{"segments": [{"id": 1, "seek": 4792, "start": 21.24, "end": 47.92, "text": "بسم الله الرحمن الرحيم اليوم ان شاء الله عندنا مناقشة لما سبقت دراسته في chapter الأول و هو chapter ال groups تمام؟ في عندنا مجموعة من المسائل الطلبنا المرة اللي فاتت اتحلوها و بنتوقف عندها اليوم في هذه المحاضرة ان شاء الله السؤال الأول هو السؤال الخامس بيقول لي هاتلي معكوس المصوفة اتنين ستة تلاتة خمسة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 16472, 13412, 16606, 21984, 43242, 8315, 3714, 8315, 4587, 8592, 3660, 5296, 15042, 8608, 3555, 38149, 11778, 23557, 14851, 3224, 8978, 7187, 16247, 12610, 4032, 31439, 7187, 2423, 3935, 46811, 10943, 22807, 8978, 43242, 8315, 3714, 7435, 2304, 2407, 27884, 9154, 9673, 3794, 16373, 1211, 41950, 46152, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 1975, 2655, 5016, 1211, 2407, 11296, 4032, 44945, 2655, 30543, 5172, 43242, 11296, 45595, 20498, 8978, 29538, 9673, 5016, 46958, 25720, 16472, 13412, 16606, 21984, 21136, 33604, 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{"start": 963.66, "end": 964.14, "word": " واحد", "probability": 0.989013671875}, {"start": 964.14, "end": 964.84, "word": " هذا", "probability": 0.96875}, {"start": 964.84, "end": 965.4, "word": " الكلام", "probability": 0.9651692708333334}, {"start": 965.4, "end": 965.96, "word": " كله", "probability": 0.989013671875}, {"start": 965.96, "end": 966.42, "word": " ايه", "probability": 0.9593098958333334}], "temperature": 1.0}, {"id": 41, "seek": 99473, "start": 966.97, "end": 994.73, "text": "كله مضيوله in تمام يعني كل ال in هذي بده يشيلها طيب هذي in تربيه باعتبارها قداش zero سالب اتنين in كمان zero لإن كل in بده كده تحذفها ومضعفها تقدرش بيضل عندنا بيضل اللي هو الواحد يبقى بناء عليه عند العنصرين هدول هم اللذان يحققان", "tokens": [28820, 3224, 3714, 11242, 1829, 12610, 3224, 294, 46811, 10943, 37495, 22653, 28242, 2423, 294, 8032, 8848, 1829, 47525, 3224, 7251, 8592, 26895, 11296, 23032, 1829, 3555, 8032, 8848, 1829, 294, 6055, 2288, 21292, 3224, 4724, 995, 34268, 3555, 9640, 11296, 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هيك", "probability": 0.964111328125}, {"start": 1004.13, "end": 1006.21, "word": " سؤال", "probability": 0.718017578125}, {"start": 1006.21, "end": 1006.79, "word": " سبعتاش", "probability": 0.94384765625}, {"start": 1006.79, "end": 1007.23, "word": " نمسح", "probability": 0.9697265625}, {"start": 1007.23, "end": 1007.75, "word": " الناحية", "probability": 0.86962890625}, {"start": 1007.75, "end": 1008.19, "word": " هذه", "probability": 0.31298828125}], "temperature": 1.0}, {"id": 43, "seek": 105094, "start": 1023.16, "end": 1050.94, "text": "السؤال السبعتاشر بيقول ما ياتي ان جي أبيليان if and only if السؤال السبعتاشر جي أبيليان if and only if اللي هو من ال a b الكل inverse ال a b الكل inverse بده ساوي ال a inverse", "tokens": [6027, 3794, 33604, 6027, 21136, 3555, 34268, 33599, 2288, 4724, 1829, 39648, 19446, 7251, 9307, 1829, 16472, 10874, 1829, 5551, 21292, 20292, 7649, 498, 293, 787, 498, 21136, 33604, 6027, 21136, 3555, 34268, 33599, 2288, 10874, 1829, 5551, 21292, 20292, 7649, 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if", "probability": 0.4853515625}, {"start": 1028.18, "end": 1028.54, "word": " and", "probability": 0.94873046875}, {"start": 1028.54, "end": 1028.9, "word": " only", "probability": 0.8525390625}, {"start": 1028.9, "end": 1029.44, "word": " if", "probability": 0.9658203125}, {"start": 1029.44, "end": 1030.54, "word": " السؤال", "probability": 0.7513020833333334}, {"start": 1030.54, "end": 1031.6, "word": " السبعتاشر", "probability": 0.93095703125}, {"start": 1031.6, "end": 1032.26, "word": " جي", "probability": 0.860595703125}, {"start": 1032.26, "end": 1034.76, "word": " أبيليان", "probability": 0.941162109375}, {"start": 1034.76, "end": 1036.08, "word": " if", "probability": 0.96240234375}, {"start": 1036.08, "end": 1036.6, "word": " and", "probability": 0.9638671875}, {"start": 1036.6, "end": 1037.06, "word": " only", "probability": 0.90234375}, {"start": 1037.06, "end": 1037.78, "word": " if", "probability": 0.9833984375}, {"start": 1037.78, "end": 1038.86, "word": " اللي", 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1075.46, "end": 1076.02, "word": " assume", "probability": 0.95361328125}, {"start": 1076.02, "end": 1077.78, "word": " that", "probability": 0.939453125}, {"start": 1077.78, "end": 1078.68, "word": " ان", "probability": 0.77880859375}, {"start": 1078.68, "end": 1079.0, "word": " ال", "probability": 0.9580078125}, {"start": 1079.0, "end": 1079.32, "word": " g", "probability": 0.958984375}, {"start": 1079.32, "end": 1079.92, "word": " is", "probability": 0.95068359375}, {"start": 1079.92, "end": 1081.16, "word": " abelian", "probability": 0.9103190104166666}], "temperature": 1.0}, {"id": 46, "seek": 111261, "start": 1085.58, "end": 1112.62, "text": "مدام ابيليان بدي اثبت ايش بدي اثبت انه a b لكل inverse بدي يسوي a inverse b inverse لكن احنا اثبتنا سابقا ان ال a b لكل inverse يسوي b inverse a inverse يبقى هذا الكلام باجي بقوله ال a b inverse بدي يسوي اللي هو b inverse a inverse مظبوط", "tokens": [2304, 3215, 10943, 1975, 21292, 20292, 7649, 4724, 16254, 1975, 12984, 3555, 2655, 1975, 1829, 8592, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 3224, 257, 272, 5296, 28820, 17340, 4724, 16254, 7251, 3794, 45865, 257, 17340, 272, 17340, 44381, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 8608, 16758, 4587, 995, 16472, 2423, 257, 272, 5296, 28820, 17340, 7251, 3794, 45865, 272, 17340, 257, 17340, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 4724, 26108, 1829, 4724, 39648, 3224, 2423, 257, 272, 17340, 4724, 16254, 7251, 3794, 45865, 13672, 1829, 31439, 272, 17340, 257, 17340, 3714, 19913, 3555, 2407, 9566], "avg_logprob": -0.2060643517144836, "compression_ratio": 2.18125, "no_speech_prob": 0.0, "words": [{"start": 1085.58, "end": 1086.12, "word": "مدام", "probability": 0.5062662760416666}, {"start": 1086.12, "end": 1086.74, "word": " ابيليان", "probability": 0.593505859375}, {"start": 1086.74, "end": 1087.0, "word": " بدي", "probability": 0.64208984375}, {"start": 1087.0, "end": 1087.44, "word": " اثبت", "probability": 0.9371337890625}, {"start": 1087.44, "end": 1087.8, "word": " ايش", "probability": 0.82568359375}, {"start": 1087.8, "end": 1088.18, "word": " بدي", "probability": 0.7017822265625}, {"start": 1088.18, "end": 1088.68, "word": " اثبت", "probability": 0.9781494140625}, {"start": 1088.68, "end": 1089.02, "word": " انه", "probability": 0.64404296875}, {"start": 1089.02, "end": 1089.2, "word": " a", "probability": 0.403076171875}, {"start": 1089.2, "end": 1089.52, "word": " b", "probability": 0.488525390625}, {"start": 1089.52, "end": 1090.12, "word": " لكل", "probability": 0.7193603515625}, {"start": 1090.12, "end": 1091.0, "word": " inverse", "probability": 0.7958984375}, {"start": 1091.0, "end": 1091.68, "word": " بدي", "probability": 0.70703125}, {"start": 1091.68, "end": 1092.08, "word": " يسوي", "probability": 0.8028971354166666}, {"start": 1092.08, "end": 1092.4, "word": " a", "probability": 0.951171875}, {"start": 1092.4, "end": 1092.96, "word": " inverse", "probability": 0.87890625}, {"start": 1092.96, "end": 1093.16, "word": " b", "probability": 0.6787109375}, {"start": 1093.16, "end": 1093.46, "word": " inverse", "probability": 0.83349609375}, {"start": 1093.46, "end": 1093.76, "word": " لكن", "probability": 0.8427734375}, {"start": 1093.76, "end": 1094.32, "word": " احنا", "probability": 0.9864908854166666}, {"start": 1094.32, "end": 1095.4, "word": " اثبتنا", "probability": 0.916015625}, {"start": 1095.4, "end": 1096.34, "word": " سابقا", "probability": 0.9927978515625}, {"start": 1096.34, "end": 1096.9, "word": " ان", "probability": 0.92822265625}, {"start": 1096.9, "end": 1097.16, "word": " ال", "probability": 0.71826171875}, {"start": 1097.16, "end": 1097.38, "word": " a", "probability": 0.9462890625}, {"start": 1097.38, "end": 1097.66, "word": " b", "probability": 0.927734375}, {"start": 1097.66, "end": 1098.0, "word": " لكل", "probability": 0.96875}, {"start": 1098.0, "end": 1098.38, "word": " inverse", "probability": 0.94873046875}, {"start": 1098.38, "end": 1098.84, "word": " يسوي", "probability": 0.84130859375}, {"start": 1098.84, "end": 1099.3, "word": " b", "probability": 0.84033203125}, {"start": 1099.3, "end": 1099.86, "word": " inverse", "probability": 0.85009765625}, {"start": 1099.86, "end": 1100.22, "word": " a", "probability": 0.96826171875}, {"start": 1100.22, "end": 1100.8, "word": " inverse", "probability": 0.83740234375}, {"start": 1100.8, "end": 1101.72, "word": " يبقى", "probability": 0.9490966796875}, {"start": 1101.72, "end": 1102.02, "word": " هذا", "probability": 0.95263671875}, {"start": 1102.02, "end": 1102.58, "word": " الكلام", "probability": 0.96240234375}, {"start": 1102.58, "end": 1102.98, "word": " باجي", "probability": 0.8191731770833334}, {"start": 1102.98, "end": 1103.58, "word": " بقوله", "probability": 0.9306640625}, {"start": 1103.58, "end": 1103.84, "word": " ال", "probability": 0.8603515625}, {"start": 1103.84, "end": 1104.44, "word": " a", "probability": 0.95654296875}, {"start": 1104.44, "end": 1105.12, "word": " b", "probability": 0.95947265625}, {"start": 1105.12, "end": 1106.66, "word": " inverse", "probability": 0.92578125}, {"start": 1106.66, "end": 1107.14, "word": " بدي", "probability": 0.874755859375}, {"start": 1107.14, "end": 1107.7, "word": " يسوي", "probability": 0.8876953125}, {"start": 1107.7, "end": 1108.38, "word": " اللي", "probability": 0.85498046875}, {"start": 1108.38, "end": 1108.52, "word": " هو", "probability": 0.880859375}, {"start": 1108.52, "end": 1108.96, "word": " b", "probability": 0.9140625}, {"start": 1108.96, "end": 1109.96, "word": " inverse", "probability": 0.84326171875}, {"start": 1109.96, "end": 1110.5, "word": " a", "probability": 0.98974609375}, {"start": 1110.5, "end": 1111.36, "word": " inverse", "probability": 0.83056640625}, {"start": 1111.36, "end": 1112.62, "word": " مظبوط", "probability": 0.933984375}], "temperature": 1.0}, {"id": 47, "seek": 114080, "start": 1113.12, "end": 1140.8, "text": "لكن هو ايش قال لي جي مالها يبقى بقدر ابدل زي ما انا عايزه مالوش كلام عندي يبقى هنا هذا الكلام بده يساوي A inverse B inverse ليش؟ because السبب ان ال G is abelian يبقى اثبتنا الاتجاه الأول بده اروح الآن لمن؟ للاتجاه الثاني", "tokens": [1211, 19452, 31439, 1975, 1829, 8592, 50239, 32239, 10874, 1829, 3714, 6027, 11296, 7251, 3555, 4587, 7578, 4724, 28543, 2288, 1975, 44510, 1211, 30767, 1829, 19446, 1975, 8315, 6225, 47302, 11622, 3224, 3714, 6027, 2407, 8592, 28242, 10943, 18871, 16254, 7251, 3555, 4587, 7578, 34105, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 316, 17340, 363, 17340, 32239, 8592, 22807, 570, 21136, 3555, 3555, 16472, 2423, 460, 307, 410, 338, 952, 7251, 3555, 4587, 7578, 1975, 12984, 3555, 2655, 8315, 2423, 9307, 7435, 40294, 16247, 12610, 47525, 3224, 1975, 32887, 5016, 6024, 48506, 5296, 27842, 22807, 24976, 9307, 7435, 40294, 6024, 104, 7649, 1829], "avg_logprob": -0.24678738846957127, "compression_ratio": 1.721698113207547, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1113.12, "end": 1113.52, "word": "لكن", "probability": 0.5914306640625}, {"start": 1113.52, "end": 1113.64, "word": " هو", "probability": 0.29443359375}, {"start": 1113.64, "end": 1113.92, "word": " ايش", "probability": 0.781005859375}, {"start": 1113.92, "end": 1114.2, "word": " قال", "probability": 0.876953125}, {"start": 1114.2, "end": 1114.38, "word": " لي", "probability": 0.3740234375}, {"start": 1114.38, "end": 1114.58, "word": " جي", "probability": 0.666015625}, {"start": 1114.58, "end": 1115.38, "word": " مالها", "probability": 0.8052571614583334}, {"start": 1115.38, "end": 1116.52, "word": " يبقى", "probability": 0.880126953125}, {"start": 1116.52, "end": 1116.92, "word": " بقدر", "probability": 0.8487955729166666}, {"start": 1116.92, "end": 1117.3, "word": " ابدل", "probability": 0.8082682291666666}, {"start": 1117.3, "end": 1117.52, "word": " زي", "probability": 0.95654296875}, {"start": 1117.52, "end": 1117.64, "word": " ما", "probability": 0.78173828125}, {"start": 1117.64, "end": 1117.74, "word": " انا", "probability": 0.786865234375}, {"start": 1117.74, "end": 1118.04, "word": " عايزه", "probability": 0.8421630859375}, {"start": 1118.04, "end": 1118.28, "word": " مالوش", "probability": 0.68115234375}, {"start": 1118.28, "end": 1118.6, "word": " كلام", "probability": 0.86474609375}, {"start": 1118.6, "end": 1119.08, "word": " عندي", "probability": 0.6524658203125}, {"start": 1119.08, "end": 1120.06, "word": " يبقى", "probability": 0.97705078125}, {"start": 1120.06, "end": 1120.36, "word": " هنا", "probability": 0.95361328125}, {"start": 1120.36, "end": 1120.78, "word": " هذا", "probability": 0.9482421875}, {"start": 1120.78, "end": 1121.42, "word": " الكلام", "probability": 0.9524739583333334}, {"start": 1121.42, "end": 1121.8, "word": " بده", "probability": 0.472900390625}, {"start": 1121.8, "end": 1122.32, "word": " يساوي", "probability": 0.8275146484375}, {"start": 1122.32, "end": 1122.94, "word": " A", "probability": 0.50048828125}, {"start": 1122.94, "end": 1123.68, "word": " inverse", "probability": 0.7333984375}, {"start": 1123.68, "end": 1123.98, "word": " B", "probability": 0.6953125}, {"start": 1123.98, "end": 1124.42, "word": " inverse", "probability": 0.80859375}, {"start": 1124.42, "end": 1125.38, "word": " ليش؟", "probability": 0.7783203125}, {"start": 1125.38, "end": 1126.42, "word": " because", "probability": 0.61328125}, {"start": 1126.42, "end": 1127.46, "word": " السبب", "probability": 0.97802734375}, {"start": 1127.46, "end": 1128.2, "word": " ان", "probability": 0.7919921875}, {"start": 1128.2, "end": 1128.58, "word": " ال", "probability": 0.75732421875}, {"start": 1128.58, "end": 1128.98, "word": " G", "probability": 0.57177734375}, {"start": 1128.98, "end": 1129.72, "word": " is", "probability": 0.91259765625}, {"start": 1129.72, "end": 1132.0, "word": " abelian", "probability": 0.857421875}, {"start": 1132.0, "end": 1134.22, "word": " يبقى", "probability": 0.9921875}, {"start": 1134.22, "end": 1134.76, "word": " اثبتنا", "probability": 0.90595703125}, {"start": 1134.76, "end": 1135.56, "word": " الاتجاه", "probability": 0.942626953125}, {"start": 1135.56, "end": 1136.1, "word": " الأول", "probability": 0.798828125}, {"start": 1136.1, "end": 1136.88, "word": " بده", "probability": 0.529296875}, {"start": 1136.88, "end": 1137.18, "word": " اروح", "probability": 0.8525390625}, {"start": 1137.18, "end": 1137.66, "word": " الآن", "probability": 0.6778564453125}, {"start": 1137.66, "end": 1138.68, "word": " لمن؟", "probability": 0.7102864583333334}, {"start": 1138.68, "end": 1139.94, "word": " للاتجاه", "probability": 0.9573974609375}, {"start": 1139.94, "end": 1140.8, "word": " الثاني", "probability": 0.9720458984375}], "temperature": 1.0}, {"id": 48, "seek": 117429, "start": 1147.57, "end": 1174.29, "text": "الان بجيب اقوله conversely assume افترض ان ال a b لكل inverse بدي سوى a inverse b inverse بدي اثبتله ايش ليه قابله طيب بدي اقوله consider خدلي", "tokens": [6027, 7649, 4724, 7435, 1829, 3555, 1975, 39648, 3224, 2615, 736, 6552, 1975, 5172, 2655, 43042, 16472, 2423, 257, 272, 5296, 28820, 17340, 4724, 16254, 8608, 2407, 7578, 257, 17340, 272, 17340, 4724, 16254, 1975, 12984, 3555, 2655, 43761, 1975, 1829, 8592, 32239, 3224, 12174, 16758, 43761, 23032, 1829, 3555, 4724, 16254, 1975, 39648, 3224, 1949, 16490, 3215, 20292], "avg_logprob": -0.37526041865348814, "compression_ratio": 1.4964028776978417, "no_speech_prob": 0.0, "words": [{"start": 1147.57, "end": 1148.19, "word": "الان", "probability": 0.723388671875}, {"start": 1148.19, "end": 1148.61, "word": " بجيب", "probability": 0.55133056640625}, {"start": 1148.61, "end": 1149.05, "word": " اقوله", "probability": 0.6223958333333334}, {"start": 1149.05, "end": 1150.05, "word": " conversely", "probability": 0.864501953125}, {"start": 1150.05, "end": 1154.17, "word": " assume", "probability": 0.457275390625}, {"start": 1154.17, "end": 1156.45, "word": " افترض", "probability": 0.949462890625}, {"start": 1156.45, "end": 1157.45, "word": " ان", "probability": 0.93798828125}, {"start": 1157.45, "end": 1158.41, "word": " ال", "probability": 0.8994140625}, {"start": 1158.41, "end": 1158.85, "word": " a", "probability": 0.59033203125}, {"start": 1158.85, "end": 1159.45, "word": " b", "probability": 0.36962890625}, {"start": 1159.45, "end": 1160.15, "word": " لكل", "probability": 0.76123046875}, {"start": 1160.15, "end": 1161.03, "word": " inverse", "probability": 0.81884765625}, {"start": 1161.03, "end": 1161.85, "word": " بدي", "probability": 0.564453125}, {"start": 1161.85, "end": 1162.41, "word": " سوى", "probability": 0.6024576822916666}, {"start": 1162.41, "end": 1162.81, "word": " a", "probability": 0.96435546875}, {"start": 1162.81, "end": 1163.55, "word": " inverse", "probability": 0.833984375}, {"start": 1163.55, "end": 1163.85, "word": " b", "probability": 0.5908203125}, {"start": 1163.85, "end": 1164.43, "word": " inverse", "probability": 0.84521484375}, {"start": 1164.43, "end": 1165.31, "word": " بدي", "probability": 0.7161865234375}, {"start": 1165.31, "end": 1165.81, "word": " اثبتله", "probability": 0.86845703125}, {"start": 1165.81, "end": 1167.55, "word": " ايش", "probability": 0.79833984375}, {"start": 1167.55, "end": 1168.77, "word": " ليه", "probability": 0.6378173828125}, {"start": 1168.77, "end": 1169.25, "word": " قابله", "probability": 0.4676106770833333}, {"start": 1169.25, "end": 1170.75, "word": " طيب", "probability": 0.8395182291666666}, {"start": 1170.75, "end": 1171.31, "word": " بدي", "probability": 0.695556640625}, {"start": 1171.31, "end": 1172.15, "word": " اقوله", "probability": 0.7400716145833334}, {"start": 1172.15, "end": 1173.03, "word": " consider", "probability": 0.88623046875}, {"start": 1173.03, "end": 1174.29, "word": " خدلي", "probability": 0.78173828125}], "temperature": 1.0}, {"id": 49, "seek": 120374, "start": 1175.48, "end": 1203.74, "text": "يعني بدي أثبت أن الـ A في B بدي أثبت بي في A لكل الـ A و B اللي موجودة في G consider A و B any elements أي عناصر in G طيب لو أخدت الآن الـ A بي الكل inverse", "tokens": [40228, 22653, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 2423, 39184, 316, 8978, 363, 4724, 16254, 5551, 12984, 3555, 2655, 4724, 1829, 8978, 316, 5296, 28820, 2423, 39184, 316, 4032, 363, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 460, 1949, 316, 4032, 363, 604, 4959, 36632, 18871, 33546, 2288, 294, 460, 23032, 1829, 3555, 45164, 5551, 9778, 3215, 2655, 6024, 48506, 2423, 39184, 316, 4724, 1829, 2423, 28820, 17340], "avg_logprob": -0.3180803584200995, "compression_ratio": 1.481012658227848, "no_speech_prob": 0.0, "words": [{"start": 1175.48, "end": 1175.92, "word": "يعني", "probability": 0.50408935546875}, {"start": 1175.92, "end": 1176.24, "word": " بدي", "probability": 0.6942138671875}, {"start": 1176.24, "end": 1176.74, "word": " أثبت", "probability": 0.9150390625}, {"start": 1176.74, "end": 1177.0, "word": " أن", "probability": 0.53857421875}, {"start": 1177.0, "end": 1177.36, "word": " الـ", "probability": 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يبقى السعر عندي ب في a في ال identity element بدي سوى ال identity element في a,b طب ال identity element لما تضرب في أي element تطلع من نفس ال element يبقى b في a بدي سوى a في b", "tokens": [2304, 8592, 36764, 24401, 20449, 4117, 41779, 16712, 7649, 1829, 7251, 3555, 4587, 7578, 11331, 33546, 1211, 48812, 25513, 3224, 15042, 20666, 6575, 4478, 7251, 3555, 4587, 7578, 21136, 3615, 2288, 18871, 16254, 4724, 8978, 257, 8978, 2423, 6575, 4478, 4724, 16254, 8608, 2407, 7578, 2423, 6575, 4478, 8978, 257, 11, 65, 23032, 3555, 2423, 6575, 4478, 5296, 15042, 6055, 11242, 25513, 8978, 36632, 4478, 6055, 9566, 1211, 3615, 9154, 8717, 36178, 2423, 4478, 7251, 3555, 4587, 7578, 272, 8978, 257, 4724, 16254, 8608, 2407, 7578, 257, 8978, 272], "avg_logprob": -0.21822916252745522, "compression_ratio": 1.937142857142857, "no_speech_prob": 0.0, "words": [{"start": 1299.49, "end": 1299.77, "word": "مش", "probability": 0.52081298828125}, {"start": 1299.77, "end": 1300.07, "word": " واحد", "probability": 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على", "probability": 0.68359375}, {"start": 1331.27, "end": 1331.55, "word": " ا", "probability": 0.454345703125}, {"start": 1331.55, "end": 1331.73, "word": " و", "probability": 0.380859375}, {"start": 1331.73, "end": 1333.33, "word": " ب؟", "probability": 0.6434326171875}, {"start": 1333.33, "end": 1333.59, "word": " اي", "probability": 0.8046875}, {"start": 1333.59, "end": 1334.21, "word": " عناصر", "probability": 0.9899088541666666}, {"start": 1334.21, "end": 1334.37, "word": " في", "probability": 0.90478515625}, {"start": 1334.37, "end": 1334.59, "word": " جي", "probability": 0.60888671875}, {"start": 1334.59, "end": 1334.73, "word": " يبقى", "probability": 0.9063720703125}, {"start": 1334.73, "end": 1335.09, "word": " بنان", "probability": 0.785888671875}, {"start": 1335.09, "end": 1335.39, "word": " عليه", "probability": 0.36279296875}, {"start": 1335.39, "end": 1336.59, "word": " مالها؟", "probability": 0.7357177734375}, {"start": 1336.59, "end": 1336.79, "word": " جي", "probability": 0.7298583984375}, {"start": 1336.79, "end": 1337.03, "word": " is", "probability": 0.734375}, {"start": 1337.03, "end": 1337.63, "word": " abelian", "probability": 0.81298828125}, {"start": 1337.63, "end": 1338.79, "word": " يبقى", "probability": 0.9476318359375}, {"start": 1338.79, "end": 1339.19, "word": " هنا", "probability": 0.9765625}, {"start": 1339.19, "end": 1340.19, "word": " سا", "probability": 0.37255859375}, {"start": 1340.19, "end": 1341.95, "word": " جي", "probability": 0.8486328125}, {"start": 1341.95, "end": 1342.61, "word": " is", "probability": 0.91650390625}, {"start": 1342.61, "end": 1344.15, "word": " abelian", "probability": 0.9488932291666666}], "temperature": 1.0}, {"id": 56, "seek": 137262, "start": 1349.98, "end": 1372.62, "text": "هذا سؤال سبعتاش سؤال سؤال سؤال تمانتاش هذا حلناه في المحاضرة أخدناه كمثال طيب سؤال تسعتاش بيقولي لأي element a و b من group G and any integer n prove that", "tokens": [3224, 15730, 8608, 33604, 6027, 8608, 3555, 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"probability": 0.9527994791666666}, {"start": 1357.22, "end": 1358.34, "word": " تمانتاش", "probability": 0.937255859375}, {"start": 1358.34, "end": 1358.6, "word": " هذا", "probability": 0.78271484375}, {"start": 1358.6, "end": 1359.12, "word": " حلناه", "probability": 0.9345703125}, {"start": 1359.12, "end": 1359.18, "word": " في", "probability": 0.833984375}, {"start": 1359.18, "end": 1359.82, "word": " المحاضرة", "probability": 0.9617919921875}, {"start": 1359.82, "end": 1360.5, "word": " أخدناه", "probability": 0.844384765625}, {"start": 1360.5, "end": 1361.28, "word": " كمثال", "probability": 0.9842529296875}, {"start": 1361.28, "end": 1362.32, "word": " طيب", "probability": 0.9332682291666666}, {"start": 1362.32, "end": 1362.72, "word": " سؤال", "probability": 0.9861653645833334}, {"start": 1362.72, "end": 1363.74, "word": " تسعتاش", "probability": 0.8590087890625}, {"start": 1363.74, "end": 1364.74, "word": " بيقولي", "probability": 0.84246826171875}, {"start": 1364.74, "end": 1365.06, "word": " لأي", "probability": 0.9114583333333334}, {"start": 1365.06, "end": 1365.5, "word": " element", "probability": 0.951171875}, {"start": 1365.5, "end": 1365.76, "word": " a", "probability": 0.73681640625}, {"start": 1365.76, "end": 1365.88, "word": " و", "probability": 0.8486328125}, {"start": 1365.88, "end": 1366.04, "word": " b", "probability": 0.53173828125}, {"start": 1366.04, "end": 1366.3, "word": " من", "probability": 0.97607421875}, {"start": 1366.3, "end": 1366.78, "word": " group", "probability": 0.72900390625}, {"start": 1366.78, "end": 1367.58, "word": " G", "probability": 0.57861328125}, {"start": 1367.58, "end": 1369.42, "word": " and", "probability": 0.916015625}, {"start": 1369.42, "end": 1369.84, "word": " any", "probability": 0.87744140625}, {"start": 1369.84, "end": 1370.68, "word": " integer", "probability": 0.89404296875}, {"start": 1370.68, "end": 1371.42, "word": " n", "probability": 0.6103515625}, {"start": 1371.42, "end": 1372.1, "word": " prove", "probability": 0.646484375}, {"start": 1372.1, "end": 1372.62, "word": " that", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 57, "seek": 139795, "start": 1373.05, "end": 1397.95, "text": "ثم اثبت ان ال a inverse b a to the power n يسوى a inverse b in a و ال n هدا is an integer", "tokens": [12984, 2304, 1975, 12984, 3555, 2655, 16472, 2423, 257, 17340, 272, 257, 281, 264, 1347, 297, 7251, 3794, 2407, 7578, 257, 17340, 272, 294, 257, 4032, 2423, 297, 8032, 28259, 307, 364, 24922], "avg_logprob": -0.4664522093885085, "compression_ratio": 1.1473684210526316, "no_speech_prob": 0.0, "words": [{"start": 1373.05, "end": 1373.31, "word": "ثم", "probability": 0.4893798828125}, {"start": 1373.31, "end": 1373.95, "word": " اثبت", "probability": 0.921630859375}, {"start": 1373.95, "end": 1377.39, "word": " ان", "probability": 0.58935546875}, {"start": 1377.39, "end": 1378.59, "word": " ال", "probability": 0.7431640625}, {"start": 1378.59, "end": 1379.19, "word": " a", "probability": 0.170166015625}, {"start": 1379.19, "end": 1381.81, "word": " inverse", "probability": 0.361083984375}, {"start": 1381.81, "end": 1382.31, "word": " b", "probability": 0.315673828125}, {"start": 1382.31, "end": 1382.97, "word": " a", "probability": 0.509765625}, {"start": 1382.97, "end": 1386.91, "word": " to", "probability": 0.4169921875}, {"start": 1386.91, "end": 1387.23, "word": " the", "probability": 0.86767578125}, {"start": 1387.23, "end": 1387.77, "word": " power", "probability": 0.89990234375}, {"start": 1387.77, "end": 1388.21, "word": " n", "probability": 0.76513671875}, {"start": 1388.21, "end": 1389.27, "word": " يسوى", "probability": 0.60577392578125}, {"start": 1389.27, "end": 1389.73, "word": " a", "probability": 0.91064453125}, {"start": 1389.73, "end": 1390.49, "word": " inverse", "probability": 0.8515625}, {"start": 1390.49, "end": 1391.13, "word": " b", "probability": 0.90625}, {"start": 1391.13, "end": 1391.83, "word": " in", "probability": 0.84716796875}, {"start": 1391.83, "end": 1392.67, "word": " a", "probability": 0.904296875}, {"start": 1392.67, "end": 1393.41, "word": " و", "probability": 0.325927734375}, {"start": 1393.41, "end": 1393.65, "word": " ال", "probability": 0.81396484375}, {"start": 1393.65, "end": 1394.03, "word": " n", "probability": 0.2490234375}, {"start": 1394.03, "end": 1394.83, "word": " هدا", "probability": 0.450439453125}, {"start": 1394.83, "end": 1396.29, "word": " is", "probability": 0.79833984375}, {"start": 1396.29, "end": 1397.23, "word": " an", "probability": 0.7548828125}, {"start": 1397.23, "end": 1397.95, "word": " integer", "probability": 0.93017578125}], "temperature": 1.0}, {"id": 58, "seek": 141945, "start": 1400.71, "end": 1419.45, "text": "قال يثبت ان الطرفين هدول متساوين حد فيكوا حل هذا السؤال؟ و لو نص حل يعني بال induction بس ال induction اللي اتعلمناه على عدد صحيح موجة صح؟", "tokens": [4587, 6027, 7251, 12984, 3555, 2655, 16472, 41950, 28480, 9957, 8032, 3215, 12610, 44650, 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بس", "probability": 0.794189453125}, {"start": 1412.87, "end": 1413.05, "word": " ال", "probability": 0.8125}, {"start": 1413.05, "end": 1413.57, "word": " induction", "probability": 0.9951171875}, {"start": 1413.57, "end": 1413.91, "word": " اللي", "probability": 0.8193359375}, {"start": 1413.91, "end": 1415.49, "word": " اتعلمناه", "probability": 0.9457194010416666}, {"start": 1415.49, "end": 1415.99, "word": " على", "probability": 0.88134765625}, {"start": 1415.99, "end": 1416.73, "word": " عدد", "probability": 0.9791666666666666}, {"start": 1416.73, "end": 1417.89, "word": " صحيح", "probability": 0.9945068359375}, {"start": 1417.89, "end": 1418.43, "word": " موجة", "probability": 0.8219401041666666}, {"start": 1418.43, "end": 1419.45, "word": " صح؟", "probability": 0.8997395833333334}], "temperature": 1.0}, {"id": 59, "seek": 143486, "start": 1420.2, "end": 1434.86, "text": "سكت الشعور مش شكت في المبادئ أخدنا ال induction على إن عدد صحيح موجه طيب نشوف بدنا نروح نستخدم ال induction و نشوف هل الكلام هذا صحيح ولا لأ بس هنا جالي انتجار", "tokens": [3794, 4117, 2655, 25124, 3615, 13063, 37893, 13412, 4117, 2655, 8978, 9673, 3555, 18513, 19986, 5551, 9778, 3215, 8315, 2423, 33371, 15844, 36145, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3224, 23032, 1829, 3555, 8717, 8592, 38688, 47525, 8315, 8717, 32887, 5016, 8717, 14851, 9778, 40448, 2423, 33371, 4032, 8717, 8592, 38688, 8032, 1211, 2423, 28820, 10943, 23758, 20328, 5016, 1829, 5016, 49429, 5296, 10721, 4724, 3794, 34105, 10874, 6027, 1829, 16472, 2655, 7435, 9640], "avg_logprob": -0.15655048802877083, "compression_ratio": 1.6144578313253013, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1420.2, "end": 1420.68, "word": "سكت", "probability": 0.5509440104166666}, {"start": 1420.68, "end": 1421.2, "word": " الشعور", "probability": 0.6427408854166666}, {"start": 1421.2, "end": 1421.54, "word": " مش", "probability": 0.8095703125}, {"start": 1421.54, "end": 1421.88, "word": " شكت", 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نشوف", "probability": 0.9127604166666666}, {"start": 1428.34, "end": 1428.84, "word": " بدنا", "probability": 0.8125}, {"start": 1428.84, "end": 1429.2, "word": " نروح", "probability": 0.966796875}, {"start": 1429.2, "end": 1429.76, "word": " نستخدم", "probability": 0.9647216796875}, {"start": 1429.76, "end": 1429.9, "word": " ال", "probability": 0.955078125}, {"start": 1429.9, "end": 1430.36, "word": " induction", "probability": 0.9912109375}, {"start": 1430.36, "end": 1430.9, "word": " و", "probability": 0.978515625}, {"start": 1430.9, "end": 1431.28, "word": " نشوف", "probability": 0.8753255208333334}, {"start": 1431.28, "end": 1431.5, "word": " هل", "probability": 0.9638671875}, {"start": 1431.5, "end": 1432.04, "word": " الكلام", "probability": 0.9625651041666666}, {"start": 1432.04, "end": 1432.4, "word": " هذا", "probability": 0.904296875}, {"start": 1432.4, "end": 1432.72, "word": " صحيح", "probability": 0.99462890625}, {"start": 1432.72, "end": 1432.84, "word": " ولا", 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"word": " بداجي", "probability": 0.61767578125}, {"start": 1450.65, "end": 1451.09, "word": " اقول", "probability": 0.917724609375}, {"start": 1451.09, "end": 1451.75, "word": " هنا", "probability": 0.9892578125}, {"start": 1451.75, "end": 1453.07, "word": " solution", "probability": 0.75}, {"start": 1453.07, "end": 1455.03, "word": " لو", "probability": 0.85546875}, {"start": 1455.03, "end": 1455.71, "word": " كانت", "probability": 0.95458984375}, {"start": 1455.71, "end": 1456.01, "word": " ال", "probability": 0.98046875}, {"start": 1456.01, "end": 1456.41, "word": " n", "probability": 0.6513671875}, {"start": 1456.41, "end": 1456.63, "word": " ب", "probability": 0.89599609375}, {"start": 1456.63, "end": 1457.25, "word": " zero", "probability": 0.259521484375}, {"start": 1457.25, "end": 1458.23, "word": " if", "probability": 0.89111328125}, {"start": 1458.23, "end": 1459.05, "word": " ال", "probability": 0.93896484375}, {"start": 1459.05, "end": 1459.55, "word": " n", "probability": 0.8525390625}, {"start": 1459.55, "end": 1460.25, "word": " تساوي", "probability": 0.8226318359375}, {"start": 1460.25, "end": 1460.69, "word": " zero", "probability": 0.66552734375}, {"start": 1460.69, "end": 1461.13, "word": " then", "probability": 0.8447265625}], "temperature": 1.0}, {"id": 61, "seek": 147844, "start": 1461.98, "end": 1478.44, "text": "العلاقة هذه صحيحة ولا لأ تعالى نشوف اي عدد مرفوع للـ O0 بكام بال identity يبقى ال E يبقى A inverse ب O0 بال identity في A", "tokens": [6027, 3615, 15040, 28671, 29538, 20328, 5016, 1829, 5016, 3660, 49429, 5296, 10721, 37279, 6027, 7578, 8717, 8592, 38688, 1975, 1829, 6225, 3215, 3215, 3714, 28480, 45367, 24976, 39184, 422, 15, 4724, 4117, 10943, 20666, 6575, 7251, 3555, 4587, 7578, 2423, 462, 7251, 3555, 4587, 7578, 316, 17340, 4724, 422, 15, 20666, 6575, 8978, 316], "avg_logprob": -0.40318081421511515, "compression_ratio": 1.3098591549295775, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1461.98, "end": 1462.66, 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"end": 1468.5, "word": " بكام", "probability": 0.678466796875}, {"start": 1468.5, "end": 1469.16, "word": " بال", "probability": 0.9580078125}, {"start": 1469.16, "end": 1470.02, "word": " identity", "probability": 0.47607421875}, {"start": 1470.02, "end": 1470.86, "word": " يبقى", "probability": 0.940673828125}, {"start": 1470.86, "end": 1471.04, "word": " ال", "probability": 0.869140625}, {"start": 1471.04, "end": 1471.38, "word": " E", "probability": 0.6416015625}, {"start": 1471.38, "end": 1472.2, "word": " يبقى", "probability": 0.5914306640625}, {"start": 1472.2, "end": 1473.1, "word": " A", "probability": 0.28076171875}, {"start": 1473.1, "end": 1474.5, "word": " inverse", "probability": 0.302734375}, {"start": 1474.5, "end": 1475.26, "word": " ب", "probability": 0.58544921875}, {"start": 1475.26, "end": 1476.2, "word": " O0", "probability": 0.572265625}, {"start": 1476.2, "end": 1476.52, "word": " بال", "probability": 0.93896484375}, {"start": 1476.52, "end": 1477.5, "word": " identity", "probability": 0.80078125}, {"start": 1477.5, "end": 1478.0, "word": " في", "probability": 0.70703125}, {"start": 1478.0, "end": 1478.44, "word": " A", "probability": 0.86474609375}], "temperature": 1.0}, {"id": 62, "seek": 150831, "start": 1478.81, "end": 1508.31, "text": "معناته ايش ان ال E بده يساوي ال A inverse A يبقى ال E بده يساوي ال E يبقى ال statement صحيحة يبقى باجي بقول هذا بده يعطينا ان the statement hold صحيحة طيب لو كانت ال N بواحد F ال N تساوي واحد", "tokens": [2304, 3615, 8315, 47395, 1975, 1829, 8592, 16472, 2423, 462, 47525, 3224, 7251, 3794, 995, 45865, 2423, 316, 17340, 316, 7251, 3555, 4587, 7578, 2423, 462, 47525, 3224, 7251, 3794, 995, 45865, 2423, 462, 7251, 3555, 4587, 7578, 2423, 5629, 20328, 5016, 1829, 5016, 3660, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 264, 5629, 1797, 20328, 5016, 1829, 5016, 3660, 23032, 1829, 3555, 45164, 25961, 2655, 2423, 426, 4724, 14407, 24401, 479, 2423, 426, 6055, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.1959134687434186, "compression_ratio": 1.812121212121212, "no_speech_prob": 0.0, "words": [{"start": 1478.81, "end": 1479.81, "word": "معناته", "probability": 0.85443115234375}, {"start": 1479.81, "end": 1480.31, "word": " ايش", "probability": 0.666015625}, {"start": 1480.31, "end": 1480.71, "word": " ان", "probability": 0.59619140625}, {"start": 1480.71, "end": 1481.07, "word": " ال", "probability": 0.75244140625}, {"start": 1481.07, "end": 1481.49, "word": " E", "probability": 0.365966796875}, {"start": 1481.49, "end": 1482.35, "word": " بده", "probability": 0.352691650390625}, {"start": 1482.35, "end": 1482.81, "word": " يساوي", "probability": 0.8065185546875}, {"start": 1482.81, "end": 1483.05, "word": " ال", "probability": 0.75}, {"start": 1483.05, "end": 1483.37, "word": " A", "probability": 0.74560546875}, {"start": 1483.37, "end": 1484.13, "word": " inverse", "probability": 0.7470703125}, {"start": 1484.13, "end": 1484.71, "word": " A", "probability": 0.50439453125}, {"start": 1484.71, "end": 1485.57, "word": " يبقى", "probability": 0.9569091796875}, {"start": 1485.57, "end": 1485.75, "word": " ال", "probability": 0.89501953125}, {"start": 1485.75, "end": 1485.93, "word": " E", "probability": 0.763671875}, {"start": 1485.93, "end": 1486.31, "word": " بده", "probability": 0.84130859375}, {"start": 1486.31, "end": 1486.63, "word": " يساوي", "probability": 0.980224609375}, {"start": 1486.63, "end": 1486.79, "word": " ال", "probability": 0.9423828125}, {"start": 1486.79, "end": 1486.95, "word": " E", "probability": 0.94921875}, {"start": 1486.95, "end": 1487.11, "word": " يبقى", "probability": 0.8907470703125}, {"start": 1487.11, "end": 1487.27, "word": " ال", "probability": 0.841796875}, {"start": 1487.27, "end": 1487.81, "word": " statement", "probability": 0.96826171875}, {"start": 1487.81, "end": 1488.85, "word": " صحيحة", "probability": 0.961328125}, {"start": 1488.85, "end": 1489.53, "word": " يبقى", "probability": 0.96728515625}, {"start": 1489.53, "end": 1489.95, "word": " باجي", "probability": 0.8556315104166666}, {"start": 1489.95, "end": 1490.33, "word": " بقول", "probability": 0.9267578125}, {"start": 1490.33, "end": 1490.79, "word": " هذا", "probability": 0.5576171875}, {"start": 1490.79, "end": 1491.29, "word": " بده", "probability": 0.761962890625}, {"start": 1491.29, "end": 1492.15, "word": " يعطينا", "probability": 0.936767578125}, {"start": 1492.15, "end": 1492.99, "word": " ان", "probability": 0.634765625}, {"start": 1492.99, "end": 1493.69, "word": " the", "probability": 0.39501953125}, {"start": 1493.69, "end": 1495.91, "word": " statement", "probability": 0.9560546875}, {"start": 1495.91, "end": 1498.37, "word": " hold", "probability": 0.462158203125}, {"start": 1498.37, "end": 1499.85, "word": " صحيحة", "probability": 0.94892578125}, {"start": 1499.85, "end": 1500.99, "word": " طيب", "probability": 0.9454752604166666}, {"start": 1500.99, "end": 1501.85, "word": " لو", "probability": 0.931640625}, {"start": 1501.85, "end": 1502.35, "word": " كانت", "probability": 0.9619140625}, {"start": 1502.35, "end": 1502.57, "word": " ال", "probability": 0.984375}, {"start": 1502.57, "end": 1502.81, "word": " N", "probability": 0.7568359375}, {"start": 1502.81, "end": 1503.47, "word": " بواحد", "probability": 0.9150390625}, {"start": 1503.47, "end": 1505.05, "word": " F", "probability": 0.46923828125}, {"start": 1505.05, "end": 1506.37, "word": " ال", "probability": 0.9453125}, {"start": 1506.37, "end": 1506.83, "word": " N", "probability": 0.96923828125}, {"start": 1506.83, "end": 1507.73, "word": " تساوي", "probability": 0.9681396484375}, {"start": 1507.73, "end": 1508.31, "word": " واحد", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 63, "seek": 151758, "start": 1509.52, "end": 1517.58, "text": "then the statement برضه hold ولا لا؟", "tokens": [19096, 264, 5629, 4724, 43042, 3224, 1797, 49429, 20193, 22807], "avg_logprob": -0.2823153409090909, "compression_ratio": 0.8679245283018868, "no_speech_prob": 0.0, "words": [{"start": 1509.52, "end": 1510.16, "word": "then", "probability": 0.59912109375}, {"start": 1510.16, "end": 1512.04, "word": " the", "probability": 0.8095703125}, {"start": 1512.04, "end": 1514.26, "word": " statement", "probability": 0.9580078125}, {"start": 1514.26, "end": 1516.46, "word": " برضه", "probability": 0.9021809895833334}, {"start": 1516.46, "end": 1516.76, "word": " hold", "probability": 0.400390625}, {"start": 1516.76, "end": 1516.94, "word": " ولا", "probability": 0.8828125}, {"start": 1516.94, "end": 1517.58, "word": " لا؟", "probability": 0.740234375}], "temperature": 1.0}, {"id": 64, "seek": 154688, "start": 1529.88, "end": 1546.88, "text": "أفترض أنها صحيحة عند N تساوي K و أثبت صحتها عند N تساوي K زائد واحد يبقى هنا ماجي بداجي أقول له assume that", "tokens": [10721, 5172, 2655, 43042, 14739, 11296, 20328, 5016, 1829, 5016, 3660, 43242, 426, 6055, 3794, 995, 45865, 591, 4032, 5551, 12984, 3555, 2655, 20328, 33753, 11296, 43242, 426, 6055, 3794, 995, 45865, 591, 30767, 16373, 3215, 36764, 24401, 7251, 3555, 4587, 7578, 34105, 3714, 26108, 1829, 47525, 26108, 1829, 5551, 39648, 46740, 6552, 300], "avg_logprob": -0.3622159025885842, "compression_ratio": 1.3511450381679388, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1529.8799999999999, "end": 1531.02, "word": "أفترض", "probability": 0.468505859375}, {"start": 1531.02, "end": 1531.9, "word": " أنها", "probability": 0.274627685546875}, {"start": 1531.9, "end": 1532.58, "word": " صحيحة", "probability": 0.92353515625}, {"start": 1532.58, "end": 1532.88, "word": " عند", "probability": 0.95654296875}, {"start": 1532.88, "end": 1533.4, "word": " N", "probability": 0.2919921875}, {"start": 1533.4, "end": 1534.32, "word": " تساوي", "probability": 0.743438720703125}, {"start": 1534.32, "end": 1534.84, "word": " K", "probability": 0.798828125}, {"start": 1534.84, "end": 1535.48, "word": " و", "probability": 0.5185546875}, {"start": 1535.48, "end": 1536.1, "word": " أثبت", "probability": 0.8841552734375}, {"start": 1536.1, "end": 1536.88, "word": " صحتها", "probability": 0.8916015625}, {"start": 1536.88, "end": 1537.18, "word": " عند", "probability": 0.97705078125}, {"start": 1537.18, "end": 1537.56, "word": " N", "probability": 0.8955078125}, {"start": 1537.56, "end": 1538.12, "word": " تساوي", "probability": 0.985107421875}, {"start": 1538.12, "end": 1538.6, "word": " K", "probability": 0.91943359375}, {"start": 1538.6, "end": 1539.46, "word": " زائد", "probability": 0.659912109375}, {"start": 1539.46, "end": 1539.9, "word": " واحد", "probability": 0.865234375}, {"start": 1539.9, "end": 1540.86, "word": " يبقى", "probability": 0.775146484375}, {"start": 1540.86, "end": 1541.18, "word": " هنا", "probability": 0.7314453125}, {"start": 1541.18, "end": 1541.7, "word": " ماجي", "probability": 0.578125}, {"start": 1541.7, "end": 1542.28, "word": " بداجي", "probability": 0.8377278645833334}, {"start": 1542.28, "end": 1542.62, "word": " أقول", "probability": 0.691162109375}, {"start": 1542.62, "end": 1542.86, "word": " له", "probability": 0.28076171875}, {"start": 1542.86, "end": 1543.66, "word": " assume", "probability": 0.841796875}, {"start": 1543.66, "end": 1546.88, "word": " that", "probability": 0.85791015625}], "temperature": 1.0}, {"id": 65, "seek": 157579, "start": 1547.93, "end": 1575.79, "text": "إن الـ a inverse b a to the power k بدي سوى a inverse b ka و ال k أكبر من الواحد كمان و ال k integer أكبر من الواحد هذا ال k integer and ال k greater than one", "tokens": [28814, 1863, 2423, 39184, 257, 17340, 272, 257, 281, 264, 1347, 350, 4724, 16254, 8608, 2407, 7578, 257, 17340, 272, 6799, 4032, 2423, 350, 5551, 4117, 26890, 9154, 2423, 14407, 24401, 9122, 2304, 7649, 4032, 2423, 350, 24922, 5551, 4117, 26890, 9154, 2423, 14407, 24401, 23758, 2423, 350, 24922, 293, 2423, 350, 5044, 813, 472], "avg_logprob": -0.2770647459796497, "compression_ratio": 1.6153846153846154, "no_speech_prob": 0.0, "words": [{"start": 1547.93, "end": 1548.45, "word": "إن", "probability": 0.634765625}, {"start": 1548.45, "end": 1548.91, "word": " الـ", "probability": 0.6630859375}, {"start": 1548.91, "end": 1549.19, "word": " a", "probability": 0.234375}, {"start": 1549.19, "end": 1550.25, "word": " inverse", "probability": 0.68408203125}, {"start": 1550.25, "end": 1550.95, "word": " b", "probability": 0.2491455078125}, {"start": 1550.95, "end": 1551.85, "word": " a", "probability": 0.79541015625}, {"start": 1551.85, "end": 1552.57, "word": " to", "probability": 0.806640625}, {"start": 1552.57, "end": 1552.81, "word": " the", "probability": 0.92822265625}, {"start": 1552.81, "end": 1553.47, "word": " power", "probability": 0.90478515625}, {"start": 1553.47, "end": 1554.11, "word": " k", "probability": 0.7314453125}, {"start": 1554.11, "end": 1554.87, "word": " بدي", "probability": 0.5965576171875}, {"start": 1554.87, "end": 1555.45, "word": " سوى", "probability": 0.5896809895833334}, {"start": 1555.45, "end": 1555.91, "word": " a", "probability": 0.96240234375}, {"start": 1555.91, "end": 1556.85, "word": " inverse", "probability": 0.86083984375}, {"start": 1556.85, "end": 1557.85, "word": " b", "probability": 0.89990234375}, {"start": 1557.85, "end": 1558.97, "word": " ka", "probability": 0.45947265625}, {"start": 1558.97, "end": 1559.91, "word": " و", "probability": 0.54541015625}, {"start": 1559.91, "end": 1560.29, "word": " ال", "probability": 0.71337890625}, {"start": 1560.29, "end": 1560.81, "word": " k", "probability": 0.5986328125}, {"start": 1560.81, "end": 1561.91, "word": " أكبر", "probability": 0.9431966145833334}, {"start": 1561.91, "end": 1562.15, "word": " من", "probability": 0.9892578125}, {"start": 1562.15, "end": 1562.65, "word": " الواحد", "probability": 0.721435546875}, {"start": 1562.65, "end": 1563.81, "word": " كمان", "probability": 0.8961588541666666}, {"start": 1563.81, "end": 1564.83, "word": " و", "probability": 0.6513671875}, {"start": 1564.83, "end": 1565.03, "word": " ال", "probability": 0.9228515625}, {"start": 1565.03, "end": 1565.45, "word": " k", "probability": 0.84814453125}, {"start": 1565.45, "end": 1566.19, "word": " integer", "probability": 0.943359375}, {"start": 1566.19, "end": 1567.01, "word": " أكبر", "probability": 0.97021484375}, {"start": 1567.01, "end": 1567.25, "word": " من", "probability": 0.9970703125}, {"start": 1567.25, "end": 1567.79, "word": " الواحد", "probability": 0.9690755208333334}, {"start": 1567.79, "end": 1569.11, "word": " هذا", "probability": 0.7861328125}, {"start": 1569.11, "end": 1569.41, "word": " ال", "probability": 0.93310546875}, {"start": 1569.41, "end": 1569.75, "word": " k", "probability": 0.86572265625}, {"start": 1569.75, "end": 1570.93, "word": " integer", "probability": 0.9638671875}, {"start": 1570.93, "end": 1573.29, "word": " and", "probability": 0.8798828125}, {"start": 1573.29, "end": 1574.17, "word": " ال", "probability": 0.77392578125}, {"start": 1574.17, "end": 1574.47, "word": " k", "probability": 0.96826171875}, {"start": 1574.47, "end": 1574.97, "word": " greater", "probability": 0.8984375}, {"start": 1574.97, "end": 1575.45, "word": " than", "probability": 0.9560546875}, {"start": 1575.45, "end": 1575.79, "word": " one", "probability": 0.8115234375}], "temperature": 1.0}, {"id": 66, "seek": 157918, "start": 1578.32, "end": 1579.18, "text": "طيب تمام", "tokens": [9566, 1829, 3555, 46811, 10943], "avg_logprob": -0.041829428325096764, "compression_ratio": 0.625, "no_speech_prob": 0.0, "words": [{"start": 1578.32, "end": 1578.76, "word": "طيب", "probability": 0.98681640625}, {"start": 1578.76, "end": 1579.18, "word": " تمام", "probability": 0.993896484375}], "temperature": 1.0}, {"id": 67, "seek": 161150, "start": 1582.7, "end": 1611.5, "text": "بدي أحاول أثبت صحة هذا الموضوع عند كزايد واحد يبقى باجي بقوله consider خدلي a inverse ba to the power k plus one انطلع الناتج a inverse bk plus one في a بصير كلامنا معله صحيح يبقى هذا الكلام بده يساوي a inverse ba في k", "tokens": [3555, 16254, 5551, 5016, 995, 12610, 5551, 12984, 3555, 2655, 20328, 5016, 3660, 23758, 9673, 2407, 11242, 45367, 43242, 9122, 11622, 995, 25708, 36764, 24401, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 1949, 16490, 3215, 20292, 257, 17340, 4773, 281, 264, 1347, 350, 1804, 472, 16472, 9566, 1211, 3615, 28239, 9307, 7435, 257, 17340, 272, 74, 1804, 472, 8978, 257, 4724, 9381, 13546, 28242, 10943, 8315, 20449, 43761, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 257, 17340, 4773, 8978, 350], "avg_logprob": -0.2406249943532442, "compression_ratio": 1.5902439024390245, "no_speech_prob": 0.0, "words": [{"start": 1582.7, "end": 1583.14, "word": "بدي", "probability": 0.152191162109375}, {"start": 1583.14, "end": 1583.54, "word": " أحاول", "probability": 0.821044921875}, {"start": 1583.54, "end": 1584.02, "word": " أثبت", "probability": 0.9354248046875}, {"start": 1584.02, "end": 1584.5, "word": " صحة", "probability": 0.9124348958333334}, {"start": 1584.5, "end": 1584.78, "word": " هذا", "probability": 0.8759765625}, {"start": 1584.78, "end": 1585.24, "word": " الموضوع", "probability": 0.995849609375}, {"start": 1585.24, "end": 1585.54, "word": " عند", "probability": 0.52099609375}, {"start": 1585.54, "end": 1587.3, "word": " كزايد", "probability": 0.386383056640625}, {"start": 1587.3, "end": 1587.62, "word": " واحد", "probability": 0.970458984375}, {"start": 1587.62, "end": 1588.42, "word": " يبقى", "probability": 0.8927001953125}, {"start": 1588.42, "end": 1588.84, "word": " باجي", "probability": 0.8489583333333334}, {"start": 1588.84, "end": 1589.44, "word": " بقوله", "probability": 0.7666015625}, {"start": 1589.44, "end": 1590.36, "word": " consider", "probability": 0.77392578125}, {"start": 1590.36, "end": 1591.68, "word": " خدلي", "probability": 0.6234537760416666}, {"start": 1591.68, "end": 1592.2, "word": " a", "probability": 0.6025390625}, {"start": 1592.2, "end": 1593.04, "word": " inverse", "probability": 0.85205078125}, {"start": 1593.04, "end": 1593.9, "word": " ba", "probability": 0.2900390625}, {"start": 1593.9, "end": 1594.8, "word": " to", "probability": 0.84033203125}, {"start": 1594.8, "end": 1595.02, "word": " the", "probability": 0.91455078125}, {"start": 1595.02, "end": 1595.52, "word": " power", "probability": 0.91015625}, {"start": 1595.52, "end": 1595.94, "word": " k", "probability": 0.681640625}, {"start": 1595.94, "end": 1596.48, "word": " plus", "probability": 0.869140625}, {"start": 1596.48, "end": 1596.96, "word": " one", "probability": 0.91943359375}, {"start": 1596.96, "end": 1598.16, "word": " انطلع", "probability": 0.9593505859375}, {"start": 1598.16, "end": 1598.76, "word": " الناتج", "probability": 0.6924641927083334}, {"start": 1598.76, "end": 1599.16, "word": " a", "probability": 0.9580078125}, {"start": 1599.16, "end": 1599.8, "word": " 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"probability": 0.9549153645833334}, {"start": 1606.12, "end": 1606.56, "word": " بده", "probability": 0.799560546875}, {"start": 1606.56, "end": 1607.16, "word": " يساوي", "probability": 0.980224609375}, {"start": 1607.16, "end": 1608.18, "word": " a", "probability": 0.939453125}, {"start": 1608.18, "end": 1609.22, "word": " inverse", "probability": 0.84375}, {"start": 1609.22, "end": 1610.54, "word": " ba", "probability": 0.8095703125}, {"start": 1610.54, "end": 1610.94, "word": " في", "probability": 0.9658203125}, {"start": 1610.94, "end": 1611.5, "word": " k", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 68, "seek": 162987, "start": 1620.59, "end": 1629.87, "text": "هذا الكلام انا فارضه هنا يبقى a inverse", "tokens": [3224, 15730, 2423, 28820, 10943, 1975, 8315, 6156, 9640, 11242, 3224, 34105, 7251, 3555, 4587, 7578, 257, 17340], "avg_logprob": -0.5061677380612022, "compression_ratio": 0.9692307692307692, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 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minus n a هذا يعني هذا في هذا مش يساوي هذا في هذا بده يعطينا ال identity صح هي الكلامي صح ولا غلط هذا صح ليش", "tokens": [65, 257, 281, 264, 1347, 297, 47525, 3224, 7251, 3794, 995, 45865, 257, 17340, 272, 281, 264, 3175, 297, 257, 23758, 37495, 22653, 23758, 8978, 23758, 37893, 7251, 3794, 995, 45865, 23758, 8978, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 2423, 6575, 20328, 5016, 39896, 2423, 28820, 10943, 1829, 20328, 5016, 49429, 32771, 1211, 9566, 23758, 20328, 5016, 32239, 8592], "avg_logprob": -0.2346311436324823, "compression_ratio": 1.5782312925170068, "no_speech_prob": 0.0, "words": [{"start": 1780.36, "end": 1780.88, "word": "b", "probability": 0.041290283203125}, {"start": 1780.88, "end": 1781.52, "word": " a", "probability": 0.395263671875}, {"start": 1781.52, "end": 1781.8, "word": " to", "probability": 0.67236328125}, {"start": 1781.8, "end": 1782.02, "word": " the", "probability": 0.91162109375}, {"start": 1782.02, "end": 1782.68, "word": " power", "probability": 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true because السبب ان ناقص in greater than zero لأن المبرهنها هي فوق", "tokens": [1211, 33456, 8717, 995, 4587, 9381, 294, 5551, 4117, 26890, 9154, 4018, 4032, 1975, 5016, 8315, 34105, 5296, 15042, 6055, 3555, 4587, 7578, 2423, 294, 5551, 4117, 26890, 9154, 4018, 1975, 12984, 3555, 2655, 8315, 2423, 5629, 3714, 6027, 11296, 20328, 5016, 1829, 5016, 3660, 7251, 3555, 4587, 7578, 341, 307, 257, 2074, 570, 21136, 3555, 3555, 16472, 8717, 995, 4587, 9381, 294, 5044, 813, 4018, 5296, 33456, 9673, 26890, 3224, 1863, 11296, 39896, 6156, 30543], "avg_logprob": -0.2086038945557235, "compression_ratio": 1.5773809523809523, "no_speech_prob": 0.0, "words": [{"start": 1807.29, "end": 1807.75, "word": "لأن", "probability": 0.5555419921875}, {"start": 1807.75, "end": 1808.47, "word": " ناقص", "probability": 0.8675537109375}, {"start": 1808.47, "end": 1808.77, "word": " in", "probability": 0.279541015625}, {"start": 1808.77, "end": 1809.43, "word": " أكبر", "probability": 0.9352213541666666}, 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