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اللي معناها لما نصلّمين إلى صحة Q إذاً an implication B implies Q can be proved by showing that if B is true then Q is also true", "tokens": [6027, 20292, 39896, 28242, 21542, 4587, 16373, 4587, 13672, 1829, 20449, 8315, 11296, 4032, 28820, 13672, 1829, 39896, 9673, 3615, 9566, 1829, 9307, 13672, 1829, 20449, 8315, 11296, 5296, 15042, 8717, 36520, 11703, 2304, 9957, 30731, 20328, 5016, 3660, 1249, 11933, 15730, 14111, 364, 37814, 363, 18779, 1249, 393, 312, 14617, 538, 4099, 300, 498, 363, 307, 2074, 550, 1249, 307, 611, 2074], "avg_logprob": -0.24938963586464524, "compression_ratio": 1.4736842105263157, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 179.61, "end": 180.11, "word": "اللي", "probability": 0.327362060546875}, {"start": 180.11, "end": 180.43, "word": " هي", "probability": 0.9091796875}, {"start": 180.43, "end": 180.79, "word": " كل", "probability": 0.90185546875}, {"start": 180.79, "end": 181.57, "word": " الحقائق", "probability": 0.9923095703125}, {"start": 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517.69, "end": 518.41, "word": " بدنا", "probability": 0.811279296875}, {"start": 518.41, "end": 519.21, "word": " نسميهم", "probability": 0.80303955078125}, {"start": 519.21, "end": 519.95, "word": " let", "probability": 0.7802734375}, {"start": 519.95, "end": 520.23, "word": " n", "probability": 0.75390625}, {"start": 520.23, "end": 520.93, "word": " بتساوي", "probability": 0.86962890625}, {"start": 520.93, "end": 521.81, "word": " اتنين", "probability": 0.86358642578125}, {"start": 521.81, "end": 522.33, "word": " k", "probability": 0.33251953125}, {"start": 522.33, "end": 522.93, "word": " زائد", "probability": 0.9471028645833334}, {"start": 522.93, "end": 523.47, "word": " واحد", "probability": 0.98779296875}, {"start": 523.47, "end": 524.05, "word": " و", "probability": 0.9541015625}, {"start": 524.05, "end": 524.29, "word": " m", "probability": 0.2384033203125}, {"start": 524.29, "end": 524.49, "word": " ايش", "probability": 0.8190104166666666}, {"start": 524.49, "end": 525.17, 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مجموحا", "probability": 0.905517578125}, {"start": 534.61, "end": 535.37, "word": " بدك", "probability": 0.7578125}, {"start": 535.37, "end": 535.85, "word": " تقول", "probability": 0.995849609375}, {"start": 535.85, "end": 536.27, "word": " n", "probability": 0.86572265625}, {"start": 536.27, "end": 536.87, "word": " زائد", "probability": 0.9713541666666666}, {"start": 536.87, "end": 537.29, "word": " m", "probability": 0.962890625}, {"start": 537.29, "end": 537.73, "word": " ايش", "probability": 0.8251953125}, {"start": 537.73, "end": 538.59, "word": " هيساوي؟", "probability": 0.87666015625}], "temperature": 1.0}, {"id": 25, "seek": 55046, "start": 539.02, "end": 550.46, "text": "2k و2j و1 زائد واحد يعني هيصير عند ال N زائد M عبارة عن 2k زائد 2j زائد 2", "tokens": [17, 74, 4032, 17, 73, 4032, 16, 30767, 16373, 3215, 36764, 24401, 37495, 22653, 8032, 1829, 9381, 13546, 43242, 2423, 426, 30767, 16373, 3215, 376, 6225, 3555, 9640, 3660, 18871, 568, 74, 30767, 16373, 3215, 568, 73, 30767, 16373, 3215, 568], "avg_logprob": -0.2706473178806759, "compression_ratio": 1.380952380952381, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 539.02, "end": 539.92, "word": "2k", "probability": 0.4949951171875}, {"start": 539.92, "end": 541.02, "word": " و2j", "probability": 0.5707194010416666}, {"start": 541.02, "end": 542.14, "word": " و1", "probability": 0.6416015625}, {"start": 542.14, "end": 542.72, "word": " زائد", "probability": 0.6214599609375}, {"start": 542.72, "end": 543.12, "word": " واحد", "probability": 0.7239990234375}, {"start": 543.12, "end": 543.38, "word": " يعني", "probability": 0.761474609375}, {"start": 543.38, "end": 543.82, "word": " هيصير", "probability": 0.7166748046875}, {"start": 543.82, "end": 544.06, "word": " عند", "probability": 0.8515625}, {"start": 544.06, "end": 544.24, "word": " ال", "probability": 0.6455078125}, {"start": 544.24, "end": 544.38, "word": " N", "probability": 0.2305908203125}, {"start": 544.38, "end": 544.88, "word": " زائد", "probability": 0.8976236979166666}, {"start": 544.88, "end": 545.14, "word": " M", "probability": 0.90478515625}, {"start": 545.14, "end": 545.68, "word": " عبارة", "probability": 0.9881591796875}, {"start": 545.68, "end": 545.84, "word": " عن", "probability": 0.97021484375}, {"start": 545.84, "end": 547.1, "word": " 2k", "probability": 0.8662109375}, {"start": 547.1, "end": 547.9, "word": " زائد", "probability": 0.8972981770833334}, {"start": 547.9, "end": 548.86, "word": " 2j", "probability": 0.951416015625}, {"start": 548.86, "end": 550.0, "word": " زائد", "probability": 0.9778645833333334}, {"start": 550.0, "end": 550.46, "word": " 2", "probability": 0.9296875}], "temperature": 1.0}, {"id": 26, "seek": 57597, "start": 551.81, "end": 575.97, "text": "أذا الان خد الاتنين عامل مشترك فيهم بيصير N زائد M اللي هو مجموح N زائد M بيساوي اتنين في العامل المشترك K زائد J زائد 1 يعني ال N زائد M كتبناه على صورة 2 زائد اللي هو اتنين M prime مثلا اللي هو is even integer", 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{"start": 564.15, "end": 564.93, "word": " يعني", "probability": 0.9189453125}, {"start": 564.93, "end": 565.09, "word": " ال", "probability": 0.88037109375}, {"start": 565.09, "end": 565.25, "word": " N", "probability": 0.8603515625}, {"start": 565.25, "end": 565.55, "word": " زائد", "probability": 0.9111328125}, {"start": 565.55, "end": 565.71, "word": " M", "probability": 0.99169921875}, {"start": 565.71, "end": 566.25, "word": " كتبناه", "probability": 0.93740234375}, {"start": 566.25, "end": 566.45, "word": " على", "probability": 0.90673828125}, {"start": 566.45, "end": 566.91, "word": " صورة", "probability": 0.9894205729166666}, {"start": 566.91, "end": 567.67, "word": " 2", "probability": 0.6328125}, {"start": 567.67, "end": 568.97, "word": " زائد", "probability": 0.9176432291666666}, {"start": 568.97, "end": 569.81, "word": " اللي", "probability": 0.6259765625}, {"start": 569.81, "end": 570.03, "word": " هو", "probability": 0.93212890625}, {"start": 570.03, "end": 570.81, 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656.38, "end": 683.26, "text": "إذا بدنا نثبت أن M في N برضه مربع كامل اضرب M في N بصير S تربيع في T تربيع اللي هو عبارة عن S في T في الكل تربيع أو اللي هو زي ما اعمل S في S في T في T انتوا عارفينه هذا الكلام سهل S في T اللي هو في S في T اللي هو عبارة عن S في T لكل تربيع يعني M في N كتبناه على صورة ST لكل تربيع ST عبارة عن رقم انتجار لأن هذا انتجار و هذا انتجار", "tokens": [28814, 15730, 47525, 8315, 8717, 12984, 3555, 2655, 14739, 376, 8978, 426, 4724, 43042, 3224, 3714, 25513, 3615, 9122, 10943, 1211, 1975, 11242, 25513, 376, 8978, 426, 4724, 9381, 13546, 318, 6055, 2288, 21292, 3615, 8978, 314, 6055, 2288, 21292, 3615, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 318, 8978, 314, 8978, 2423, 28820, 6055, 2288, 21292, 3615, 34051, 13672, 1829, 31439, 30767, 1829, 19446, 1975, 25957, 1211, 318, 8978, 318, 8978, 314, 8978, 314, 16472, 2655, 14407, 6225, 9640, 5172, 9957, 3224, 23758, 2423, 28820, 10943, 8608, 3224, 1211, 318, 8978, 314, 13672, 1829, 31439, 8978, 318, 8978, 314, 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{"start": 985.72, "end": 986.32, "word": " يعطينا", "probability": 0.9749755859375}, {"start": 986.32, "end": 986.5, "word": " أن", "probability": 0.86865234375}, {"start": 986.5, "end": 986.86, "word": " M", "probability": 0.89013671875}, {"start": 986.86, "end": 987.22, "word": " أكبر", "probability": 0.9811197916666666}, {"start": 987.22, "end": 987.32, "word": " من", "probability": 0.99560546875}, {"start": 987.32, "end": 987.58, "word": " خمس", "probability": 0.9689127604166666}, {"start": 987.58, "end": 988.16, "word": " وعشرين", "probability": 0.9874267578125}, {"start": 988.16, "end": 988.68, "word": " أو", "probability": 0.9306640625}, {"start": 988.68, "end": 989.22, "word": " N", "probability": 0.95703125}, {"start": 989.22, "end": 989.64, "word": " أكبر", "probability": 0.9847005208333334}, {"start": 989.64, "end": 989.76, "word": " من", "probability": 0.998046875}, {"start": 989.76, "end": 990.02, "word": " خمس", "probability": 0.99462890625}, {"start": 990.02, "end": 990.54, "word": " وعشرين", "probability": 0.9920654296875}], "temperature": 1.0}, {"id": 45, "seek": 100626, "start": 990.9, "end": 1006.26, "text": "الـ Contrapositive لها أنه احنا بنفترض عكس الجملة هذه كلها على بعضها و بنصل لعكس هذه يعني بدنا نفترض ايش معناه عكس M أكبر من 25 or N أكبر من 25 ايش نفيه جملة or يعني M", "tokens": [6027, 39184, 4839, 4007, 329, 2187, 5296, 11296, 14739, 3224, 1975, 5016, 8315, 44945, 5172, 2655, 43042, 6225, 4117, 3794, 25724, 2304, 37977, 29538, 28242, 11296, 15844, 45030, 11242, 11296, 4032, 44945, 36520, 5296, 3615, 4117, 3794, 29538, 37495, 22653, 47525, 8315, 8717, 5172, 2655, 43042, 1975, 1829, 8592, 20449, 8315, 3224, 6225, 4117, 3794, 376, 5551, 4117, 26890, 9154, 3552, 420, 426, 5551, 4117, 26890, 9154, 3552, 1975, 1829, 8592, 8717, 41185, 3224, 10874, 2304, 37977, 420, 37495, 22653, 376], "avg_logprob": -0.2076981683693281, "compression_ratio": 1.6153846153846154, "no_speech_prob": 9.47713851928711e-06, "words": [{"start": 990.9, "end": 991.16, "word": "الـ", "probability": 0.742431640625}, {"start": 991.16, "end": 991.94, "word": " Contrapositive", "probability": 0.8616943359375}, {"start": 991.94, "end": 992.42, "word": " لها", "probability": 0.59075927734375}, {"start": 992.42, "end": 992.84, "word": " أنه", "probability": 0.45745849609375}, {"start": 992.84, "end": 993.0, "word": " احنا", "probability": 0.795654296875}, {"start": 993.0, "end": 993.52, "word": " بنفترض", "probability": 0.95751953125}, {"start": 993.52, "end": 993.88, "word": " عكس", "probability": 0.9881184895833334}, {"start": 993.88, "end": 994.28, "word": " الجملة", "probability": 0.96337890625}, {"start": 994.28, "end": 994.58, "word": " هذه", "probability": 0.75048828125}, {"start": 994.58, "end": 995.12, "word": " كلها", "probability": 0.96240234375}, {"start": 995.12, "end": 995.32, "word": " على", "probability": 0.439208984375}, {"start": 995.32, "end": 995.92, "word": " بعضها", "probability": 0.9986979166666666}, {"start": 995.92, "end": 996.38, "word": " و", "probability": 0.51904296875}, {"start": 996.38, "end": 996.8, "word": " بنصل", "probability": 0.873046875}, {"start": 996.8, "end": 997.32, "word": " لعكس", "probability": 0.9547119140625}, {"start": 997.32, "end": 997.68, "word": " هذه", "probability": 0.81982421875}, {"start": 997.68, "end": 998.36, "word": " يعني", "probability": 0.885009765625}, {"start": 998.36, "end": 998.66, "word": " بدنا", "probability": 0.9111328125}, {"start": 998.66, "end": 999.2, "word": " نفترض", "probability": 0.9951171875}, {"start": 999.2, "end": 999.44, "word": " ايش", "probability": 0.7770182291666666}, {"start": 999.44, "end": 999.76, "word": " معناه", "probability": 0.837890625}, {"start": 999.76, "end": 1000.22, "word": " عكس", "probability": 0.9827473958333334}, {"start": 1000.22, "end": 1000.4, "word": " M", "probability": 0.70654296875}, {"start": 1000.4, "end": 1000.7, "word": " أكبر", "probability": 0.8883463541666666}, {"start": 1000.7, "end": 1000.76, "word": " من", "probability": 0.9365234375}, {"start": 1000.76, "end": 1001.14, "word": " 25", "probability": 0.97216796875}, {"start": 1001.14, "end": 1001.48, "word": " or", "probability": 0.1539306640625}, {"start": 1001.48, "end": 1001.7, "word": " N", "probability": 0.63427734375}, {"start": 1001.7, "end": 1002.0, "word": " أكبر", "probability": 0.97900390625}, {"start": 1002.0, "end": 1002.1, "word": " من", "probability": 0.99560546875}, {"start": 1002.1, "end": 1002.68, "word": " 25", "probability": 0.98583984375}, {"start": 1002.68, "end": 1003.72, "word": " ايش", "probability": 0.818359375}, {"start": 1003.72, "end": 1004.2, "word": " نفيه", "probability": 0.6853841145833334}, {"start": 1004.2, "end": 1004.6, "word": " جملة", "probability": 0.90283203125}, {"start": 1004.6, "end": 1005.1, "word": " or", "probability": 0.72705078125}, {"start": 1005.1, "end": 1005.8, "word": " يعني", "probability": 0.869873046875}, {"start": 1005.8, "end": 1006.26, "word": " M", "probability": 0.70703125}], "temperature": 1.0}, {"id": 46, "seek": 103196, "start": 1007.18, "end": 1031.96, "text": "أكبر من 25 false and أن أكبر من 25 false إيش يعني؟ يعني أم أصغر أو يساوي 25 and أن أصغر أو يساوي 25 إذا assume not q اللي هي هذه يعني بمعنى آخر assume أن أم أصغر أو يساوي 25 and أن أصغر أو يساوي 25 بناء على هذا الحديث", "tokens": [10721, 4117, 26890, 9154, 3552, 7908, 293, 14739, 5551, 4117, 26890, 9154, 3552, 7908, 11933, 1829, 8592, 37495, 22653, 22807, 37495, 22653, 5551, 2304, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 293, 14739, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 11933, 15730, 6552, 406, 9505, 13672, 1829, 39896, 29538, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 6552, 14739, 5551, 2304, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 293, 14739, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 44945, 16606, 15844, 23758, 21542, 16254, 12984], "avg_logprob": -0.1707589249221646, "compression_ratio": 2.067484662576687, "no_speech_prob": 8.106231689453125e-06, "words": [{"start": 1007.18, "end": 1007.68, "word": "أكبر", "probability": 0.71826171875}, {"start": 1007.68, "end": 1007.8, "word": " من", "probability": 0.99072265625}, {"start": 1007.8, "end": 1008.38, "word": " 25", "probability": 0.828125}, {"start": 1008.38, "end": 1009.14, "word": " false", "probability": 0.307861328125}, {"start": 1009.14, "end": 1010.18, "word": " and", "probability": 0.83203125}, {"start": 1010.18, "end": 1010.8, "word": " أن", "probability": 0.346923828125}, {"start": 1010.8, "end": 1011.2, "word": " أكبر", "probability": 0.9890950520833334}, {"start": 1011.2, "end": 1011.3, "word": " من", "probability": 0.9951171875}, {"start": 1011.3, "end": 1011.94, "word": " 25", "probability": 0.986328125}, {"start": 1011.94, "end": 1012.52, "word": " false", "probability": 0.84033203125}, {"start": 1012.52, "end": 1012.86, "word": " إيش", "probability": 0.728759765625}, {"start": 1012.86, "end": 1013.52, "word": " يعني؟", "probability": 0.7256673177083334}, {"start": 1013.52, "end": 1014.08, "word": " يعني", "probability": 0.918212890625}, {"start": 1014.08, "end": 1014.46, "word": " أم", "probability": 0.5552978515625}, {"start": 1014.46, "end": 1015.0, "word": " أصغر", "probability": 0.99267578125}, {"start": 1015.0, "end": 1015.16, "word": " أو", "probability": 0.9580078125}, {"start": 1015.16, "end": 1015.58, "word": " يساوي", "probability": 0.9720458984375}, {"start": 1015.58, "end": 1016.24, "word": " 25", "probability": 0.83349609375}, {"start": 1016.24, "end": 1017.48, "word": " and", "probability": 0.74560546875}, {"start": 1017.48, "end": 1017.88, "word": " أن", "probability": 0.86376953125}, {"start": 1017.88, "end": 1018.54, "word": " أصغر", "probability": 0.9964599609375}, {"start": 1018.54, "end": 1018.72, "word": " أو", "probability": 0.9677734375}, {"start": 1018.72, "end": 1019.38, "word": " يساوي", "probability": 0.9931640625}, {"start": 1019.38, "end": 1020.32, "word": " 25", "probability": 0.9833984375}, {"start": 1020.32, "end": 1021.24, "word": " إذا", "probability": 0.8046875}, {"start": 1021.24, "end": 1021.94, "word": " assume", "probability": 0.281982421875}, {"start": 1021.94, "end": 1022.3, "word": " not", "probability": 0.63134765625}, {"start": 1022.3, "end": 1022.7, "word": " q", "probability": 0.4462890625}, {"start": 1022.7, "end": 1022.92, "word": " اللي", "probability": 0.775634765625}, {"start": 1022.92, "end": 1023.16, "word": " هي", "probability": 0.79736328125}, {"start": 1023.16, "end": 1023.6, "word": " هذه", "probability": 0.78125}, {"start": 1023.6, "end": 1024.28, "word": " يعني", "probability": 0.929443359375}, {"start": 1024.28, "end": 1024.72, "word": " بمعنى", "probability": 0.99150390625}, {"start": 1024.72, "end": 1025.06, "word": " آخر", "probability": 0.804443359375}, {"start": 1025.06, "end": 1025.54, "word": " assume", "probability": 0.7431640625}, {"start": 1025.54, "end": 1025.78, "word": " أن", "probability": 0.90625}, {"start": 1025.78, "end": 1026.08, "word": " أم", "probability": 0.83447265625}, {"start": 1026.08, "end": 1026.38, "word": " أصغر", "probability": 0.9931640625}, {"start": 1026.38, "end": 1026.46, "word": " أو", "probability": 0.94677734375}, {"start": 1026.46, "end": 1026.6, "word": " يساوي", "probability": 0.986328125}, {"start": 1026.6, "end": 1027.18, "word": " 25", "probability": 0.9755859375}, {"start": 1027.18, "end": 1028.14, "word": " and", "probability": 0.9296875}, {"start": 1028.14, "end": 1028.4, "word": " أن", "probability": 0.97607421875}, {"start": 1028.4, "end": 1028.96, "word": " أصغر", "probability": 0.9967041015625}, {"start": 1028.96, "end": 1029.18, "word": " أو", "probability": 0.97802734375}, {"start": 1029.18, "end": 1029.6, "word": " يساوي", "probability": 0.992431640625}, {"start": 1029.6, "end": 1030.3, "word": " 25", "probability": 0.986328125}, {"start": 1030.3, "end": 1030.72, "word": " بناء", "probability": 0.94384765625}, {"start": 1030.72, "end": 1031.02, "word": " على", "probability": 0.76025390625}, {"start": 1031.02, "end": 1031.34, "word": " هذا", "probability": 0.95263671875}, {"start": 1031.34, "end": 1031.96, "word": " الحديث", "probability": 0.7529296875}], "temperature": 1.0}, {"id": 47, "seek": 105048, "start": 1032.36, "end": 1050.48, "text": "M زائد N أصغر أو سوى 25 زائد 25 يعني M زائد N أصغر أو سوى 50 مدام M زائد N أصغر أو سوى 50 إذن هي عكس هذه اللي هي عكس M زائد N أكبر من 50 إذن وصلنا نط Q نط هذه", "tokens": [44, 30767, 16373, 3215, 426, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 3552, 30767, 16373, 3215, 3552, 37495, 22653, 376, 30767, 16373, 3215, 426, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 2625, 3714, 3215, 10943, 376, 30767, 16373, 3215, 426, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 2625, 11933, 8848, 1863, 39896, 6225, 4117, 3794, 29538, 13672, 1829, 39896, 6225, 4117, 3794, 376, 30767, 16373, 3215, 426, 5551, 4117, 26890, 9154, 2625, 11933, 8848, 1863, 4032, 36520, 8315, 8717, 9566, 1249, 8717, 9566, 29538], "avg_logprob": -0.21519885754043405, "compression_ratio": 2.0, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1032.36, "end": 1032.62, "word": "M", "probability": 0.29833984375}, {"start": 1032.62, "end": 1033.02, "word": " زائد", "probability": 0.4358164469401042}, {"start": 1033.02, "end": 1033.22, "word": " N", "probability": 0.91357421875}, {"start": 1033.22, "end": 1033.88, "word": " أصغر", "probability": 0.853271484375}, {"start": 1033.88, "end": 1033.98, "word": " أو", "probability": 0.845703125}, {"start": 1033.98, "end": 1034.26, "word": " سوى", "probability": 0.7869466145833334}, {"start": 1034.26, "end": 1034.78, "word": " 25", "probability": 0.82666015625}, {"start": 1034.78, "end": 1035.24, "word": " زائد", "probability": 0.6560872395833334}, {"start": 1035.24, "end": 1035.78, "word": " 25", "probability": 0.953125}, {"start": 1035.78, "end": 1036.84, "word": " يعني", "probability": 0.630859375}, {"start": 1036.84, "end": 1037.06, "word": " M", "probability": 0.86328125}, {"start": 1037.06, "end": 1037.38, "word": " زائد", "probability": 0.93408203125}, {"start": 1037.38, "end": 1037.56, "word": " N", "probability": 0.9658203125}, {"start": 1037.56, "end": 1038.02, "word": " أصغر", "probability": 0.9722900390625}, {"start": 1038.02, "end": 1038.16, "word": " أو", "probability": 0.8974609375}, {"start": 1038.16, "end": 1038.5, "word": " سوى", "probability": 0.9306640625}, {"start": 1038.5, "end": 1039.58, "word": " 50", "probability": 0.438720703125}, {"start": 1039.58, "end": 1040.78, "word": " مدام", "probability": 0.6800130208333334}, {"start": 1040.78, "end": 1041.04, "word": " M", "probability": 0.48876953125}, {"start": 1041.04, "end": 1041.54, "word": " زائد", "probability": 0.8743489583333334}, {"start": 1041.54, "end": 1041.66, "word": " N", "probability": 0.97607421875}, {"start": 1041.66, "end": 1041.96, "word": " أصغر", "probability": 0.9619140625}, {"start": 1041.96, "end": 1042.04, "word": " أو", "probability": 0.88623046875}, {"start": 1042.04, "end": 1042.16, "word": " سوى", "probability": 0.9303385416666666}, {"start": 1042.16, "end": 1042.62, "word": " 50", "probability": 0.96533203125}, {"start": 1042.62, "end": 1042.98, "word": " إذن", "probability": 0.6189778645833334}, {"start": 1042.98, "end": 1043.16, "word": " هي", "probability": 0.4814453125}, {"start": 1043.16, "end": 1043.62, "word": " عكس", "probability": 0.99365234375}, {"start": 1043.62, "end": 1044.04, "word": " هذه", "probability": 0.69384765625}, {"start": 1044.04, "end": 1044.9, "word": " اللي", "probability": 0.70458984375}, {"start": 1044.9, "end": 1045.1, "word": " هي", "probability": 0.80078125}, {"start": 1045.1, "end": 1045.56, "word": " عكس", "probability": 0.998046875}, {"start": 1045.56, "end": 1045.76, "word": " M", "probability": 0.9306640625}, {"start": 1045.76, "end": 1046.08, "word": " زائد", "probability": 0.9178059895833334}, {"start": 1046.08, "end": 1046.26, "word": " N", "probability": 0.9912109375}, {"start": 1046.26, "end": 1046.58, "word": " أكبر", "probability": 0.9669596354166666}, {"start": 1046.58, "end": 1046.7, "word": " من", "probability": 0.9775390625}, {"start": 1046.7, "end": 1047.12, "word": " 50", "probability": 0.94677734375}, {"start": 1047.12, "end": 1047.42, "word": " إذن", "probability": 0.7884928385416666}, {"start": 1047.42, "end": 1047.94, "word": " وصلنا", "probability": 0.97412109375}, {"start": 1047.94, "end": 1049.16, "word": " نط", "probability": 0.74658203125}, {"start": 1049.16, "end": 1049.54, "word": " Q", "probability": 0.8173828125}, {"start": 1049.54, "end": 1050.02, "word": " نط", "probability": 0.928466796875}, {"start": 1050.02, "end": 1050.48, "word": " هذه", "probability": 0.82666015625}], "temperature": 1.0}, {"id": 48, "seek": 107999, "start": 1050.85, "end": 1079.99, "text": "أدت إلى نط بي اللي هي نط هذه وهذا هو ال contrapositive فبنكون هيك احنا أثبتنا ال example بواسطة إثبات ال contrapositive أو بواسطة ال indirect approve الان في سؤال بيقولي approve or disapprove يعني اثبت او اللي هو اثبت صحة او اثبت عدم صحة that يعني بيقول الجملة التالية صحيحة ولا مش صحيحة", "tokens": [10721, 3215, 2655, 30731, 8717, 9566, 4724, 1829, 13672, 1829, 39896, 8717, 9566, 29538, 37037, 15730, 31439, 2423, 660, 4007, 329, 2187, 6156, 3555, 1863, 30544, 39896, 4117, 1975, 5016, 8315, 5551, 12984, 3555, 2655, 8315, 2423, 1365, 4724, 14407, 3794, 9566, 3660, 11933, 12984, 3555, 9307, 2423, 660, 4007, 329, 2187, 34051, 4724, 14407, 3794, 9566, 3660, 2423, 19523, 18827, 2423, 7649, 8978, 8608, 33604, 6027, 4724, 1829, 39648, 1829, 18827, 420, 4518, 32467, 37495, 22653, 1975, 12984, 3555, 2655, 1975, 2407, 13672, 1829, 31439, 1975, 12984, 3555, 2655, 20328, 5016, 3660, 1975, 2407, 1975, 12984, 3555, 2655, 6225, 40448, 20328, 5016, 3660, 300, 37495, 22653, 4724, 1829, 39648, 25724, 2304, 37977, 16712, 6027, 10632, 20328, 5016, 1829, 5016, 3660, 49429, 37893, 20328, 5016, 1829, 5016, 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"end": 1077.89, "word": " يعني", "probability": 0.965576171875}, {"start": 1077.89, "end": 1078.17, "word": " بيقول", "probability": 0.953125}, {"start": 1078.17, "end": 1078.57, "word": " الجملة", "probability": 0.8798828125}, {"start": 1078.57, "end": 1078.95, "word": " التالية", "probability": 0.99267578125}, {"start": 1078.95, "end": 1079.37, "word": " صحيحة", "probability": 0.96884765625}, {"start": 1079.37, "end": 1079.47, "word": " ولا", "probability": 0.552734375}, {"start": 1079.47, "end": 1079.61, "word": " مش", "probability": 0.98583984375}, {"start": 1079.61, "end": 1079.99, "word": " صحيحة", "probability": 0.98759765625}], "temperature": 1.0}, {"id": 49, "seek": 110465, "start": 1080.77, "end": 1104.65, "text": "بقول that the product of two irrational numbers is irrational بقول لي هل حاصل ضرب two irrational numbers لازم يطلع irrational عشان نثبت لازم نثبت لكل الحالات يعني نفترض انه اي اتنين irrational و نصل الهين irrational لو في حالة واحدة بس يعني مثال واحد اللي هو هذا بنتقش يعني لو جدرنا نجيب", "tokens": [3555, 39648, 300, 264, 1674, 295, 732, 39914, 3547, 307, 39914, 4724, 39648, 32239, 8032, 1211, 11331, 33546, 1211, 48812, 25513, 732, 39914, 3547, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 39914, 6225, 8592, 7649, 8717, 12984, 3555, 2655, 5296, 31377, 2304, 8717, 12984, 3555, 2655, 5296, 28820, 21542, 6027, 9307, 37495, 22653, 8717, 5172, 2655, 43042, 16472, 3224, 1975, 1829, 1975, 2655, 1863, 9957, 39914, 4032, 8717, 36520, 2423, 3224, 9957, 39914, 45164, 8978, 11331, 6027, 3660, 36764, 24401, 3660, 4724, 3794, 37495, 22653, 50113, 6027, 36764, 24401, 13672, 1829, 31439, 23758, 4724, 29399, 4587, 8592, 37495, 22653, 45164, 10874, 3215, 2288, 8315, 8717, 7435, 1829, 3555], "avg_logprob": -0.127723623853211, "compression_ratio": 1.86784140969163, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1080.77, "end": 1081.29, "word": "بقول", "probability": 0.77734375}, {"start": 1081.29, "end": 1082.05, "word": " that", "probability": 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"word": " لو", "probability": 0.974609375}, {"start": 1098.37, "end": 1098.59, "word": " في", "probability": 0.82421875}, {"start": 1098.59, "end": 1099.07, "word": " حالة", "probability": 0.994140625}, {"start": 1099.07, "end": 1099.51, "word": " واحدة", "probability": 0.9734700520833334}, {"start": 1099.51, "end": 1099.87, "word": " بس", "probability": 0.9921875}, {"start": 1099.87, "end": 1100.25, "word": " يعني", "probability": 0.955078125}, {"start": 1100.25, "end": 1100.67, "word": " مثال", "probability": 0.98095703125}, {"start": 1100.67, "end": 1101.27, "word": " واحد", "probability": 0.995361328125}, {"start": 1101.27, "end": 1101.93, "word": " اللي", "probability": 0.973388671875}, {"start": 1101.93, "end": 1102.15, "word": " هو", "probability": 0.98046875}, {"start": 1102.15, "end": 1102.49, "word": " هذا", "probability": 0.87890625}, {"start": 1102.49, "end": 1103.21, "word": " بنتقش", "probability": 0.62213134765625}, {"start": 1103.21, "end": 1103.43, "word": " يعني", "probability": 0.966064453125}, {"start": 1103.43, "end": 1103.63, "word": " لو", "probability": 0.98046875}, {"start": 1103.63, "end": 1104.09, "word": " جدرنا", "probability": 0.9591064453125}, {"start": 1104.09, "end": 1104.65, "word": " نجيب", "probability": 0.9959716796875}], "temperature": 1.0}, {"id": 50, "seek": 111982, "start": 1104.8, "end": 1119.82, "text": "اللي هو عددين irrational حاصر ضربهم مش irrational بتكون هذه الجملة مش صحيحة وفي هذه الحالة بنقول هذا العمل هو disapprove و ال disapprove بنجيب counter example يعني بنجيب مثال عددي", "tokens": [6027, 20292, 31439, 6225, 3215, 3215, 9957, 39914, 11331, 33546, 2288, 48812, 25513, 16095, 37893, 39914, 39894, 30544, 29538, 25724, 2304, 37977, 37893, 20328, 5016, 1829, 5016, 3660, 4032, 41185, 29538, 21542, 6027, 3660, 44945, 39648, 23758, 18863, 42213, 31439, 4518, 32467, 4032, 2423, 4518, 32467, 44945, 7435, 1829, 3555, 5682, 1365, 37495, 22653, 44945, 7435, 1829, 3555, 50113, 6027, 6225, 3215, 16254], "avg_logprob": 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{"start": 1329.15, "end": 1330.01, "word": " بنعرفها", "probability": 0.961181640625}, {"start": 1330.01, "end": 1330.77, "word": " يعني", "probability": 0.95166015625}, {"start": 1330.77, "end": 1331.13, "word": " اللي", "probability": 0.93212890625}, {"start": 1331.13, "end": 1331.31, "word": " هو", "probability": 0.97705078125}, {"start": 1331.31, "end": 1331.61, "word": " proved", "probability": 0.30126953125}, {"start": 1331.61, "end": 1331.81, "word": " by", "probability": 0.9814453125}, {"start": 1331.81, "end": 1332.37, "word": " contradiction", "probability": 0.919921875}, {"start": 1332.37, "end": 1333.17, "word": " يتلخص", "probability": 0.8595703125}, {"start": 1333.17, "end": 1333.53, "word": " فيما", "probability": 0.788818359375}, {"start": 1333.53, "end": 1333.99, "word": " يليه", "probability": 0.93359375}], "temperature": 1.0}, {"id": 60, "seek": 135544, "start": 1334.24, "end": 1355.44, "text": "بنقول Assume B and Assume Not Q وبنصل لتناقض تشوف كيف بنحصل على تناقض show that هي مثال if the square of an integer number is odd then the integer is odd بيقول إذا كان مربع", "tokens": [3555, 1863, 39648, 6281, 2540, 363, 293, 6281, 2540, 1726, 1249, 46599, 1863, 36520, 5296, 2655, 8315, 4587, 11242, 6055, 8592, 38688, 9122, 33911, 44945, 5016, 36520, 15844, 6055, 8315, 4587, 11242, 855, 300, 39896, 50113, 6027, 498, 264, 3732, 295, 364, 24922, 1230, 307, 7401, 550, 264, 24922, 307, 7401, 4724, 1829, 39648, 11933, 15730, 25961, 3714, 25513, 3615], "avg_logprob": -0.2797131264796022, "compression_ratio": 1.3470588235294119, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 1334.24, "end": 1335.16, "word": "بنقول", "probability": 0.5641276041666666}, {"start": 1335.16, "end": 1336.06, "word": " Assume", "probability": 0.634033203125}, {"start": 1336.06, "end": 1338.02, "word": " B", "probability": 0.388671875}, {"start": 1338.02, "end": 1338.8, "word": " and", "probability": 0.8349609375}, {"start": 1338.8, "end": 1339.64, "word": " Assume", 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هي", "probability": 0.2109375}, {"start": 1347.4, "end": 1347.92, "word": " مثال", "probability": 0.93017578125}, {"start": 1347.92, "end": 1348.18, "word": " if", "probability": 0.5380859375}, {"start": 1348.18, "end": 1348.44, "word": " the", "probability": 0.89208984375}, {"start": 1348.44, "end": 1348.84, "word": " square", "probability": 0.89111328125}, {"start": 1348.84, "end": 1349.02, "word": " of", "probability": 0.966796875}, {"start": 1349.02, "end": 1349.22, "word": " an", "probability": 0.71337890625}, {"start": 1349.22, "end": 1349.64, "word": " integer", "probability": 0.9443359375}, {"start": 1349.64, "end": 1350.3, "word": " number", "probability": 0.94482421875}, {"start": 1350.3, "end": 1350.6, "word": " is", "probability": 0.94677734375}, {"start": 1350.6, "end": 1350.96, "word": " odd", "probability": 0.85205078125}, {"start": 1350.96, "end": 1351.62, "word": " then", "probability": 0.71923828125}, {"start": 1351.62, "end": 1351.82, "word": " the", "probability": 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odd", "probability": 0.79296875}, {"start": 1364.87, "end": 1366.09, "word": " هيعطينا", "probability": 0.91220703125}, {"start": 1366.09, "end": 1366.65, "word": " الان", "probability": 0.5660400390625}, {"start": 1366.65, "end": 1367.35, "word": " is", "probability": 0.8623046875}, {"start": 1367.35, "end": 1367.85, "word": " odd", "probability": 0.876953125}, {"start": 1367.85, "end": 1368.61, "word": " الان", "probability": 0.6676025390625}, {"start": 1368.61, "end": 1369.15, "word": " assume", "probability": 0.6953125}, {"start": 1369.15, "end": 1369.51, "word": " that", "probability": 0.91357421875}, {"start": 1369.51, "end": 1370.19, "word": " hypothesis", "probability": 0.346435546875}, {"start": 1370.19, "end": 1370.61, "word": " B", "probability": 0.52685546875}, {"start": 1370.61, "end": 1370.87, "word": " of", "probability": 0.927734375}, {"start": 1370.87, "end": 1371.13, "word": " this", "probability": 0.94970703125}, {"start": 1371.13, "end": 1371.85, "word": " 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{"start": 1462.13, "end": 1462.51, "word": " وصلنا", "probability": 0.9869791666666666}, {"start": 1462.51, "end": 1462.59, "word": " ل", "probability": 0.7568359375}, {"start": 1462.59, "end": 1462.69, "word": " X", "probability": 0.88916015625}, {"start": 1462.69, "end": 1463.15, "word": " تربيع", "probability": 0.981201171875}, {"start": 1463.15, "end": 1463.35, "word": " is", "probability": 0.94091796875}, {"start": 1463.35, "end": 1463.59, "word": " odd", "probability": 0.896484375}, {"start": 1463.59, "end": 1463.81, "word": " and", "probability": 0.82373046875}, {"start": 1463.81, "end": 1464.07, "word": " not", "probability": 0.95654296875}, {"start": 1464.07, "end": 1464.35, "word": " odd", "probability": 0.921875}, {"start": 1464.35, "end": 1464.67, "word": " which", "probability": 0.7490234375}, {"start": 1464.67, "end": 1465.03, "word": " is", "probability": 0.9638671875}, {"start": 1465.03, "end": 1465.15, "word": " a", "probability": 0.86376953125}, {"start": 1465.15, "end": 1465.67, "word": " contradiction", "probability": 0.8125}], "temperature": 1.0}, {"id": 66, "seek": 148510, "start": 1466.1, "end": 1485.1, "text": "Therefore الفرضية الأولى إن فرضنا عكس المطلوب مش صحيحة إذن لما ال X تربيع is odd لازم تطلع ال X is odd هذا المرهان by contradiction الآن نيجي ناخد مثال آخر المثال كماني", "tokens": [9077, 845, 27188, 43042, 10632, 16247, 12610, 7578, 36145, 6156, 43042, 8315, 6225, 4117, 3794, 9673, 9566, 1211, 37746, 37893, 20328, 5016, 1829, 5016, 3660, 11933, 8848, 1863, 5296, 15042, 2423, 1783, 6055, 25513, 40228, 307, 7401, 5296, 31377, 2304, 6055, 9566, 1211, 3615, 2423, 1783, 307, 7401, 23758, 9673, 2288, 3224, 7649, 538, 34937, 6024, 48506, 8717, 1829, 7435, 1829, 8717, 47283, 3215, 50113, 6027, 19753, 34740, 9673, 12984, 6027, 9122, 2304, 7649, 1829], "avg_logprob": -0.19346217771894053, "compression_ratio": 1.488888888888889, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1466.1, "end": 1467.14, "word": "Therefore", 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"probability": 0.7783203125}, {"start": 1473.94, "end": 1474.36, "word": " تربيع", "probability": 0.7374674479166666}, {"start": 1474.36, "end": 1474.54, "word": " is", "probability": 0.09698486328125}, {"start": 1474.54, "end": 1474.76, "word": " odd", "probability": 0.7119140625}, {"start": 1474.76, "end": 1475.82, "word": " لازم", "probability": 0.9837239583333334}, {"start": 1475.82, "end": 1476.62, "word": " تطلع", "probability": 0.986083984375}, {"start": 1476.62, "end": 1476.9, "word": " ال", "probability": 0.94287109375}, {"start": 1476.9, "end": 1477.38, "word": " X", "probability": 0.98974609375}, {"start": 1477.38, "end": 1478.12, "word": " is", "probability": 0.86962890625}, {"start": 1478.12, "end": 1478.38, "word": " odd", "probability": 0.9619140625}, {"start": 1478.38, "end": 1478.72, "word": " هذا", "probability": 0.86669921875}, {"start": 1478.72, "end": 1479.4, "word": " المرهان", "probability": 0.8046875}, {"start": 1479.4, "end": 1479.84, "word": " by", 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by contradiction بنفترض من عكس المطلوب", "tokens": [3555, 39648, 718, 275, 4032, 297, 4478, 294, 297, 855, 300, 498, 275, 30767, 18513, 297, 5551, 9381, 17082, 2288, 9154, 4289, 550, 275, 5551, 9381, 17082, 2288, 9154, 6905, 420, 297, 5551, 9381, 17082, 2288, 9154, 6905, 538, 34937, 9122, 33911, 22807, 44945, 5172, 2655, 43042, 9673, 3615, 9566, 2407, 27884, 30767, 1829, 19446, 31439, 44945, 5172, 2655, 43042, 14739, 275, 30767, 18513, 297, 5551, 9381, 17082, 2288, 9154, 4289, 46599, 1863, 5172, 2655, 43042, 6225, 4117, 3794, 9673, 9566, 1211, 37746, 11933, 15730, 538, 34937, 44945, 5172, 2655, 43042, 9154, 6225, 4117, 3794, 9673, 9566, 1211, 37746], "avg_logprob": -0.1807812497019768, "compression_ratio": 1.8021390374331552, "no_speech_prob": 0.0, "words": [{"start": 1486.4, "end": 1486.8, "word": "بقول", "probability": 0.6820068359375}, {"start": 1486.8, "end": 1487.08, "word": " let", "probability": 0.152099609375}, {"start": 1487.08, "end": 1487.38, "word": " m", "probability": 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1490.86, "word": " من", "probability": 0.98583984375}, {"start": 1490.86, "end": 1491.3, "word": " 90", "probability": 0.7626953125}, {"start": 1491.3, "end": 1491.54, "word": " then", "probability": 0.56201171875}, {"start": 1491.54, "end": 1491.9, "word": " m", "probability": 0.90576171875}, {"start": 1491.9, "end": 1492.2, "word": " أصغر", "probability": 0.982666015625}, {"start": 1492.2, "end": 1492.28, "word": " من", "probability": 0.986328125}, {"start": 1492.28, "end": 1492.84, "word": " 45", "probability": 0.9619140625}, {"start": 1492.84, "end": 1493.24, "word": " or", "probability": 0.65771484375}, {"start": 1493.24, "end": 1493.52, "word": " n", "probability": 0.94677734375}, {"start": 1493.52, "end": 1493.92, "word": " أصغر", "probability": 0.9915771484375}, {"start": 1493.92, "end": 1494.0, "word": " من", "probability": 0.994140625}, {"start": 1494.0, "end": 1494.66, "word": " 45", "probability": 0.96875}, {"start": 1494.66, "end": 1495.3, "word": " by", "probability": 0.469482421875}, {"start": 1495.3, "end": 1496.0, "word": " contradiction", "probability": 0.884765625}, {"start": 1496.0, "end": 1496.88, "word": " كيف؟", "probability": 0.7801920572916666}, {"start": 1496.88, "end": 1497.62, "word": " بنفترض", "probability": 0.917236328125}, {"start": 1497.62, "end": 1498.34, "word": " المعطوعة", "probability": 0.72802734375}, {"start": 1498.34, "end": 1498.58, "word": " زي", "probability": 0.9833984375}, {"start": 1498.58, "end": 1498.66, "word": " ما", "probability": 0.98681640625}, {"start": 1498.66, "end": 1498.88, "word": " هو", "probability": 0.99267578125}, {"start": 1498.88, "end": 1499.54, "word": " بنفترض", "probability": 0.84637451171875}, {"start": 1499.54, "end": 1499.68, "word": " أن", "probability": 0.65087890625}, {"start": 1499.68, "end": 1499.92, "word": " m", "probability": 0.46240234375}, {"start": 1499.92, "end": 1500.22, "word": " زاد", "probability": 0.967041015625}, {"start": 1500.22, "end": 1500.4, "word": " n", "probability": 0.91943359375}, {"start": 1500.4, "end": 1500.7, "word": " أصغر", "probability": 0.992431640625}, {"start": 1500.7, "end": 1500.84, "word": " من", "probability": 0.99560546875}, {"start": 1500.84, "end": 1501.32, "word": " 90", "probability": 0.96533203125}, {"start": 1501.32, "end": 1502.98, "word": " وبنفترض", "probability": 0.885693359375}, {"start": 1502.98, "end": 1503.66, "word": " عكس", "probability": 0.9923502604166666}, {"start": 1503.66, "end": 1504.76, "word": " المطلوب", "probability": 0.989501953125}, {"start": 1504.76, "end": 1505.1, "word": " إذا", "probability": 0.5726318359375}, {"start": 1505.1, "end": 1505.3, "word": " by", "probability": 0.8974609375}, {"start": 1505.3, "end": 1505.92, "word": " contradiction", "probability": 0.875}, {"start": 1505.92, "end": 1506.58, "word": " بنفترض", "probability": 0.9493408203125}, {"start": 1506.58, "end": 1506.86, "word": " من", "probability": 0.701171875}, {"start": 1506.86, "end": 1507.56, "word": " عكس", 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{"start": 1593.72, "end": 1594.18, "word": " جمحن", "probability": 0.66619873046875}, {"start": 1594.18, "end": 1594.56, "word": " أكبر", "probability": 0.9832356770833334}, {"start": 1594.56, "end": 1594.86, "word": " ويساوي", "probability": 0.96240234375}, {"start": 1594.86, "end": 1595.34, "word": " 45", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 72, "seek": 161859, "start": 1596.19, "end": 1618.59, "text": "اللي صارت عندي M زاد N أكبر وسوء وخمسة واربعين و M زاد N أصغر من تسعين إذا هذا contradiction therefore اللي هو الفرضية اللي فرضناها مش صحيحة يعني بمعنى أخر لما ال M زاد N أصغر من تسعين يعطينا ال M أصغر من خمسة واربعين or N أصغر من مين من خمسة واربعين هذه تسعين برضه", "tokens": [6027, 20292, 20328, 9640, 2655, 18871, 16254, 376, 30767, 18513, 426, 5551, 4117, 26890, 4032, 3794, 2407, 38207, 4032, 9778, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 4032, 376, 30767, 18513, 426, 5551, 9381, 17082, 2288, 9154, 6055, 3794, 3615, 9957, 11933, 15730, 23758, 34937, 4412, 13672, 1829, 31439, 27188, 43042, 10632, 13672, 1829, 6156, 43042, 8315, 11296, 37893, 20328, 5016, 1829, 5016, 3660, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 5296, 15042, 2423, 376, 30767, 18513, 426, 5551, 9381, 17082, 2288, 9154, 6055, 3794, 3615, 9957, 37495, 9566, 1829, 8315, 2423, 376, 5551, 9381, 17082, 2288, 9154, 16490, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 420, 426, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 16490, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 29538, 6055, 3794, 3615, 9957, 4724, 43042, 3224], "avg_logprob": -0.15681612923525381, "compression_ratio": 2.09478672985782, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1596.19, "end": 1596.45, "word": "اللي", "probability": 0.517578125}, {"start": 1596.45, "end": 1596.97, "word": " صارت", "probability": 0.7841796875}, {"start": 1596.97, "end": 1597.19, "word": " عندي", "probability": 0.7381591796875}, {"start": 1597.19, "end": 1597.37, "word": " M", 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صحيحة", "probability": 0.9890625}, {"start": 1608.31, "end": 1608.85, "word": " يعني", "probability": 0.887939453125}, {"start": 1608.85, "end": 1609.21, "word": " بمعنى", "probability": 0.9875}, {"start": 1609.21, "end": 1609.51, "word": " أخر", "probability": 0.7479248046875}, {"start": 1609.51, "end": 1609.79, "word": " لما", "probability": 0.8818359375}, {"start": 1609.79, "end": 1609.93, "word": " ال", "probability": 0.74609375}, {"start": 1609.93, "end": 1610.07, "word": " M", "probability": 0.931640625}, {"start": 1610.07, "end": 1610.37, "word": " زاد", "probability": 0.975341796875}, {"start": 1610.37, "end": 1610.59, "word": " N", "probability": 0.98828125}, {"start": 1610.59, "end": 1611.03, "word": " أصغر", "probability": 0.9918212890625}, {"start": 1611.03, "end": 1611.15, "word": " من", "probability": 0.99560546875}, {"start": 1611.15, "end": 1611.77, "word": " تسعين", "probability": 0.9915771484375}, {"start": 1611.77, "end": 1612.69, "word": " يعطينا", "probability": 0.9669189453125}, {"start": 1612.69, "end": 1612.83, "word": " ال", "probability": 0.8466796875}, {"start": 1612.83, "end": 1612.97, "word": " M", "probability": 0.9384765625}, {"start": 1612.97, "end": 1613.23, "word": " أصغر", "probability": 0.9937744140625}, {"start": 1613.23, "end": 1613.31, "word": " من", "probability": 0.994140625}, {"start": 1613.31, "end": 1613.63, "word": " خمسة", "probability": 0.92626953125}, {"start": 1613.63, "end": 1614.07, "word": " واربعين", "probability": 0.970703125}, {"start": 1614.07, "end": 1614.39, "word": " or", "probability": 0.395751953125}, {"start": 1614.39, "end": 1614.67, "word": " N", "probability": 0.64208984375}, {"start": 1614.67, "end": 1615.25, "word": " أصغر", "probability": 0.9925537109375}, {"start": 1615.25, "end": 1615.47, "word": " من", "probability": 0.9970703125}, {"start": 1615.47, "end": 1615.95, "word": " مين", "probability": 0.6990966796875}, {"start": 1615.95, "end": 1616.57, "word": " من", "probability": 0.9697265625}, {"start": 1616.57, "end": 1617.23, "word": " خمسة", "probability": 0.99365234375}, {"start": 1617.23, "end": 1617.63, "word": " واربعين", "probability": 0.9884765625}, {"start": 1617.63, "end": 1617.81, "word": " هذه", "probability": 0.3505859375}, {"start": 1617.81, "end": 1618.21, "word": " تسعين", "probability": 0.9842529296875}, {"start": 1618.21, "end": 1618.59, "word": " برضه", "probability": 0.9874674479166666}], "temperature": 1.0}, {"id": 73, "seek": 163565, "start": 1619.25, "end": 1635.65, "text": "الان اخر جزء في المحاضرة هيكون ان ال mathematical induction او الاستقراء الرياضي هي طريقة للبرهان لبرهان بعض الجمل المعينة اللي بتكون بدلالة اللي هي ال natural numbers او ال integers", "tokens": [6027, 7649, 1975, 34740, 10874, 11622, 38207, 8978, 9673, 5016, 46958, 25720, 39896, 30544, 16472, 2423, 18894, 33371, 1975, 2407, 42963, 14851, 4587, 2288, 16606, 2423, 16572, 46958, 1829, 39896, 23032, 16572, 28671, 24976, 26890, 3224, 7649, 5296, 26890, 3224, 7649, 45030, 11242, 25724, 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"probability": 0.595703125}, {"start": 1623.91, "end": 1624.71, "word": " induction", "probability": 0.98193359375}, {"start": 1624.71, "end": 1625.47, "word": " او", "probability": 0.845947265625}, {"start": 1625.47, "end": 1626.19, "word": " الاستقراء", "probability": 0.93896484375}, {"start": 1626.19, "end": 1626.91, "word": " الرياضي", "probability": 0.9295654296875}, {"start": 1626.91, "end": 1627.39, "word": " هي", "probability": 0.87060546875}, {"start": 1627.39, "end": 1627.91, "word": " طريقة", "probability": 0.990234375}, {"start": 1627.91, "end": 1628.83, "word": " للبرهان", "probability": 0.9342041015625}, {"start": 1628.83, "end": 1629.55, "word": " لبرهان", "probability": 0.878173828125}, {"start": 1629.55, "end": 1629.89, "word": " بعض", "probability": 0.9580078125}, {"start": 1629.89, "end": 1630.49, "word": " الجمل", "probability": 0.700439453125}, {"start": 1630.49, "end": 1631.57, "word": " المعينة", "probability": 0.9791259765625}, {"start": 1631.57, "end": 1631.83, 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خلصنا هذا الكلام هذه و هذه كلها على بعض أثبتناها بنكون أثبتنا اللي هو then b of n must be true for any n element in N هذا الطريقة بنسميها اللي هي ال mathematical induction أو الاستقراء الرياضي بنثبت الجملة صحيحة عند واحد", "tokens": [6027, 20292, 39896, 6156, 43042, 10632, 42963, 14851, 4587, 2288, 16606, 257, 4032, 27842, 11296, 44945, 12984, 3555, 2655, 272, 74, 30767, 16373, 3215, 36764, 24401, 45164, 16490, 1211, 9381, 8315, 23758, 2423, 28820, 10943, 29538, 4032, 29538, 28242, 11296, 15844, 45030, 11242, 5551, 12984, 3555, 2655, 8315, 11296, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 13672, 1829, 31439, 550, 272, 295, 297, 1633, 312, 2074, 337, 604, 297, 4478, 294, 426, 23758, 41950, 16572, 28671, 44945, 38251, 1829, 11296, 13672, 1829, 39896, 2423, 18894, 33371, 34051, 42963, 14851, 4587, 2288, 16606, 2423, 16572, 46958, 1829, 44945, 12984, 3555, 2655, 25724, 2304, 37977, 20328, 5016, 1829, 5016, 3660, 43242, 36764, 24401], "avg_logprob": -0.13595145754516125, 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بالاستعانة بمين بال induction hypothesis اللي فرضته هذا اللي هي دي K في K بساوة K في K زائد واحد على اتنين دعونا نشوف كده الآن ناخد الطرف الأيمن هذا proof", "tokens": [3555, 3215, 10721, 5551, 12984, 3555, 2655, 4724, 3794, 995, 2407, 3660, 3714, 9957, 5551, 8592, 26895, 28242, 591, 4032, 5551, 11242, 3615, 3714, 41361, 11296, 591, 30767, 16373, 3215, 36764, 24401, 37495, 22653, 591, 30767, 16373, 3215, 36764, 24401, 8978, 13672, 1829, 39896, 4724, 43042, 3224, 591, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 37495, 22653, 6024, 48506, 41850, 47525, 10721, 5551, 12984, 3555, 2655, 29538, 25724, 2304, 37977, 20666, 995, 14851, 3615, 7649, 3660, 4724, 2304, 9957, 20666, 33371, 17291, 13672, 1829, 6156, 43042, 47395, 23758, 13672, 1829, 39896, 11778, 1829, 591, 8978, 591, 4724, 3794, 995, 2407, 3660, 591, 8978, 591, 30767, 16373, 3215, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 11778, 3615, 2407, 8315, 8717, 8592, 38688, 9122, 3215, 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إيش هذي بيصير بدل هذه من هنا لهنا اللي هي K في K زائد واحد على اتنين بعوض عنها بيصير K في K زائد واحد على اتنين زائد الأصلي هذه K زائد واحد", "tokens": [1863, 32887, 5172, 46740, 24192, 4386, 8717, 32887, 5172, 46740, 24192, 39896, 43242, 8315, 5551, 9778, 3215, 2655, 41950, 28480, 16247, 1829, 3794, 2288, 34105, 39896, 9154, 34105, 46740, 8315, 47525, 10721, 5551, 8592, 26895, 23758, 9154, 34105, 46740, 8315, 36764, 24401, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 4032, 5551, 2655, 4587, 1211, 43242, 2423, 591, 4032, 5551, 3615, 2407, 11242, 11296, 9154, 23758, 13672, 1829, 6156, 43042, 47395, 23758, 20449, 8315, 3224, 10874, 1863, 18871, 11296, 11778, 1829, 591, 11331, 35457, 34105, 11933, 1829, 8592, 8032, 8848, 1829, 4724, 1829, 9381, 13546, 47525, 1211, 29538, 9154, 34105, 46740, 8315, 13672, 1829, 39896, 591, 8978, 591, 30767, 16373, 3215, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 45030, 2407, 11242, 18871, 11296, 4724, 1829, 9381, 13546, 591, 8978, 591, 30767, 16373, 3215, 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المقدار يعني أثبتت اللي هو هذه اللي هو أثبتت صحة واحد لمين لان بتساوي K زائد واحد ومدام أثبتتها لK زائد واحد معناته أنا اللي هو خلصت ال induction hypothesis معناته جملتيها ��ي صارت صحيحة لكل N element in N يعني لو لخصنا أيش اللي سوناه أثبتنا صحة هذه أول إشي لان بتساوي واحد و بعدين فرضنا صحتها لان بتساوي K", "tokens": [3555, 3794, 995, 45865, 23758, 9673, 28543, 9640, 37495, 22653, 5551, 12984, 3555, 2655, 2655, 13672, 1829, 31439, 29538, 13672, 1829, 31439, 5551, 12984, 3555, 2655, 2655, 20328, 5016, 3660, 36764, 24401, 32767, 9957, 5296, 7649, 39894, 3794, 995, 45865, 591, 30767, 16373, 3215, 36764, 24401, 4032, 2304, 3215, 10943, 5551, 12984, 3555, 2655, 2655, 11296, 5296, 42, 30767, 16373, 3215, 36764, 24401, 20449, 8315, 47395, 41850, 13672, 1829, 31439, 16490, 1211, 9381, 2655, 2423, 33371, 17291, 20449, 8315, 47395, 10874, 42213, 31371, 11296, 11778, 1829, 20328, 9640, 2655, 20328, 5016, 1829, 5016, 3660, 5296, 28820, 426, 4478, 294, 426, 37495, 22653, 45164, 5296, 9778, 9381, 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"probability": 0.9619140625}, {"start": 2360.25, "end": 2360.45, "word": " لو", "probability": 0.9755859375}, {"start": 2360.45, "end": 2361.01, "word": " لخصنا", "probability": 0.95166015625}, {"start": 2361.01, "end": 2361.17, "word": " أيش", "probability": 0.66845703125}, {"start": 2361.17, "end": 2361.31, "word": " اللي", "probability": 0.991943359375}, {"start": 2361.31, "end": 2362.15, "word": " سوناه", "probability": 0.8668212890625}, {"start": 2362.15, "end": 2362.75, "word": " أثبتنا", "probability": 0.99189453125}, {"start": 2362.75, "end": 2363.19, "word": " صحة", "probability": 0.9033203125}, {"start": 2363.19, "end": 2363.39, "word": " هذه", "probability": 0.60302734375}, {"start": 2363.39, "end": 2363.63, "word": " أول", "probability": 0.869873046875}, {"start": 2363.63, "end": 2363.91, "word": " إشي", "probability": 0.6449381510416666}, {"start": 2363.91, "end": 2364.11, "word": " لان", "probability": 0.88818359375}, {"start": 2364.11, "end": 2364.53, "word": " بتساوي", "probability": 0.9840087890625}, {"start": 2364.53, "end": 2364.97, "word": " واحد", "probability": 0.9873046875}, {"start": 2364.97, "end": 2365.41, "word": " و", "probability": 0.71630859375}, {"start": 2365.41, "end": 2365.85, "word": " بعدين", "probability": 0.8203125}, {"start": 2365.85, "end": 2366.55, "word": " فرضنا", "probability": 0.9928385416666666}, {"start": 2366.55, "end": 2367.15, "word": " صحتها", "probability": 0.8251139322916666}, {"start": 2367.15, "end": 2367.43, "word": " لان", "probability": 0.943603515625}, {"start": 2367.43, "end": 2368.01, "word": " بتساوي", "probability": 0.9903564453125}, {"start": 2368.01, "end": 2368.27, "word": " K", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 106, "seek": 239000, "start": 2368.54, "end": 2390.0, "text": "ومنها أثبتنا صحتها ل K زائد واحد وهذا كله على بعض هو اللي بنسميه ال mathematical induction أو الاستقراء الرياضي وبكون هيك أثبتناها لكل N element in N ناخد مثال أخر شوفوا المثال صلوا على النبي عليه الصلاة والسلام اللي بيقول show that N أصغر من 2N لكل N element in N طبعا عارفينها دي", "tokens": [20498, 1863, 11296, 5551, 12984, 3555, 2655, 8315, 20328, 33753, 11296, 5296, 591, 30767, 16373, 3215, 36764, 24401, 37037, 15730, 28242, 3224, 15844, 45030, 11242, 31439, 13672, 1829, 44945, 38251, 1829, 3224, 2423, 18894, 33371, 34051, 42963, 14851, 4587, 2288, 16606, 2423, 16572, 46958, 1829, 46599, 30544, 39896, 4117, 5551, 12984, 3555, 2655, 8315, 11296, 5296, 28820, 426, 4478, 294, 426, 8717, 47283, 3215, 50113, 6027, 5551, 34740, 13412, 38688, 14407, 9673, 12984, 6027, 20328, 1211, 14407, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 13672, 1829, 4724, 1829, 39648, 855, 300, 426, 5551, 9381, 17082, 2288, 9154, 568, 45, 5296, 28820, 426, 4478, 294, 426, 23032, 3555, 3615, 995, 6225, 9640, 5172, 9957, 11296, 11778, 1829], "avg_logprob": -0.16380207911133765, "compression_ratio": 1.696629213483146, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2368.54, 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{"start": 2379.04, "end": 2379.4, "word": " N", "probability": 0.291259765625}, {"start": 2379.4, "end": 2380.24, "word": " element", "probability": 0.85693359375}, {"start": 2380.24, "end": 2380.5, "word": " in", "probability": 0.78125}, {"start": 2380.5, "end": 2380.66, "word": " N", "probability": 0.931640625}, {"start": 2380.66, "end": 2381.38, "word": " ناخد", "probability": 0.9606119791666666}, {"start": 2381.38, "end": 2381.68, "word": " مثال", "probability": 0.99462890625}, {"start": 2381.68, "end": 2382.02, "word": " أخر", "probability": 0.704833984375}, {"start": 2382.02, "end": 2382.66, "word": " شوفوا", "probability": 0.8294270833333334}, {"start": 2382.66, "end": 2382.96, "word": " المثال", "probability": 0.9073893229166666}, {"start": 2382.96, "end": 2383.28, "word": " صلوا", "probability": 0.7303059895833334}, {"start": 2383.28, "end": 2383.36, "word": " على", "probability": 0.63818359375}, {"start": 2383.36, "end": 2383.54, "word": " النبي", "probability": 0.919677734375}, {"start": 2383.54, "end": 2383.7, "word": " عليه", "probability": 0.77587890625}, {"start": 2383.7, "end": 2384.02, "word": " الصلاة", "probability": 0.95458984375}, {"start": 2384.02, "end": 2384.36, "word": " والسلام", "probability": 0.9591471354166666}, {"start": 2384.36, "end": 2384.92, "word": " اللي", "probability": 0.974365234375}, {"start": 2384.92, "end": 2385.22, "word": " بيقول", "probability": 0.7340494791666666}, {"start": 2385.22, "end": 2385.48, "word": " show", "probability": 0.42431640625}, {"start": 2385.48, "end": 2385.86, "word": " that", "probability": 0.8916015625}, {"start": 2385.86, "end": 2386.12, "word": " N", "probability": 0.55078125}, {"start": 2386.12, "end": 2386.48, "word": " أصغر", "probability": 0.967041015625}, {"start": 2386.48, "end": 2386.6, "word": " من", "probability": 0.98486328125}, {"start": 2386.6, "end": 2387.82, "word": " 2N", "probability": 0.65625}, {"start": 2387.82, "end": 2388.2, "word": " لكل", "probability": 0.94287109375}, {"start": 2388.2, "end": 2388.46, "word": " N", "probability": 0.9677734375}, {"start": 2388.46, "end": 2388.76, "word": " element", "probability": 0.95947265625}, {"start": 2388.76, "end": 2388.94, "word": " in", "probability": 0.92041015625}, {"start": 2388.94, "end": 2389.06, "word": " N", "probability": 0.98486328125}, {"start": 2389.06, "end": 2389.32, "word": " طبعا", "probability": 0.9376220703125}, {"start": 2389.32, "end": 2389.8, "word": " عارفينها", "probability": 0.847216796875}, {"start": 2389.8, "end": 2390.0, "word": " دي", "probability": 0.923095703125}], "temperature": 1.0}, {"id": 107, "seek": 240258, "start": 2390.76, "end": 2402.58, "text": "الان كيف نرتبطها؟ برضه بنرتبطها بـ Mathematical Induction لأنه اللي هي جملة تعتمد على اللي هو ال integers أو الأعداد الطبيعية نشوف ال proof أول حاجة ال basic step", "tokens": [6027, 7649, 9122, 33911, 8717, 43500, 3555, 9566, 11296, 22807, 4724, 43042, 3224, 44945, 43500, 3555, 9566, 11296, 4724, 39184, 15776, 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