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-rw-r--r--etc/isar/AThousandTheorems.thy1008
1 files changed, 1008 insertions, 0 deletions
diff --git a/etc/isar/AThousandTheorems.thy b/etc/isar/AThousandTheorems.thy
new file mode 100644
index 00000000..77be15b0
--- /dev/null
+++ b/etc/isar/AThousandTheorems.thy
@@ -0,0 +1,1008 @@
+theory AThousandLines imports Main
+begin
+
+(* set global_timing *)
+
+lemma foo: "P --> P" by auto
+lemma foo2: "P --> P" by auto
+lemma foo3: "P --> P" by auto
+lemma foo4: "P --> P" by auto
+lemma foo5: "P --> P" by auto
+lemma foo6: "P --> P" by auto
+lemma foo7: "P --> P" by auto
+lemma foo8: "P --> P" by auto
+lemma foo9: "P --> P" by auto
+lemma foo10: "P --> P" by auto
+lemma foo11: "P --> P" by auto
+lemma foo12: "P --> P" by auto
+lemma foo13: "P --> P" by auto
+lemma foo14: "P --> P" by auto
+lemma foo15: "P --> P" by auto
+lemma foo16: "P --> P" by auto
+lemma foo17: "P --> P" by auto
+lemma foo18: "P --> P" by auto
+lemma foo19: "P --> P" by auto
+lemma foo20: "P --> P" by auto
+lemma foo21: "P --> P" by auto
+lemma foo22: "P --> P" by auto
+lemma foo23: "P --> P" by auto
+lemma foo24: "P --> P" by auto
+lemma foo25: "P --> P" by auto
+lemma foo26: "P --> P" by auto
+lemma foo27: "P --> P" by auto
+lemma foo28: "P --> P" by auto
+lemma foo29: "P --> P" by auto
+lemma foo30: "P --> P" by auto
+lemma foo31: "P --> P" by auto
+lemma foo32: "P --> P" by auto
+lemma foo33: "P --> P" by auto
+lemma foo34: "P --> P" by auto
+lemma foo35: "P --> P" by auto
+lemma foo36: "P --> P" by auto
+lemma foo37: "P --> P" by auto
+lemma foo38: "P --> P" by auto
+lemma foo39: "P --> P" by auto
+lemma foo40: "P --> P" by auto
+lemma foo41: "P --> P" by auto
+lemma foo42: "P --> P" by auto
+lemma foo43: "P --> P" by auto
+lemma foo44: "P --> P" by auto
+lemma foo45: "P --> P" by auto
+lemma foo46: "P --> P" by auto
+lemma foo47: "P --> P" by auto
+lemma foo48: "P --> P" by auto
+lemma foo49: "P --> P" by auto
+lemma foo50: "P --> P" by auto
+lemma foo51: "P --> P" by auto
+lemma foo52: "P --> P" by auto
+lemma foo53: "P --> P" by auto
+lemma foo54: "P --> P" by auto
+lemma foo55: "P --> P" by auto
+lemma foo56: "P --> P" by auto
+lemma foo57: "P --> P" by auto
+lemma foo58: "P --> P" by auto
+lemma foo59: "P --> P" by auto
+lemma foo60: "P --> P" by auto
+lemma foo61: "P --> P" by auto
+lemma foo62: "P --> P" by auto
+lemma foo63: "P --> P" by auto
+lemma foo64: "P --> P" by auto
+lemma foo65: "P --> P" by auto
+lemma foo66: "P --> P" by auto
+lemma foo67: "P --> P" by auto
+lemma foo68: "P --> P" by auto
+lemma foo69: "P --> P" by auto
+lemma foo70: "P --> P" by auto
+lemma foo71: "P --> P" by auto
+lemma foo72: "P --> P" by auto
+lemma foo73: "P --> P" by auto
+lemma foo74: "P --> P" by auto
+lemma foo75: "P --> P" by auto
+lemma foo76: "P --> P" by auto
+lemma foo77: "P --> P" by auto
+lemma foo78: "P --> P" by auto
+lemma foo79: "P --> P" by auto
+lemma foo80: "P --> P" by auto
+lemma foo81: "P --> P" by auto
+lemma foo82: "P --> P" by auto
+lemma foo83: "P --> P" by auto
+lemma foo84: "P --> P" by auto
+lemma foo85: "P --> P" by auto
+lemma foo86: "P --> P" by auto
+lemma foo87: "P --> P" by auto
+lemma foo88: "P --> P" by auto
+lemma foo89: "P --> P" by auto
+lemma foo90: "P --> P" by auto
+lemma foo91: "P --> P" by auto
+lemma foo92: "P --> P" by auto
+lemma foo93: "P --> P" by auto
+lemma foo94: "P --> P" by auto
+lemma foo95: "P --> P" by auto
+lemma foo96: "P --> P" by auto
+lemma foo97: "P --> P" by auto
+lemma foo98: "P --> P" by auto
+lemma foo99: "P --> P" by auto
+lemma foo100: "P --> P" by auto
+lemma foo101: "P --> P" by auto
+lemma foo102: "P --> P" by auto
+lemma foo103: "P --> P" by auto
+lemma foo104: "P --> P" by auto
+lemma foo105: "P --> P" by auto
+lemma foo106: "P --> P" by auto
+lemma foo107: "P --> P" by auto
+lemma foo108: "P --> P" by auto
+lemma foo109: "P --> P" by auto
+lemma foo110: "P --> P" by auto
+lemma foo111: "P --> P" by auto
+lemma foo112: "P --> P" by auto
+lemma foo113: "P --> P" by auto
+lemma foo114: "P --> P" by auto
+lemma foo115: "P --> P" by auto
+lemma foo116: "P --> P" by auto
+lemma foo117: "P --> P" by auto
+lemma foo118: "P --> P" by auto
+lemma foo119: "P --> P" by auto
+lemma foo120: "P --> P" by auto
+lemma foo121: "P --> P" by auto
+lemma foo122: "P --> P" by auto
+lemma foo123: "P --> P" by auto
+lemma foo124: "P --> P" by auto
+lemma foo125: "P --> P" by auto
+lemma foo126: "P --> P" by auto
+lemma foo127: "P --> P" by auto
+lemma foo128: "P --> P" by auto
+lemma foo129: "P --> P" by auto
+lemma foo130: "P --> P" by auto
+lemma foo131: "P --> P" by auto
+lemma foo132: "P --> P" by auto
+lemma foo133: "P --> P" by auto
+lemma foo134: "P --> P" by auto
+lemma foo135: "P --> P" by auto
+lemma foo136: "P --> P" by auto
+lemma foo137: "P --> P" by auto
+lemma foo138: "P --> P" by auto
+lemma foo139: "P --> P" by auto
+lemma foo140: "P --> P" by auto
+lemma foo141: "P --> P" by auto
+lemma foo142: "P --> P" by auto
+lemma foo143: "P --> P" by auto
+lemma foo144: "P --> P" by auto
+lemma foo145: "P --> P" by auto
+lemma foo146: "P --> P" by auto
+lemma foo147: "P --> P" by auto
+lemma foo148: "P --> P" by auto
+lemma foo149: "P --> P" by auto
+lemma foo150: "P --> P" by auto
+lemma foo151: "P --> P" by auto
+lemma foo152: "P --> P" by auto
+lemma foo153: "P --> P" by auto
+lemma foo154: "P --> P" by auto
+lemma foo155: "P --> P" by auto
+lemma foo156: "P --> P" by auto
+lemma foo157: "P --> P" by auto
+lemma foo158: "P --> P" by auto
+lemma foo159: "P --> P" by auto
+lemma foo160: "P --> P" by auto
+lemma foo161: "P --> P" by auto
+lemma foo162: "P --> P" by auto
+lemma foo163: "P --> P" by auto
+lemma foo164: "P --> P" by auto
+lemma foo165: "P --> P" by auto
+lemma foo166: "P --> P" by auto
+lemma foo167: "P --> P" by auto
+lemma foo168: "P --> P" by auto
+lemma foo169: "P --> P" by auto
+lemma foo170: "P --> P" by auto
+lemma foo171: "P --> P" by auto
+lemma foo172: "P --> P" by auto
+lemma foo173: "P --> P" by auto
+lemma foo174: "P --> P" by auto
+lemma foo175: "P --> P" by auto
+lemma foo176: "P --> P" by auto
+lemma foo177: "P --> P" by auto
+lemma foo178: "P --> P" by auto
+lemma foo179: "P --> P" by auto
+lemma foo180: "P --> P" by auto
+lemma foo181: "P --> P" by auto
+lemma foo182: "P --> P" by auto
+lemma foo183: "P --> P" by auto
+lemma foo184: "P --> P" by auto
+lemma foo185: "P --> P" by auto
+lemma foo186: "P --> P" by auto
+lemma foo187: "P --> P" by auto
+lemma foo188: "P --> P" by auto
+lemma foo189: "P --> P" by auto
+lemma foo190: "P --> P" by auto
+lemma foo191: "P --> P" by auto
+lemma foo192: "P --> P" by auto
+lemma foo193: "P --> P" by auto
+lemma foo194: "P --> P" by auto
+lemma foo195: "P --> P" by auto
+lemma foo196: "P --> P" by auto
+lemma foo197: "P --> P" by auto
+lemma foo198: "P --> P" by auto
+lemma foo199: "P --> P" by auto
+lemma foo200: "P --> P" by auto
+lemma foo201: "P --> P" by auto
+lemma foo202: "P --> P" by auto
+lemma foo203: "P --> P" by auto
+lemma foo204: "P --> P" by auto
+lemma foo205: "P --> P" by auto
+lemma foo206: "P --> P" by auto
+lemma foo207: "P --> P" by auto
+lemma foo208: "P --> P" by auto
+lemma foo209: "P --> P" by auto
+lemma foo210: "P --> P" by auto
+lemma foo211: "P --> P" by auto
+lemma foo212: "P --> P" by auto
+lemma foo213: "P --> P" by auto
+lemma foo214: "P --> P" by auto
+lemma foo215: "P --> P" by auto
+lemma foo216: "P --> P" by auto
+lemma foo217: "P --> P" by auto
+lemma foo218: "P --> P" by auto
+lemma foo219: "P --> P" by auto
+lemma foo220: "P --> P" by auto
+lemma foo221: "P --> P" by auto
+lemma foo222: "P --> P" by auto
+lemma foo223: "P --> P" by auto
+lemma foo224: "P --> P" by auto
+lemma foo225: "P --> P" by auto
+lemma foo226: "P --> P" by auto
+lemma foo227: "P --> P" by auto
+lemma foo228: "P --> P" by auto
+lemma foo229: "P --> P" by auto
+lemma foo230: "P --> P" by auto
+lemma foo231: "P --> P" by auto
+lemma foo232: "P --> P" by auto
+lemma foo233: "P --> P" by auto
+lemma foo234: "P --> P" by auto
+lemma foo235: "P --> P" by auto
+lemma foo236: "P --> P" by auto
+lemma foo237: "P --> P" by auto
+lemma foo238: "P --> P" by auto
+lemma foo239: "P --> P" by auto
+lemma foo240: "P --> P" by auto
+lemma foo241: "P --> P" by auto
+lemma foo242: "P --> P" by auto
+lemma foo243: "P --> P" by auto
+lemma foo244: "P --> P" by auto
+lemma foo245: "P --> P" by auto
+lemma foo246: "P --> P" by auto
+lemma foo247: "P --> P" by auto
+lemma foo248: "P --> P" by auto
+lemma foo249: "P --> P" by auto
+lemma foo250: "P --> P" by auto
+lemma foo251: "P --> P" by auto
+lemma foo252: "P --> P" by auto
+lemma foo253: "P --> P" by auto
+lemma foo254: "P --> P" by auto
+lemma foo255: "P --> P" by auto
+lemma foo256: "P --> P" by auto
+lemma foo257: "P --> P" by auto
+lemma foo258: "P --> P" by auto
+lemma foo259: "P --> P" by auto
+lemma foo260: "P --> P" by auto
+lemma foo261: "P --> P" by auto
+lemma foo262: "P --> P" by auto
+lemma foo263: "P --> P" by auto
+lemma foo264: "P --> P" by auto
+lemma foo265: "P --> P" by auto
+lemma foo266: "P --> P" by auto
+lemma foo267: "P --> P" by auto
+lemma foo268: "P --> P" by auto
+lemma foo269: "P --> P" by auto
+lemma foo270: "P --> P" by auto
+lemma foo271: "P --> P" by auto
+lemma foo272: "P --> P" by auto
+lemma foo273: "P --> P" by auto
+lemma foo274: "P --> P" by auto
+lemma foo275: "P --> P" by auto
+lemma foo276: "P --> P" by auto
+lemma foo277: "P --> P" by auto
+lemma foo278: "P --> P" by auto
+lemma foo279: "P --> P" by auto
+lemma foo280: "P --> P" by auto
+lemma foo281: "P --> P" by auto
+lemma foo282: "P --> P" by auto
+lemma foo283: "P --> P" by auto
+lemma foo284: "P --> P" by auto
+lemma foo285: "P --> P" by auto
+lemma foo286: "P --> P" by auto
+lemma foo287: "P --> P" by auto
+lemma foo288: "P --> P" by auto
+lemma foo289: "P --> P" by auto
+lemma foo290: "P --> P" by auto
+lemma foo291: "P --> P" by auto
+lemma foo292: "P --> P" by auto
+lemma foo293: "P --> P" by auto
+lemma foo294: "P --> P" by auto
+lemma foo295: "P --> P" by auto
+lemma foo296: "P --> P" by auto
+lemma foo297: "P --> P" by auto
+lemma foo298: "P --> P" by auto
+lemma foo299: "P --> P" by auto
+lemma foo300: "P --> P" by auto
+lemma foo301: "P --> P" by auto
+lemma foo302: "P --> P" by auto
+lemma foo303: "P --> P" by auto
+lemma foo304: "P --> P" by auto
+lemma foo305: "P --> P" by auto
+lemma foo306: "P --> P" by auto
+lemma foo307: "P --> P" by auto
+lemma foo308: "P --> P" by auto
+lemma foo309: "P --> P" by auto
+lemma foo310: "P --> P" by auto
+lemma foo311: "P --> P" by auto
+lemma foo312: "P --> P" by auto
+lemma foo313: "P --> P" by auto
+lemma foo314: "P --> P" by auto
+lemma foo315: "P --> P" by auto
+lemma foo316: "P --> P" by auto
+lemma foo317: "P --> P" by auto
+lemma foo318: "P --> P" by auto
+lemma foo319: "P --> P" by auto
+lemma foo320: "P --> P" by auto
+lemma foo321: "P --> P" by auto
+lemma foo322: "P --> P" by auto
+lemma foo323: "P --> P" by auto
+lemma foo324: "P --> P" by auto
+lemma foo325: "P --> P" by auto
+lemma foo326: "P --> P" by auto
+lemma foo327: "P --> P" by auto
+lemma foo328: "P --> P" by auto
+lemma foo329: "P --> P" by auto
+lemma foo330: "P --> P" by auto
+lemma foo331: "P --> P" by auto
+lemma foo332: "P --> P" by auto
+lemma foo333: "P --> P" by auto
+lemma foo334: "P --> P" by auto
+lemma foo335: "P --> P" by auto
+lemma foo336: "P --> P" by auto
+lemma foo337: "P --> P" by auto
+lemma foo338: "P --> P" by auto
+lemma foo339: "P --> P" by auto
+lemma foo340: "P --> P" by auto
+lemma foo341: "P --> P" by auto
+lemma foo342: "P --> P" by auto
+lemma foo343: "P --> P" by auto
+lemma foo344: "P --> P" by auto
+lemma foo345: "P --> P" by auto
+lemma foo346: "P --> P" by auto
+lemma foo347: "P --> P" by auto
+lemma foo348: "P --> P" by auto
+lemma foo349: "P --> P" by auto
+lemma foo350: "P --> P" by auto
+lemma foo351: "P --> P" by auto
+lemma foo352: "P --> P" by auto
+lemma foo353: "P --> P" by auto
+lemma foo354: "P --> P" by auto
+lemma foo355: "P --> P" by auto
+lemma foo356: "P --> P" by auto
+lemma foo357: "P --> P" by auto
+lemma foo358: "P --> P" by auto
+lemma foo359: "P --> P" by auto
+lemma foo360: "P --> P" by auto
+lemma foo361: "P --> P" by auto
+lemma foo362: "P --> P" by auto
+lemma foo363: "P --> P" by auto
+lemma foo364: "P --> P" by auto
+lemma foo365: "P --> P" by auto
+lemma foo366: "P --> P" by auto
+lemma foo367: "P --> P" by auto
+lemma foo368: "P --> P" by auto
+lemma foo369: "P --> P" by auto
+lemma foo370: "P --> P" by auto
+lemma foo371: "P --> P" by auto
+lemma foo372: "P --> P" by auto
+lemma foo373: "P --> P" by auto
+lemma foo374: "P --> P" by auto
+lemma foo375: "P --> P" by auto
+lemma foo376: "P --> P" by auto
+lemma foo377: "P --> P" by auto
+lemma foo378: "P --> P" by auto
+lemma foo379: "P --> P" by auto
+lemma foo380: "P --> P" by auto
+lemma foo381: "P --> P" by auto
+lemma foo382: "P --> P" by auto
+lemma foo383: "P --> P" by auto
+lemma foo384: "P --> P" by auto
+lemma foo385: "P --> P" by auto
+lemma foo386: "P --> P" by auto
+lemma foo387: "P --> P" by auto
+lemma foo388: "P --> P" by auto
+lemma foo389: "P --> P" by auto
+lemma foo390: "P --> P" by auto
+lemma foo391: "P --> P" by auto
+lemma foo392: "P --> P" by auto
+lemma foo393: "P --> P" by auto
+lemma foo394: "P --> P" by auto
+lemma foo395: "P --> P" by auto
+lemma foo396: "P --> P" by auto
+lemma foo397: "P --> P" by auto
+lemma foo398: "P --> P" by auto
+lemma foo399: "P --> P" by auto
+lemma foo400: "P --> P" by auto
+lemma foo401: "P --> P" by auto
+lemma foo402: "P --> P" by auto
+lemma foo403: "P --> P" by auto
+lemma foo404: "P --> P" by auto
+lemma foo405: "P --> P" by auto
+lemma foo406: "P --> P" by auto
+lemma foo407: "P --> P" by auto
+lemma foo408: "P --> P" by auto
+lemma foo409: "P --> P" by auto
+lemma foo410: "P --> P" by auto
+lemma foo411: "P --> P" by auto
+lemma foo412: "P --> P" by auto
+lemma foo413: "P --> P" by auto
+lemma foo414: "P --> P" by auto
+lemma foo415: "P --> P" by auto
+lemma foo416: "P --> P" by auto
+lemma foo417: "P --> P" by auto
+lemma foo418: "P --> P" by auto
+lemma foo419: "P --> P" by auto
+lemma foo420: "P --> P" by auto
+lemma foo421: "P --> P" by auto
+lemma foo422: "P --> P" by auto
+lemma foo423: "P --> P" by auto
+lemma foo424: "P --> P" by auto
+lemma foo425: "P --> P" by auto
+lemma foo426: "P --> P" by auto
+lemma foo427: "P --> P" by auto
+lemma foo428: "P --> P" by auto
+lemma foo429: "P --> P" by auto
+lemma foo430: "P --> P" by auto
+lemma foo431: "P --> P" by auto
+lemma foo432: "P --> P" by auto
+lemma foo433: "P --> P" by auto
+lemma foo434: "P --> P" by auto
+lemma foo435: "P --> P" by auto
+lemma foo436: "P --> P" by auto
+lemma foo437: "P --> P" by auto
+lemma foo438: "P --> P" by auto
+lemma foo439: "P --> P" by auto
+lemma foo440: "P --> P" by auto
+lemma foo441: "P --> P" by auto
+lemma foo442: "P --> P" by auto
+lemma foo443: "P --> P" by auto
+lemma foo444: "P --> P" by auto
+lemma foo445: "P --> P" by auto
+lemma foo446: "P --> P" by auto
+lemma foo447: "P --> P" by auto
+lemma foo448: "P --> P" by auto
+lemma foo449: "P --> P" by auto
+lemma foo450: "P --> P" by auto
+lemma foo451: "P --> P" by auto
+lemma foo452: "P --> P" by auto
+lemma foo453: "P --> P" by auto
+lemma foo454: "P --> P" by auto
+lemma foo455: "P --> P" by auto
+lemma foo456: "P --> P" by auto
+lemma foo457: "P --> P" by auto
+lemma foo458: "P --> P" by auto
+lemma foo459: "P --> P" by auto
+lemma foo460: "P --> P" by auto
+lemma foo461: "P --> P" by auto
+lemma foo462: "P --> P" by auto
+lemma foo463: "P --> P" by auto
+lemma foo464: "P --> P" by auto
+lemma foo465: "P --> P" by auto
+lemma foo466: "P --> P" by auto
+lemma foo467: "P --> P" by auto
+lemma foo468: "P --> P" by auto
+lemma foo469: "P --> P" by auto
+lemma foo470: "P --> P" by auto
+lemma foo471: "P --> P" by auto
+lemma foo472: "P --> P" by auto
+lemma foo473: "P --> P" by auto
+lemma foo474: "P --> P" by auto
+lemma foo475: "P --> P" by auto
+lemma foo476: "P --> P" by auto
+lemma foo477: "P --> P" by auto
+lemma foo478: "P --> P" by auto
+lemma foo479: "P --> P" by auto
+lemma foo480: "P --> P" by auto
+lemma foo481: "P --> P" by auto
+lemma foo482: "P --> P" by auto
+lemma foo483: "P --> P" by auto
+lemma foo484: "P --> P" by auto
+lemma foo485: "P --> P" by auto
+lemma foo486: "P --> P" by auto
+lemma foo487: "P --> P" by auto
+lemma foo488: "P --> P" by auto
+lemma foo489: "P --> P" by auto
+lemma foo490: "P --> P" by auto
+lemma foo491: "P --> P" by auto
+lemma foo492: "P --> P" by auto
+lemma foo493: "P --> P" by auto
+lemma foo494: "P --> P" by auto
+lemma foo495: "P --> P" by auto
+lemma foo496: "P --> P" by auto
+lemma foo497: "P --> P" by auto
+lemma foo498: "P --> P" by auto
+lemma foo499: "P --> P" by auto
+lemma foo500: "P --> P" by auto
+(*lemma foo500: "P --> P" by auto *)
+lemma foo501: "P --> P" by auto
+lemma foo502: "P --> P" by auto
+lemma foo503: "P --> P" by auto
+lemma foo504: "P --> P" by auto
+lemma foo505: "P --> P" by auto
+lemma foo506: "P --> P" by auto
+lemma foo507: "P --> P" by auto
+lemma foo508: "P --> P" by auto
+lemma foo509: "P --> P" by auto
+lemma foo510: "P --> P" by auto
+lemma foo511: "P --> P" by auto
+lemma foo512: "P --> P" by auto
+lemma foo513: "P --> P" by auto
+lemma foo514: "P --> P" by auto
+lemma foo515: "P --> P" by auto
+lemma foo516: "P --> P" by auto
+lemma foo517: "P --> P" by auto
+lemma foo518: "P --> P" by auto
+lemma foo519: "P --> P" by auto
+lemma foo520: "P --> P" by auto
+lemma foo521: "P --> P" by auto
+lemma foo522: "P --> P" by auto
+lemma foo523: "P --> P" by auto
+lemma foo524: "P --> P" by auto
+lemma foo525: "P --> P" by auto
+lemma foo526: "P --> P" by auto
+lemma foo527: "P --> P" by auto
+lemma foo528: "P --> P" by auto
+lemma foo529: "P --> P" by auto
+lemma foo530: "P --> P" by auto
+lemma foo531: "P --> P" by auto
+lemma foo532: "P --> P" by auto
+lemma foo533: "P --> P" by auto
+lemma foo534: "P --> P" by auto
+lemma foo535: "P --> P" by auto
+lemma foo536: "P --> P" by auto
+lemma foo537: "P --> P" by auto
+lemma foo538: "P --> P" by auto
+lemma foo539: "P --> P" by auto
+lemma foo540: "P --> P" by auto
+lemma foo541: "P --> P" by auto
+lemma foo542: "P --> P" by auto
+lemma foo543: "P --> P" by auto
+lemma foo544: "P --> P" by auto
+lemma foo545: "P --> P" by auto
+lemma foo546: "P --> P" by auto
+lemma foo547: "P --> P" by auto
+lemma foo548: "P --> P" by auto
+lemma foo549: "P --> P" by auto
+lemma foo550: "P --> P" by auto
+lemma foo551: "P --> P" by auto
+lemma foo552: "P --> P" by auto
+lemma foo553: "P --> P" by auto
+lemma foo554: "P --> P" by auto
+lemma foo555: "P --> P" by auto
+lemma foo556: "P --> P" by auto
+lemma foo557: "P --> P" by auto
+lemma foo558: "P --> P" by auto
+lemma foo559: "P --> P" by auto
+lemma foo560: "P --> P" by auto
+lemma foo561: "P --> P" by auto
+lemma foo562: "P --> P" by auto
+lemma foo563: "P --> P" by auto
+lemma foo564: "P --> P" by auto
+lemma foo565: "P --> P" by auto
+lemma foo566: "P --> P" by auto
+lemma foo567: "P --> P" by auto
+lemma foo568: "P --> P" by auto
+lemma foo569: "P --> P" by auto
+lemma foo570: "P --> P" by auto
+lemma foo571: "P --> P" by auto
+lemma foo572: "P --> P" by auto
+lemma foo573: "P --> P" by auto
+lemma foo574: "P --> P" by auto
+lemma foo575: "P --> P" by auto
+lemma foo576: "P --> P" by auto
+lemma foo577: "P --> P" by auto
+lemma foo578: "P --> P" by auto
+lemma foo579: "P --> P" by auto
+lemma foo580: "P --> P" by auto
+lemma foo581: "P --> P" by auto
+lemma foo582: "P --> P" by auto
+lemma foo583: "P --> P" by auto
+lemma foo584: "P --> P" by auto
+lemma foo585: "P --> P" by auto
+lemma foo586: "P --> P" by auto
+lemma foo587: "P --> P" by auto
+lemma foo588: "P --> P" by auto
+lemma foo589: "P --> P" by auto
+lemma foo590: "P --> P" by auto
+lemma foo591: "P --> P" by auto
+lemma foo592: "P --> P" by auto
+lemma foo593: "P --> P" by auto
+lemma foo594: "P --> P" by auto
+lemma foo595: "P --> P" by auto
+lemma foo596: "P --> P" by auto
+lemma foo597: "P --> P" by auto
+lemma foo598: "P --> P" by auto
+lemma foo599: "P --> P" by auto
+lemma foo600: "P --> P" by auto
+lemma foo601: "P --> P" by auto
+lemma foo602: "P --> P" by auto
+lemma foo603: "P --> P" by auto
+lemma foo604: "P --> P" by auto
+lemma foo605: "P --> P" by auto
+lemma foo606: "P --> P" by auto
+lemma foo607: "P --> P" by auto
+lemma foo608: "P --> P" by auto
+lemma foo609: "P --> P" by auto
+lemma foo610: "P --> P" by auto
+lemma foo611: "P --> P" by auto
+lemma foo612: "P --> P" by auto
+lemma foo613: "P --> P" by auto
+lemma foo614: "P --> P" by auto
+lemma foo615: "P --> P" by auto
+lemma foo616: "P --> P" by auto
+lemma foo617: "P --> P" by auto
+lemma foo618: "P --> P" by auto
+lemma foo619: "P --> P" by auto
+lemma foo620: "P --> P" by auto
+lemma foo621: "P --> P" by auto
+lemma foo622: "P --> P" by auto
+lemma foo623: "P --> P" by auto
+lemma foo624: "P --> P" by auto
+lemma foo625: "P --> P" by auto
+lemma foo626: "P --> P" by auto
+lemma foo627: "P --> P" by auto
+lemma foo628: "P --> P" by auto
+lemma foo629: "P --> P" by auto
+lemma foo630: "P --> P" by auto
+lemma foo631: "P --> P" by auto
+lemma foo632: "P --> P" by auto
+lemma foo633: "P --> P" by auto
+lemma foo634: "P --> P" by auto
+lemma foo635: "P --> P" by auto
+lemma foo636: "P --> P" by auto
+lemma foo637: "P --> P" by auto
+lemma foo638: "P --> P" by auto
+lemma foo639: "P --> P" by auto
+lemma foo640: "P --> P" by auto
+lemma foo641: "P --> P" by auto
+lemma foo642: "P --> P" by auto
+lemma foo643: "P --> P" by auto
+lemma foo644: "P --> P" by auto
+lemma foo645: "P --> P" by auto
+lemma foo646: "P --> P" by auto
+lemma foo647: "P --> P" by auto
+lemma foo648: "P --> P" by auto
+lemma foo649: "P --> P" by auto
+lemma foo650: "P --> P" by auto
+lemma foo651: "P --> P" by auto
+lemma foo652: "P --> P" by auto
+lemma foo653: "P --> P" by auto
+lemma foo654: "P --> P" by auto
+lemma foo655: "P --> P" by auto
+lemma foo656: "P --> P" by auto
+lemma foo657: "P --> P" by auto
+lemma foo658: "P --> P" by auto
+lemma foo659: "P --> P" by auto
+lemma foo660: "P --> P" by auto
+lemma foo661: "P --> P" by auto
+lemma foo662: "P --> P" by auto
+lemma foo663: "P --> P" by auto
+lemma foo664: "P --> P" by auto
+lemma foo665: "P --> P" by auto
+lemma foo666: "P --> P" by auto
+lemma foo667: "P --> P" by auto
+lemma foo668: "P --> P" by auto
+lemma foo669: "P --> P" by auto
+lemma foo670: "P --> P" by auto
+lemma foo671: "P --> P" by auto
+lemma foo672: "P --> P" by auto
+lemma foo673: "P --> P" by auto
+lemma foo674: "P --> P" by auto
+lemma foo675: "P --> P" by auto
+lemma foo676: "P --> P" by auto
+lemma foo677: "P --> P" by auto
+lemma foo678: "P --> P" by auto
+lemma foo679: "P --> P" by auto
+lemma foo680: "P --> P" by auto
+lemma foo681: "P --> P" by auto
+lemma foo682: "P --> P" by auto
+lemma foo683: "P --> P" by auto
+lemma foo684: "P --> P" by auto
+lemma foo685: "P --> P" by auto
+lemma foo686: "P --> P" by auto
+lemma foo687: "P --> P" by auto
+lemma foo688: "P --> P" by auto
+lemma foo689: "P --> P" by auto
+lemma foo690: "P --> P" by auto
+lemma foo691: "P --> P" by auto
+lemma foo692: "P --> P" by auto
+lemma foo693: "P --> P" by auto
+lemma foo694: "P --> P" by auto
+lemma foo695: "P --> P" by auto
+lemma foo696: "P --> P" by auto
+lemma foo697: "P --> P" by auto
+lemma foo698: "P --> P" by auto
+lemma foo699: "P --> P" by auto
+lemma foo700: "P --> P" by auto
+lemma foo701: "P --> P" by auto
+lemma foo702: "P --> P" by auto
+lemma foo703: "P --> P" by auto
+lemma foo704: "P --> P" by auto
+lemma foo705: "P --> P" by auto
+lemma foo706: "P --> P" by auto
+lemma foo707: "P --> P" by auto
+lemma foo708: "P --> P" by auto
+lemma foo709: "P --> P" by auto
+lemma foo710: "P --> P" by auto
+lemma foo711: "P --> P" by auto
+lemma foo712: "P --> P" by auto
+lemma foo713: "P --> P" by auto
+lemma foo714: "P --> P" by auto
+lemma foo715: "P --> P" by auto
+lemma foo716: "P --> P" by auto
+lemma foo717: "P --> P" by auto
+lemma foo718: "P --> P" by auto
+lemma foo719: "P --> P" by auto
+lemma foo720: "P --> P" by auto
+lemma foo721: "P --> P" by auto
+lemma foo722: "P --> P" by auto
+lemma foo723: "P --> P" by auto
+lemma foo724: "P --> P" by auto
+lemma foo725: "P --> P" by auto
+lemma foo726: "P --> P" by auto
+lemma foo727: "P --> P" by auto
+lemma foo728: "P --> P" by auto
+lemma foo729: "P --> P" by auto
+lemma foo730: "P --> P" by auto
+lemma foo731: "P --> P" by auto
+lemma foo732: "P --> P" by auto
+lemma foo733: "P --> P" by auto
+lemma foo734: "P --> P" by auto
+lemma foo735: "P --> P" by auto
+lemma foo736: "P --> P" by auto
+lemma foo737: "P --> P" by auto
+lemma foo738: "P --> P" by auto
+lemma foo739: "P --> P" by auto
+lemma foo740: "P --> P" by auto
+lemma foo741: "P --> P" by auto
+lemma foo742: "P --> P" by auto
+lemma foo743: "P --> P" by auto
+lemma foo744: "P --> P" by auto
+lemma foo745: "P --> P" by auto
+lemma foo746: "P --> P" by auto
+lemma foo747: "P --> P" by auto
+lemma foo748: "P --> P" by auto
+lemma foo749: "P --> P" by auto
+lemma foo750: "P --> P" by auto
+lemma foo751: "P --> P" by auto
+lemma foo752: "P --> P" by auto
+lemma foo753: "P --> P" by auto
+lemma foo754: "P --> P" by auto
+lemma foo755: "P --> P" by auto
+lemma foo756: "P --> P" by auto
+lemma foo757: "P --> P" by auto
+lemma foo758: "P --> P" by auto
+lemma foo759: "P --> P" by auto
+lemma foo760: "P --> P" by auto
+lemma foo761: "P --> P" by auto
+lemma foo762: "P --> P" by auto
+lemma foo763: "P --> P" by auto
+lemma foo764: "P --> P" by auto
+lemma foo765: "P --> P" by auto
+lemma foo766: "P --> P" by auto
+lemma foo767: "P --> P" by auto
+lemma foo768: "P --> P" by auto
+lemma foo769: "P --> P" by auto
+lemma foo770: "P --> P" by auto
+lemma foo771: "P --> P" by auto
+lemma foo772: "P --> P" by auto
+lemma foo773: "P --> P" by auto
+lemma foo774: "P --> P" by auto
+lemma foo775: "P --> P" by auto
+lemma foo776: "P --> P" by auto
+lemma foo777: "P --> P" by auto
+lemma foo778: "P --> P" by auto
+lemma foo779: "P --> P" by auto
+lemma foo780: "P --> P" by auto
+lemma foo781: "P --> P" by auto
+lemma foo782: "P --> P" by auto
+lemma foo783: "P --> P" by auto
+lemma foo784: "P --> P" by auto
+lemma foo785: "P --> P" by auto
+lemma foo786: "P --> P" by auto
+lemma foo787: "P --> P" by auto
+lemma foo788: "P --> P" by auto
+lemma foo789: "P --> P" by auto
+lemma foo790: "P --> P" by auto
+lemma foo791: "P --> P" by auto
+lemma foo792: "P --> P" by auto
+lemma foo793: "P --> P" by auto
+lemma foo794: "P --> P" by auto
+lemma foo795: "P --> P" by auto
+lemma foo796: "P --> P" by auto
+lemma foo797: "P --> P" by auto
+lemma foo798: "P --> P" by auto
+lemma foo799: "P --> P" by auto
+lemma foo800: "P --> P" by auto
+lemma foo801: "P --> P" by auto
+lemma foo802: "P --> P" by auto
+lemma foo803: "P --> P" by auto
+lemma foo804: "P --> P" by auto
+lemma foo805: "P --> P" by auto
+lemma foo806: "P --> P" by auto
+lemma foo807: "P --> P" by auto
+lemma foo808: "P --> P" by auto
+lemma foo809: "P --> P" by auto
+lemma foo810: "P --> P" by auto
+lemma foo811: "P --> P" by auto
+lemma foo812: "P --> P" by auto
+lemma foo813: "P --> P" by auto
+lemma foo814: "P --> P" by auto
+lemma foo815: "P --> P" by auto
+lemma foo816: "P --> P" by auto
+lemma foo817: "P --> P" by auto
+lemma foo818: "P --> P" by auto
+lemma foo819: "P --> P" by auto
+lemma foo820: "P --> P" by auto
+lemma foo821: "P --> P" by auto
+lemma foo822: "P --> P" by auto
+lemma foo823: "P --> P" by auto
+lemma foo824: "P --> P" by auto
+lemma foo825: "P --> P" by auto
+lemma foo826: "P --> P" by auto
+lemma foo827: "P --> P" by auto
+lemma foo828: "P --> P" by auto
+lemma foo829: "P --> P" by auto
+lemma foo830: "P --> P" by auto
+lemma foo831: "P --> P" by auto
+lemma foo832: "P --> P" by auto
+lemma foo833: "P --> P" by auto
+lemma foo834: "P --> P" by auto
+lemma foo835: "P --> P" by auto
+lemma foo836: "P --> P" by auto
+lemma foo837: "P --> P" by auto
+lemma foo838: "P --> P" by auto
+lemma foo839: "P --> P" by auto
+lemma foo840: "P --> P" by auto
+lemma foo841: "P --> P" by auto
+lemma foo842: "P --> P" by auto
+lemma foo843: "P --> P" by auto
+lemma foo844: "P --> P" by auto
+lemma foo845: "P --> P" by auto
+lemma foo846: "P --> P" by auto
+lemma foo847: "P --> P" by auto
+lemma foo848: "P --> P" by auto
+lemma foo849: "P --> P" by auto
+lemma foo850: "P --> P" by auto
+lemma foo851: "P --> P" by auto
+lemma foo852: "P --> P" by auto
+lemma foo853: "P --> P" by auto
+lemma foo854: "P --> P" by auto
+lemma foo855: "P --> P" by auto
+lemma foo856: "P --> P" by auto
+lemma foo857: "P --> P" by auto
+lemma foo858: "P --> P" by auto
+lemma foo859: "P --> P" by auto
+lemma foo860: "P --> P" by auto
+lemma foo861: "P --> P" by auto
+lemma foo862: "P --> P" by auto
+lemma foo863: "P --> P" by auto
+lemma foo864: "P --> P" by auto
+lemma foo865: "P --> P" by auto
+lemma foo866: "P --> P" by auto
+lemma foo867: "P --> P" by auto
+lemma foo868: "P --> P" by auto
+lemma foo869: "P --> P" by auto
+lemma foo870: "P --> P" by auto
+lemma foo871: "P --> P" by auto
+lemma foo872: "P --> P" by auto
+lemma foo873: "P --> P" by auto
+lemma foo874: "P --> P" by auto
+lemma foo875: "P --> P" by auto
+lemma foo876: "P --> P" by auto
+lemma foo877: "P --> P" by auto
+lemma foo878: "P --> P" by auto
+lemma foo879: "P --> P" by auto
+lemma foo880: "P --> P" by auto
+lemma foo881: "P --> P" by auto
+lemma foo882: "P --> P" by auto
+lemma foo883: "P --> P" by auto
+lemma foo884: "P --> P" by auto
+lemma foo885: "P --> P" by auto
+lemma foo886: "P --> P" by auto
+lemma foo887: "P --> P" by auto
+lemma foo888: "P --> P" by auto
+lemma foo889: "P --> P" by auto
+lemma foo890: "P --> P" by auto
+lemma foo891: "P --> P" by auto
+lemma foo892: "P --> P" by auto
+lemma foo893: "P --> P" by auto
+lemma foo894: "P --> P" by auto
+lemma foo895: "P --> P" by auto
+lemma foo896: "P --> P" by auto
+lemma foo897: "P --> P" by auto
+lemma foo898: "P --> P" by auto
+lemma foo899: "P --> P" by auto
+lemma foo900: "P --> P" by auto
+lemma foo901: "P --> P" by auto
+lemma foo902: "P --> P" by auto
+lemma foo903: "P --> P" by auto
+lemma foo904: "P --> P" by auto
+lemma foo905: "P --> P" by auto
+lemma foo906: "P --> P" by auto
+lemma foo907: "P --> P" by auto
+lemma foo908: "P --> P" by auto
+lemma foo909: "P --> P" by auto
+lemma foo910: "P --> P" by auto
+lemma foo911: "P --> P" by auto
+lemma foo912: "P --> P" by auto
+lemma foo913: "P --> P" by auto
+lemma foo914: "P --> P" by auto
+lemma foo915: "P --> P" by auto
+lemma foo916: "P --> P" by auto
+lemma foo917: "P --> P" by auto
+lemma foo918: "P --> P" by auto
+lemma foo919: "P --> P" by auto
+lemma foo920: "P --> P" by auto
+lemma foo921: "P --> P" by auto
+lemma foo922: "P --> P" by auto
+lemma foo923: "P --> P" by auto
+lemma foo924: "P --> P" by auto
+lemma foo925: "P --> P" by auto
+lemma foo926: "P --> P" by auto
+lemma foo927: "P --> P" by auto
+lemma foo928: "P --> P" by auto
+lemma foo929: "P --> P" by auto
+lemma foo930: "P --> P" by auto
+lemma foo931: "P --> P" by auto
+lemma foo932: "P --> P" by auto
+lemma foo933: "P --> P" by auto
+lemma foo934: "P --> P" by auto
+lemma foo935: "P --> P" by auto
+lemma foo936: "P --> P" by auto
+lemma foo937: "P --> P" by auto
+lemma foo938: "P --> P" by auto
+lemma foo939: "P --> P" by auto
+lemma foo940: "P --> P" by auto
+lemma foo941: "P --> P" by auto
+lemma foo942: "P --> P" by auto
+lemma foo943: "P --> P" by auto
+lemma foo944: "P --> P" by auto
+lemma foo945: "P --> P" by auto
+lemma foo946: "P --> P" by auto
+lemma foo947: "P --> P" by auto
+lemma foo948: "P --> P" by auto
+lemma foo949: "P --> P" by auto
+lemma foo950: "P --> P" by auto
+lemma foo951: "P --> P" by auto
+lemma foo952: "P --> P" by auto
+lemma foo953: "P --> P" by auto
+lemma foo954: "P --> P" by auto
+lemma foo955: "P --> P" by auto
+lemma foo956: "P --> P" by auto
+lemma foo957: "P --> P" by auto
+lemma foo958: "P --> P" by auto
+lemma foo959: "P --> P" by auto
+lemma foo960: "P --> P" by auto
+lemma foo961: "P --> P" by auto
+lemma foo962: "P --> P" by auto
+lemma foo963: "P --> P" by auto
+lemma foo964: "P --> P" by auto
+lemma foo965: "P --> P" by auto
+lemma foo966: "P --> P" by auto
+lemma foo967: "P --> P" by auto
+lemma foo968: "P --> P" by auto
+lemma foo969: "P --> P" by auto
+lemma foo970: "P --> P" by auto
+lemma foo971: "P --> P" by auto
+lemma foo972: "P --> P" by auto
+lemma foo973: "P --> P" by auto
+lemma foo974: "P --> P" by auto
+lemma foo975: "P --> P" by auto
+lemma foo976: "P --> P" by auto
+lemma foo977: "P --> P" by auto
+lemma foo978: "P --> P" by auto
+lemma foo979: "P --> P" by auto
+lemma foo980: "P --> P" by auto
+lemma foo981: "P --> P" by auto
+lemma foo982: "P --> P" by auto
+lemma foo983: "P --> P" by auto
+lemma foo984: "P --> P" by auto
+lemma foo985: "P --> P" by auto
+lemma foo986: "P --> P" by auto
+lemma foo987: "P --> P" by auto
+lemma foo988: "P --> P" by auto
+lemma foo989: "P --> P" by auto
+lemma foo990: "P --> P" by auto
+lemma foo991: "P --> P" by auto
+lemma foo992: "P --> P" by auto
+lemma foo993: "P --> P" by auto
+lemma foo994: "P --> P" by auto
+lemma foo995: "P --> P" by auto
+lemma foo996: "P --> P" by auto
+lemma foo997: "P --> P" by auto
+lemma foo998: "P --> P" by auto
+lemma foo999: "P --> P" by auto
+lemma foo1000: "P --> P" by auto
+
+end