Vol. 1, Issue 1 [page]

1867 The Journal of Sacred Literature  
When naturalists are coming to these conclusions, when the traditional statement that man has a soul and the brutes have none finds no longer unquestioning assent, it is time for Chris- tian divines to  ...  are instincts of an here- after, they are not proofs of an immortality; they are presages rather than proofs, hopes rather than clear arguments.  ... 

Page 231 of None Vol. 84, Issue [page]

1928 None  
not only the proof by reason, but toward the proof by experiment.  ...  It wd. be impossible to prove that he had heard of Roger Bacon, but the whole canzone is easier to understand if we suppose, or at least, one finds a con- Copyright 1928 by Ezra Pound.  ... 

Page 658 of Fraser's Magazine Vol. 18, Issue 108 [page]

1838 Fraser's Magazine  
All the peersare for the the queen’s condemnation, except the Comte de Sussex, who calls on the king, who is president, for sufficient proofs. “ We will produce the proofs,” answers the monarch ; ** meanwhile  ...  Henry (advancing towards Sussex). Mi lord ! The Peers (surrounding Susser). Count —for goodness’ sake—milord de Sus- sex, let us see (voyons) ” &e.  ... 

Page 359 of Overland Monthly and Out West Magazine Vol. 9, Issue 52 [page]

1887 Overland Monthly and Out West Magazine  
No longer a lonesome cabin.  ...  Guard had been kept to her lounge with a sprain, destined to gather proof upon proof of her husband’s failing mental powers, and increasing infirmities of temper.  ... 

Page 251 of The National Preacher and Village Pulpit Vol. 8, Issue 4 [page]

1833 The National Preacher and Village Pulpit  
Again, the manner in which men feel and act towards each other, is an evident proof of what human consciousness is on this subject.  ...  ‘That such is the case is plain from the fact that your feel- ings towards him change at once, if there is sufficient proof that thé man is not a free agent.  ... 

Page 409 of Academy of Political Science. Proceedings of the Academy of Political Science Vol. 10, Issue [page]

1922 Academy of Political Science. Proceedings of the Academy of Political Science  
And I suggest to you that an attitude which was more friendly to such proof, provided it be the best available under the cir- cumstances, would more nearly accord with a rationalistic attitude toward the  ...  circumstances, upon hearsay proof.  ... 

Page 263 of Water Environment Research Vol. 14, Issue 2 [page]

1942 Water Environment Research  
Will it be fool-proof? Trouble-proof? Nuisance-proof? Cuss-proof? How will it operate in 1950? And the crowning question— Could I operate it myself?  ...  Examine the staffs of many consulting engineering offices and you will find men who have come up from the school of operation.  ... 

Page 82 of Duke Mathematical Journal Vol. 9, Issue 1 [page]

1942 Duke Mathematical Journal  
C.F. of U, V, then U, is at least as short as the shorter of U and V, and V, is at least as short as the longer of U and V. Proof. By definition, U; is a shortest non-zero I. L.C. of U and V.  ...  The proof is similar.  ... 

Page 82 of Duke Mathematical Journal Vol. 9, Issue 1 [page]

1942 Duke Mathematical Journal  
C.F. of U, V, then U, is at least as short as the shorter of U and V, and V, is at least as short as the longer of U and V. Proof. By definition, U; is a shortest non-zero I. L.C. of U and V.  ...  The proof is similar.  ... 

Page 183 of Physical Review Vol. 17, Issue 3 [page]

1903 Physical Review  
That which he has found toward the east agrees very well with the theory; but this is now no longer proof of the motion of the earth, since the other deflection, toward the south, does not at all agree  ...  For this purpose he dropped 32 balls, finding an average easterly move- ment of 0.90 cm. and a corresponding southerly movement of 0.34 cm.  ... 
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