diff --git "a/task_a_9b/test.json" "b/task_a_9b/test.json" new file mode 100644--- /dev/null +++ "b/task_a_9b/test.json" @@ -0,0 +1,4202 @@ +[ + { + "case_id": "failed_stay_mountain_or_valley_r105", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-2, -3, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, -2, 4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-10, 5, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (2, -10, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, 5, -6): **YES**\\n2. Triple (-10, -3, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-2, -8, -6): **YES**\\n2. Triple (-10, 5, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r105.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1064", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (5, 5, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, 3, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, 10, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-5, 7, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-5, 8, 2): **YES**\\n2. Triple (-9, 1, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (4, 8, -7): **YES**\\n2. Triple (1, 1, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1064.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1070", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (1, -3, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-8, -8, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, -3, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, -4, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (7, -10, -2): **YES**\\n2. Triple (4, -9, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, -2, 8): **YES**\\n2. Triple (8, -4, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1070.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1087", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, 3, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (6, 0, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (1, -10, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (2, -3, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-10, 1, -9): **YES**\\n2. Triple (-7, 4, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (5, 8, 0): **YES**\\n2. Triple (5, 2, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1087.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1105", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (1, -10, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-6, 8, -10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, 8, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, -8, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-2, 5, -10): **YES**\\n2. Triple (-8, -2, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, -8, 3): **YES**\\n2. Triple (9, -3, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1105.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1123", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (4, 4, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-10, 2, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (1, 8, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (7, -2, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-2, -3, -2): **YES**\\n2. Triple (-8, 4, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (2, -3, 6): **YES**\\n2. Triple (4, -8, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1123.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1137", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-2, 2, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-9, 8, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (0, 1, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (10, 4, 3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (2, -4, 0): **YES**\\n2. Triple (5, 2, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (2, -10, -1): **YES**\\n2. Triple (3, 3, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1137.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1159", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-2, -2, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-9, 1, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (2, 4, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (2, 0, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, -10, -8): **YES**\\n2. Triple (-10, 2, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (1, 9, -3): **YES**\\n2. Triple (6, -2, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1159.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1175", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-10, 7, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (6, -4, -1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, 9, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-2, -8, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (5, -10, -3): **YES**\\n2. Triple (4, -3, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, -7, 9): **YES**\\n2. Triple (-2, -2, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1175.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1207", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, 8, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (10, -6, -6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-7, -2, 2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (3, -4, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-10, 6, -3): **YES**\\n2. Triple (7, 5, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-7, 9, 3): **YES**\\n2. Triple (-6, -6, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1207.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1223", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-7, 1, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-7, 2, 4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-2, 4, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-2, -8, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-7, 8, -1): **YES**\\n2. Triple (8, -6, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-7, 6, 5): **YES**\\n2. Triple (7, 6, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1223.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1236", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (3, 3, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (0, -2, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-7, -1, -10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (9, -3, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (4, -8, -1): **YES**\\n2. Triple (-3, -2, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (10, -3, 6): **YES**\\n2. Triple (10, 5, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1236.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1244", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-3, 6, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, -7, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-5, 4, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (0, 4, -9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-9, 0, -6): **YES**\\n2. Triple (2, 9, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, -9, 5): **YES**\\n2. Triple (6, 3, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1244.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1281", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-4, -8, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, -7, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-9, 7, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, 10, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, -10, 10): **YES**\\n2. Triple (-9, -6, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (4, 7, -3): **YES**\\n2. Triple (-4, 2, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1281.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1289", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-3, -7, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-9, 4, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (0, 7, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (8, -2, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-5, 2, -3): **YES**\\n2. Triple (-7, -6, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-7, -10, 4): **YES**\\n2. Triple (5, 1, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1289.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1299", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-2, 4, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, 3, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (7, 5, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-10, 10, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-9, 10, 9): **YES**\\n2. Triple (6, -4, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-8, 10, -7): **YES**\\n2. Triple (2, 3, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1299.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r130", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, -7, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (10, 1, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, 1, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (0, 8, -9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-7, 9, -6): **YES**\\n2. Triple (6, 6, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-6, 7, -3): **YES**\\n2. Triple (-2, -2, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r130.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1349", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-3, 10, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, -10, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, -3, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (6, -5, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (9, 10, 3): **YES**\\n2. Triple (9, 1, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, 8, -1): **YES**\\n2. Triple (9, 8, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1349.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1356", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (8, 0, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-2, 8, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (2, 6, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, -10, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-8, -9, 1): **YES**\\n2. Triple (-9, -1, 0): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (10, -6, -4): **YES**\\n2. Triple (-4, -8, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1356.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1359", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (2, 7, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (2, 0, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-3, -8, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-10, 4, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-5, -2, -8): **YES**\\n2. Triple (5, 4, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (8, -3, 5): **YES**\\n2. Triple (-4, -7, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1359.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1367", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-2, -2, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-3, 7, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-9, 7, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (5, 4, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (4, -7, -5): **YES**\\n2. Triple (0, 0, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (0, -9, -7): **YES**\\n2. Triple (-9, 3, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1367.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1373", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-7, 4, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-1, -6, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (10, -6, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (10, 9, 10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, 0, -9): **YES**\\n2. Triple (-10, -1, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (8, -10, -4): **YES**\\n2. Triple (5, 1, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1373.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1413", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (7, 1, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, 1, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (7, -3, 9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (1, 2, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, 10, -9): **YES**\\n2. Triple (-6, 2, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, 0, 3): **YES**\\n2. Triple (5, 2, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1413.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1416", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, -2, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-7, 8, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, -7, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (5, 6, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-2, 7, 1): **YES**\\n2. Triple (6, 2, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-6, -8, 4): **YES**\\n2. Triple (-4, -4, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1416.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1441", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (1, -7, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-9, 1, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-3, -8, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (9, -3, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (7, 6, 9): **YES**\\n2. Triple (-8, -8, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, 9, -8): **YES**\\n2. Triple (4, 4, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1441.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1444", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (10, -5, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, 7, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, 6, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, 8, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, 5, -3): **YES**\\n2. Triple (2, 4, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-5, -8, 9): **YES**\\n2. Triple (7, 5, 0): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1444.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1453", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-6, 4, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, 0, 4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-7, 9, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-5, -4, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (7, -2, -1): **YES**\\n2. Triple (-2, -5, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-10, 8, 7): **YES**\\n2. Triple (-2, 3, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1453.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1480", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (7, 0, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (4, 6, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, -7, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-2, 2, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-10, 1, -9): **YES**\\n2. Triple (-1, -3, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-8, 10, -3): **YES**\\n2. Triple (2, 2, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1480.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r149", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-6, 0, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (9, 3, 3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, -4, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (8, 9, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (10, -9, -4): **YES**\\n2. Triple (-8, -5, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, 5, -4): **YES**\\n2. Triple (2, 2, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r149.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1512", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (10, -7, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, -6, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-5, -8, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (9, 4, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (3, 10, -4): **YES**\\n2. Triple (2, -3, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (0, -8, -7): **YES**\\n2. Triple (7, 4, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1512.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r154", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (6, 8, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, 2, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-6, -7, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-10, -1, 2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-6, -9, -4): **YES**\\n2. Triple (4, -4, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (8, -1, 0): **YES**\\n2. Triple (-3, 8, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r154.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r156", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-7, -2, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-1, -4, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-6, -9, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (9, -2, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-4, -9, -7): **YES**\\n2. Triple (-7, -1, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, -8, 9): **YES**\\n2. Triple (-8, 3, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r156.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1561", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (2, 2, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (6, 9, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (3, -8, 9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (8, 0, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (3, 6, -4): **YES**\\n2. Triple (-7, -2, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-10, -3, -10): **YES**\\n2. Triple (7, -6, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1561.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r158", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, 5, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, 4, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, 9, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (10, 3, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (3, 5, -9): **YES**\\n2. Triple (-7, 0, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (1, -3, 3): **YES**\\n2. Triple (-1, -3, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r158.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1583", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (8, -2, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-2, 5, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, 7, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-4, -2, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-8, 8, -7): **YES**\\n2. Triple (3, -2, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-5, 4, -4): **YES**\\n2. Triple (9, 6, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1583.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1627", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (10, 10, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (0, -4, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (7, -5, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (0, 4, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (2, -1, 6): **YES**\\n2. Triple (-7, 0, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (8, -1, 0): **YES**\\n2. Triple (8, 7, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1627.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1647", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-5, 1, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-1, -2, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (0, -7, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (7, 6, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (4, -6, 10): **YES**\\n2. Triple (-3, 6, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-5, 7, -2): **YES**\\n2. Triple (1, 9, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1647.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1671", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-5, 7, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, -1, 2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (4, -2, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (4, 8, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-8, 10, 7): **YES**\\n2. Triple (-6, -6, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, -5, 3): **YES**\\n2. Triple (-7, -5, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1671.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1680", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-5, 10, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, 1, -9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (5, 5, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-6, 8, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-10, 0, -2): **YES**\\n2. Triple (10, 6, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-8, -4, -9): **YES**\\n2. Triple (-10, -7, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1680.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1725", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-7, -9, 10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, 3, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (1, 7, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-4, -8, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-2, -9, 7): **YES**\\n2. Triple (10, 4, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-8, 1, -9): **YES**\\n2. Triple (2, -2, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1725.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1732", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-2, 1, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (8, -3, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, 3, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (2, -7, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (10, -2, 4): **YES**\\n2. Triple (-2, -2, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-2, -5, 10): **YES**\\n2. Triple (-10, -7, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1732.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1796", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (9, 9, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, -5, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-2, 10, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-3, -9, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (1, 6, 0): **YES**\\n2. Triple (1, 2, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (6, -7, 5): **YES**\\n2. Triple (-5, 0, 0): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1796.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1849", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (10, 4, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (4, -2, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, -8, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-5, 1, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (2, -8, -7): **YES**\\n2. Triple (-1, -3, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (9, 7, 8): **YES**\\n2. Triple (-3, -5, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1849.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1862", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-4, 9, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-1, -1, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-6, -10, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-3, 7, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, -8, -3): **YES**\\n2. Triple (-7, -2, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (4, 10, -4): **YES**\\n2. Triple (-2, 4, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1862.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1927", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (5, -5, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (3, 6, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-9, 5, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-4, 7, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (1, -10, 6): **YES**\\n2. Triple (8, 6, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (6, 4, 5): **YES**\\n2. Triple (-1, 0, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1927.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1945", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (2, -9, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-7, 9, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (2, -2, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (2, -7, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, -8, 0): **YES**\\n2. Triple (-9, -2, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-6, 7, 6): **YES**\\n2. Triple (-10, -4, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1945.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1947", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (0, -9, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-3, -5, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, -3, -4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (1, -9, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, 2, -5): **YES**\\n2. Triple (1, -6, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (10, 5, 9): **YES**\\n2. Triple (8, 7, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1947.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1964", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-8, 4, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, 4, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (1, 1, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-2, -8, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-6, 1, -5): **YES**\\n2. Triple (3, 2, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, 8, 4): **YES**\\n2. Triple (9, 9, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1964.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1985", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-3, -3, 3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (6, -7, 10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (10, 10, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, 1, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-9, -6, -8): **YES**\\n2. Triple (8, 3, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, -6, -5): **YES**\\n2. Triple (-9, -8, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1985.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r1988", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-10, -8, -4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (6, 6, -6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-7, -10, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (5, 8, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (0, -2, 9): **YES**\\n2. Triple (-2, -2, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, -7, 6): **YES**\\n2. Triple (-2, 0, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r1988.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2002", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, 4, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (9, 0, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, -6, -6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (10, -6, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-9, 8, 3): **YES**\\n2. Triple (-3, 2, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-10, 9, 7): **YES**\\n2. Triple (4, 2, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2002.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2016", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, -4, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (6, -9, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (9, -4, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (9, 5, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-10, -4, -9): **YES**\\n2. Triple (10, 4, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-9, 5, -8): **YES**\\n2. Triple (-5, 2, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2016.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2020", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (5, 5, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (4, 0, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-5, -9, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-2, 6, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (10, 0, 7): **YES**\\n2. Triple (-8, -7, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (4, -8, -1): **YES**\\n2. Triple (-8, 4, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2020.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2087", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (6, 8, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (1, 7, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, 3, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (6, -5, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (9, -1, 10): **YES**\\n2. Triple (-1, -7, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, 3, 2): **YES**\\n2. Triple (8, 5, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2087.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2133", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, -6, 10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-8, 3, -10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-2, -10, -9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-2, -5, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (3, -7, 7): **YES**\\n2. Triple (4, 2, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, -3, -4): **YES**\\n2. Triple (3, -4, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2133.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2155", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, 2, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (7, 2, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-6, -4, 1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (8, 8, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, 9, -7): **YES**\\n2. Triple (-7, -1, 0): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (4, 0, 6): **YES**\\n2. Triple (-3, -3, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2155.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2189", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (4, -8, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (4, -2, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (8, 5, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, 6, -10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (2, -3, 5): **YES**\\n2. Triple (-10, -7, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (0, 6, -6): **YES**\\n2. Triple (8, -3, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2189.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2200", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (8, -5, 9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-2, -9, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, -9, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-7, -1, 1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, -7, 1): **YES**\\n2. Triple (5, 2, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, -1, -9): **YES**\\n2. Triple (-7, 5, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2200.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2229", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-7, 3, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-2, -6, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_abs_lte_12\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-2, -8, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, -7, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-5, -7, 2): **YES**\\n2. Triple (8, 7, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, 0, 3): **YES**\\n2. Triple (3, 3, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2229.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2242", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (10, 2, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-4, 4, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (8, 5, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, 9, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (1, -4, 7): **YES**\\n2. Triple (4, -3, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (7, 9, -5): **YES**\\n2. Triple (-7, 2, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2242.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2274", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (2, -6, -6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (5, -2, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-4, -5, -4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-10, -3, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (0, 9, -6): **YES**\\n2. Triple (-4, -6, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, 9, -7): **YES**\\n2. Triple (-10, 3, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2274.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2277", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-4, 0, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (5, -6, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-2, 4, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-2, -8, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (2, 3, -7): **YES**\\n2. Triple (-4, 0, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (8, -2, 4): **YES**\\n2. Triple (-1, 2, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2277.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2283", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (4, -5, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-10, 0, 4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, 4, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, 6, -10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-6, -8, 8): **YES**\\n2. Triple (8, -6, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-7, -9, -6): **YES**\\n2. Triple (1, 1, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2283.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2288", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, -3, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (5, 9, -10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, 5, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-9, 2, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-4, 3, -8): **YES**\\n2. Triple (7, 5, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (1, -4, 7): **YES**\\n2. Triple (-7, 8, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2288.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2331", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (9, 7, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, -7, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (8, -7, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-5, 2, -9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (7, 9, -3): **YES**\\n2. Triple (3, 1, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (4, -5, 8): **YES**\\n2. Triple (-7, 1, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2331.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2402", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-9, -9, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-8, -5, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (7, 1, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (3, 9, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-4, 6, -9): **YES**\\n2. Triple (9, -8, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-5, 7, -1): **YES**\\n2. Triple (7, -6, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2402.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2405", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (7, 7, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-5, 3, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-5, 9, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (6, -7, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, -2, 9): **YES**\\n2. Triple (-9, -1, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (2, 4, 2): **YES**\\n2. Triple (-10, -3, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2405.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2420", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-9, 4, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, -3, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (8, 1, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, 9, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (0, 7, 4): **YES**\\n2. Triple (-6, 4, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (4, 10, -3): **YES**\\n2. Triple (10, 2, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2420.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2432", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (9, 3, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (9, -5, 4): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (5, -2, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, 2, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-4, -5, 4): **YES**\\n2. Triple (1, 5, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, 4, 2): **YES**\\n2. Triple (-9, -9, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2432.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2435", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (1, 1, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-3, 1, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, 1, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-6, -3, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-2, 7, 2): **YES**\\n2. Triple (-6, 1, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-6, 8, -9): **YES**\\n2. Triple (-8, 0, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2435.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2469", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (3, -7, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (5, 5, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-4, 1, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-2, -4, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (1, 0, 1): **YES**\\n2. Triple (-4, -3, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (7, -3, 9): **YES**\\n2. Triple (3, -2, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2469.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r247", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-2, -2, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (6, -1, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, -6, -1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (10, -4, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (3, 9, -2): **YES**\\n2. Triple (0, -10, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (6, -10, 6): **YES**\\n2. Triple (-9, 7, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r247.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r2498", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (7, 7, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, 4, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-3, -7, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-10, 8, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (1, -2, 5): **YES**\\n2. Triple (-6, -4, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-5, -9, 5): **YES**\\n2. Triple (-2, -1, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r2498.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r250", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (0, -6, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (10, -7, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-8, 2, -1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (1, -6, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, 0, -9): **YES**\\n2. Triple (9, -3, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-2, 7, -10): **YES**\\n2. Triple (9, 7, 0): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r250.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r26", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (4, 10, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (1, -4, 9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (4, 0, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (1, -4, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-2, 1, -1): **YES**\\n2. Triple (-9, -8, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, 9, 7): **YES**\\n2. Triple (-10, -1, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r26.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r265", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (5, 5, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-4, -4, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (8, 9, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, -8, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-7, -9, 10): **YES**\\n2. Triple (-9, -4, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-10, 3, -6): **YES**\\n2. Triple (-1, -4, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r265.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r3", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-4, 3, -9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-4, 5, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-5, 4, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (7, -3, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (1, 3, -9): **YES**\\n2. Triple (-10, 3, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, -9, -3): **YES**\\n2. Triple (-8, -7, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r3.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r351", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (7, 8, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (6, -8, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, -7, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-10, -6, 1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-8, 4, -6): **YES**\\n2. Triple (-6, 2, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-7, 7, -1): **YES**\\n2. Triple (-7, -4, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r351.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r352", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-4, 10, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (4, 8, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (0, 7, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (7, -2, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (8, 9, 7): **YES**\\n2. Triple (-8, 4, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (1, 8, 7): **YES**\\n2. Triple (-6, -5, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r352.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r37", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-9, -10, 10): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-5, 5, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-1, 4, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, 4, -6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, -10, 5): **YES**\\n2. Triple (-10, 2, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-6, 7, -10): **YES**\\n2. Triple (-4, -2, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r37.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r373", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (6, -4, -4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-4, 9, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (10, -8, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, 4, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (2, 1, 9): **YES**\\n2. Triple (7, 6, 0): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-2, 10, 6): **YES**\\n2. Triple (9, 3, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r373.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r404", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (10, 10, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (1, 6, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (1, 5, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-9, -5, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (7, -6, 6): **YES**\\n2. Triple (4, 0, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (0, -10, -6): **YES**\\n2. Triple (-8, -8, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r404.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r408", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, 7, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, 0, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-7, -2, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (8, -3, -6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-4, -8, 6): **YES**\\n2. Triple (8, 4, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-6, 6, 5): **YES**\\n2. Triple (-6, -3, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r408.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r417", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (0, 9, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-5, 3, 7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (10, 5, 2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, 7, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (4, -5, 3): **YES**\\n2. Triple (0, -7, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-7, -5, -8): **YES**\\n2. Triple (-1, -9, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r417.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r51", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-3, -10, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (8, 8, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (5, 8, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (7, 0, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-4, -1, -10): **YES**\\n2. Triple (-7, -5, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-2, 6, -10): **YES**\\n2. Triple (3, -7, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r51.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r510", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (5, -1, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, 4, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (4, 2, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-8, -8, 4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (6, 9, 4): **YES**\\n2. Triple (0, 8, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (6, -7, 6): **YES**\\n2. Triple (8, 7, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r510.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r530", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (9, -10, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (7, 7, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_abs_lte_12\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (5, 8, 8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (9, -2, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-9, -7, -10): **YES**\\n2. Triple (-5, 4, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (8, 10, -7): **YES**\\n2. Triple (-6, -5, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r530.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r543", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (7, 7, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (6, 6, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, 4, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (10, -8, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (2, -2, 3): **YES**\\n2. Triple (9, 0, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-5, 6, -9): **YES**\\n2. Triple (6, 0, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r543.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r553", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-10, 3, 4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-8, -7, -2): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (10, -1, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (9, -9, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, -10, -7): **YES**\\n2. Triple (-9, -6, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (3, -4, 1): **YES**\\n2. Triple (-1, 3, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r553.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r588", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (10, 2, 0): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (4, -6, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (3, 2, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-3, -5, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (1, -7, 2): **YES**\\n2. Triple (-6, -5, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, -9, -1): **YES**\\n2. Triple (10, 0, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r588.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r621", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (1, 0, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (0, -3, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-9, 3, 6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (4, 2, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, -3, 4): **YES**\\n2. Triple (9, 4, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (1, -10, 5): **YES**\\n2. Triple (4, 4, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r621.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r647", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (1, -2, -4): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (10, 0, -6): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (4, 2, -3): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending �� YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (0, 10, -3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-1, 0, -10): **YES**\\n2. Triple (8, 6, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (8, 6, 7): **YES**\\n2. Triple (-3, 0, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r647.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r687", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-5, -10, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (10, 9, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (9, 10, 1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-2, -4, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (9, 10, 2): **YES**\\n2. Triple (1, -4, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-4, -9, 9): **YES**\\n2. Triple (7, 2, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r687.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r695", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (0, 1, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-7, -9, 5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-9, 7, -5): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-5, 0, -1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (-3, 4, -2): **YES**\\n2. Triple (8, 4, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (9, -8, 3): **YES**\\n2. Triple (-5, -5, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r695.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r697", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, -4, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (2, 0, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-6, 10, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (1, 9, -1): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (6, 3, 7): **YES**\\n2. Triple (-4, -2, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-8, -5, -8): **YES**\\n2. Triple (-10, -2, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r697.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r748", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (8, 9, 8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (6, -10, -9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (0, 7, -7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-4, -3, 10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (7, -5, -4): **YES**\\n2. Triple (-4, -2, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-8, 5, -7): **YES**\\n2. Triple (-3, 3, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r748.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r80", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (8, 8, -10): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (2, 2, -7): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (-5, 0, -2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (-1, 0, -8): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (10, -8, -1): **YES**\\n2. Triple (0, 2, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, -6, 5): **YES**\\n2. Triple (-6, -4, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r80.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r803", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (-1, -8, -8): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (7, 1, -5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_abs_lte_12\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (6, 0, 9): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (0, 6, 9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (5, -10, 3): **YES**\\n2. Triple (-9, -3, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, 8, -9): **YES**\\n2. Triple (9, 4, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r803.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r828", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (2, -4, 2): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n2. Triple (5, -9, 6): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (0, 4, 3): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n2. Triple (10, -4, 0): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (3, 10, -9): **YES**\\n2. Triple (8, -1, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (-3, 8, 7): **YES**\\n2. Triple (-5, 2, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r828.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_stay_mountain_or_valley_r829", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_stay", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_abs_lte_12\": The sum of the absolute values is at most 12\n- \"sum_of_squares_gt_50\": The sum of squares of the three numbers is greater than 50\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\n1. Triple (6, -1, -1): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n2. Triple (-3, 1, 5): **NO**\\n Rule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_of_squares_gt_50\"]}, {\"prompt\": \"**Turn 1 evidence:**\\n1. Triple (1, 0, 7): **YES**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → YES\\n - sum_of_squares_gt_50 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n2. Triple (7, -4, -9): **NO**\\n Rule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_abs_lte_12 → NO\\n - sum_of_squares_gt_50 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n1. Triple (0, -6, -2): **YES**\\n2. Triple (-9, 2, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 3 evidence:**\\n1. Triple (6, 5, 8): **YES**\\n2. Triple (5, -3, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_2_evidence_post_2_3_bench_2hard_bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0_numruns2500/failed_stay/belief_failure/failed_stay_mountain_or_valley_r829.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r0", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -7, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, -1, -6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, 4, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-6, 4, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r0.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 1, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, -2, 9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, -4, -7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (1, -4, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1000", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -6, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, 10, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, -2, -6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (6, -2, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1000.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1004", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -9, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 6, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, -9, 1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (8, -9, 1): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1004.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1027", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 0, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 9, -1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, -7, 1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-8, -7, 1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1027.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1033", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 5, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 5, 3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, -10, -5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, -10, -5): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1033.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1038", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 1, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 6, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, 1, -3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (8, 1, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1038.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1039", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 7, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -4, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, -3, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (4, -3, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1039.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1042", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 2, 3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, 9, 1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, 8, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (2, 8, -4): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1042.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1051", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -4, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 0, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, 7, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-3, 7, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1051.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1054", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, 1, 4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, 1, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (0, -1, -7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (0, -1, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1054.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1071", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, 1, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 3, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, 0, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (4, 0, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1071.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1076", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -3, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, 6, -3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, -3, 2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-6, -3, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1076.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1083", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -4, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -5, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, 8, -8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (9, 8, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1083.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1095", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -4, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, 9, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, 0, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (10, 0, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1095.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1098", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -7, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, -1, 4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, -1, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (10, -1, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1098.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1101", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 2, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-10, 4, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, 1, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (8, 1, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1101.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r114", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 2, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 8, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, -7, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (2, -7, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r114.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r116", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-4, 6, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, -8, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-2, 5, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-2, 5, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r116.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1163", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -7, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-5, 4, 1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, 4, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-8, 4, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1163.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1165", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 5, 10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -3, 10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 0, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-7, 0, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1165.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1166", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -3, -8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, 10, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (0, 6, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (0, 6, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1166.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1181", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 4, 9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, -9, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, -8, 6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-10, -8, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1181.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1184", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, -1, -1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, -7, -1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, -8, -8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-9, -8, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1184.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1186", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, -5, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 10, -3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, 0, 6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-5, 0, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1186.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1192", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, -10, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, 1, -1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, -4, -7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (9, -4, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1192.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1199", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -8, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (3, -6, -6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, 5, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-3, 5, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1199.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r12", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, 0, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, 3, 9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, -7, -8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (4, -7, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r12.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1215", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, 10, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, 8, -3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, -3, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (7, -3, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1215.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r122", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -4, -8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, -7, 2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (0, 4, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (0, 4, -9): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r122.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1236", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, 4, 9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, -10, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, -10, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (10, -10, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1236.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1237", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, -4, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 4, 1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 4, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-4, 4, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1237.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1239", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 3, 9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, -6, -7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, 0, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (6, 0, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1239.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1247", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 1, -5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, 2, -5): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, -2, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (2, -2, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1247.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1252", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -1, -6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-4, 10, 6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, -5, -2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-7, -5, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1252.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1262", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -3, -3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, -7, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, 5, -2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (7, 5, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1262.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1263", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 2, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 8, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, 5, 6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-9, 5, 6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1263.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1271", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 5, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-10, 6, -5): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, -4, -6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-3, -4, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1271.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1279", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 9, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-4, -6, 9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, 8, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-3, 8, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1279.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1286", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, -10, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 2, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, -5, 5): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-10, -5, 5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1286.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1287", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 3, -5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, -8, 1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, 4, -6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (7, 4, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1287.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1291", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 0, -2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, -1, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, 6, -8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (8, 6, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1291.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1319", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 2, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, 5, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, -9, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (10, -9, 5): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1319.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1321", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 0, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-5, -6, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, 3, 4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-3, 3, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1321.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1331", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, -8, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, -8, -8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-2, 1, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-2, 1, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1331.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1345", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 3, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 9, 6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, 10, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, 10, -7): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1345.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r135", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, -4, -6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, 9, 4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, 2, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (5, 2, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r135.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1359", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 4, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, -2, -5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, -7, -5): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-7, -7, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1359.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1365", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -1, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, 1, -2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, 2, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, 2, 7): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1365.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1369", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 0, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, 0, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, 2, -3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (2, 2, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1369.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1386", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, 5, 10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, -4, -5): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, 0, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, 0, 6): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1386.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1390", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, 2, 4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 7, 4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, -4, -1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-5, -4, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1390.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1398", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -4, -8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, 6, 10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, -2, -3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (9, -2, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1398.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1399", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, -7, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, 9, 9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, -1, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (5, -1, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1399.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1402", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -9, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 0, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, 2, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-10, 2, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1402.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1405", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -3, 10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 1, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, 1, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (9, 1, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1405.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r141", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, 5, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, -8, -2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, 4, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (8, 4, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r141.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1411", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 4, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, -4, 1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, 3, -3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (5, 3, -3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1411.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1415", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, -6, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 2, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -1, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-1, -1, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1415.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1422", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, 0, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -1, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, -7, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-7, -7, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1422.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1428", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, 0, -2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 3, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, -4, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-6, -4, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1428.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1429", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, 7, 9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, -3, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, -2, 10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (10, -2, 10): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1429.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1442", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 1, -1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, 10, -7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 2, 2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-7, 2, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1442.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1461", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, -2, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 0, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -3, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-1, -3, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1461.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1464", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 3, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 8, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, -6, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-4, -6, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1464.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1470", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -2, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 8, 1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, 8, 3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (8, 8, 3): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1470.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1474", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -1, -2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, 10, -1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, 6, 4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, 6, 4): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1474.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1482", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 1, 1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, -3, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 1, 2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-4, 1, 2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1482.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1483", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -2, -2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, -2, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, 9, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (4, 9, 2): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1483.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1485", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 2, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, -8, 6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 9, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-4, 9, 0): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1485.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r15", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, -7, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, 6, -3): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, 6, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-8, 6, 7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r15.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1507", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 1, -1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (0, 0, -3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, 4, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (9, 4, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1507.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1524", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 4, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (3, -9, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 8, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-4, 8, 7): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1524.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1527", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 1, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-5, -6, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, -9, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (1, -9, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1527.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1534", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -4, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, -1, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, -3, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (5, -3, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1534.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1548", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 0, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-10, -6, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, 7, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, 7, 5): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1548.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1564", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, 0, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (3, -2, -5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, 0, 4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-8, 0, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1564.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1566", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 4, 4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, 8, 2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -8, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-1, -8, 8): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1566.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1572", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 0, 3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (0, 0, -1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, 7, -9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (9, 7, -9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1572.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1584", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -1, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (0, 1, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, 1, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (6, 1, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1584.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1586", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 3, -3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-5, -7, -8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, 3, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (10, 3, 8): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1586.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1596", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 5, -8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, -2, -6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, -4, -8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (9, -4, -8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"range_lte_5\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1596.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1599", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -3, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, 2, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, 2, -2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, 2, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1599.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r16", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, -7, -8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 0, -3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, 4, -7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (6, 4, -7): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r16.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1601", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 5, -3): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-10, -4, 7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, 0, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (1, 0, 2): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1601.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1602", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -6, -9): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 8, -6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, -6, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-9, -6, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1602.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1608", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 2, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, -6, -1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, -5, 6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, -5, 6): **YES**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1608.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1621", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, 0, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, 10, -5): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, -2, 4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-6, -2, 4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1621.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1633", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, -7, 4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, -5, 7): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, -1, -6): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (3, -1, -6): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1633.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1634", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, -2, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, 6, 2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, -8, -10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (1, -8, -10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1634.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1636", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 1, 0): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, -1, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, 4, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-8, 4, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1636.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1639", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 3, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 3, 2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, -8, 10): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-10, -8, 10): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1639.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1645", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, 4, 5): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 1, 4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, 7, 9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-1, 7, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1645.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1662", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 4, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 2, -2): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, -5, 9): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-8, -5, 9): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1662.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r167", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-4, 1, 10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, -1, -7): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, -3, -2): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-9, -3, -2): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r167.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1677", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -6, -6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -1, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -4, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"range_lte_5\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-1, -4, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1677.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1680", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -4, -10): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, 0, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → YES\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, 3, -1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (7, 3, -1): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1680.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1691", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 8, 8): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, 7, 1): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → YES\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, 0, -4): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_divisible_by_3\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (4, 0, -4): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1691.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r1697", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 4, 4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"mountain_or_valley\", \"product_positive\", \"range_lte_5\", \"sum_divisible_by_3\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, -3, -4): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, -5, -5): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → YES\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → YES\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"product_positive\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (4, -5, -5): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r1697.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + }, + { + "case_id": "failed_update_mountain_or_valley_r17", + "task": "task_a", + "task_name": "Rule Discovery", + "model_setting": "9B", + "split": "test", + "cbm_challenge_type": "failed_update", + "oracle": "mountain_or_valley", + "target_set_json": "[]", + "system_prompt": "You are a cautious scientist tracking candidate rules in a rule-guessing game.\n\nEach turn, the host provides:\n1. A triple and its currently recorded result: YES or NO.\n2. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nAvailable rule IDs:\n- \"ascending_order\": Three numbers in strictly ascending order (a < b < c)\n- \"product_positive\": The product of all three numbers is positive\n- \"range_lte_5\": The difference between the largest and smallest number is at most 5\n- \"sum_divisible_by_3\": The sum of the three numbers is divisible by 3\n- \"sum_greater_than_10\": The sum of the three numbers is greater than 10\n- \"mountain_or_valley\": The numbers form either a 'mountain' (a < b and b > c) or a 'valley' (a > b and b < c).\n- \"one_negative_xor_ascending\": EITHER exactly one number is negative OR the numbers are strictly ascending, but NOT both.\n- \"distinct_xor_same_parity\": EITHER all three numbers are distinct OR they all share the same parity (all even or all odd), but NOT both.\n- \"endpoints_ascending_xor_middle_between\": EITHER the first number is strictly less than the last (a < c) OR the middle number is strictly between them (min(a,c) < b < max(a,c)), but NOT both.\n- \"sum_even_xnor_product_negative\": The sum of the three numbers is even IF AND ONLY IF the product of the three numbers is strictly negative. (Both True or Both False).\n\nOutput format (strict):\nrule_id_1, rule_id_2\n\n- Inside ``: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `` tag.", + "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, -5, -6): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → YES\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → YES\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"ascending_order\", \"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"one_negative_xor_ascending\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, 1, 1): **NO**\\n\\nRule predictions for this triple:\\n - ascending_order → NO\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → YES\\n - distinct_xor_same_parity → YES\\n - endpoints_ascending_xor_middle_between → YES\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\", \"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, 0, 8): **YES**\\n\\nRule predictions for this triple:\\n - ascending_order → YES\\n - product_positive → NO\\n - range_lte_5 → NO\\n - sum_divisible_by_3 → NO\\n - sum_greater_than_10 → NO\\n - mountain_or_valley → NO\\n - one_negative_xor_ascending → NO\\n - distinct_xor_same_parity → NO\\n - endpoints_ascending_xor_middle_between → NO\\n - sum_even_xnor_product_negative → NO\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"ascending_order\"]}, {\"prompt\": \"**Turn 3 evidence:**\\nCORRECTION for Turn 2:\\nTriple (-6, 0, 8): **NO**\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\", \"product_positive\", \"sum_divisible_by_3\", \"sum_greater_than_10\"]}]", + "messages_json": "[]", + "gt_survivors_json": "[]", + "selected_prompt": "", + "selected_turn": -1, + "train_kind": "", + "source_category": "belief_failure", + "source_file": "task_a/outputs/Qwen3.5-9B_belief_stats_hard_heldout_1_evidence_post_4_5bench_5heldout_hide_post_preds_seed42_target_mountain_or_valley_gpu0/failed_update/belief_failure/failed_update_mountain_or_valley_r17.json", + "source_repeat_index": -1, + "source_repeat_count": -1 + } +]