diff --git "a/task_a_7b/test.json" "b/task_a_7b/test.json"
new file mode 100644--- /dev/null
+++ "b/task_a_7b/test.json"
@@ -0,0 +1,4202 @@
+[
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r10",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -4, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, 1, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, 8, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r10.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r118",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 10, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-2, -8, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, 7, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r118.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r129",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 9, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, 5, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 3, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r129.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r130",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, -6, 1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-6, 10, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, 8, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r130.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r133",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 1, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -9, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, -3, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r133.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r140",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -6, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, -6, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, 6, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r140.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r145",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -8, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, -2, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, 5, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r145.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r149",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -5, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (2, 0, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, 6, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r149.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r153",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, 3, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (6, 0, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, -4, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r153.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r16",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, -5, 3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -9, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, -8, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r16.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r160",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, -3, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, 1, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, 8, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r160.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r164",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, -7, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -6, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, 3, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r164.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r179",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, -4, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, -4, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, -8, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r179.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r183",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 10, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (9, -9, 1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, -1, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r183.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r200",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, 1, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, 9, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (0, -5, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r200.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r206",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, -7, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, -10, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, 0, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r206.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r212",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, -7, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, 9, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, -9, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r212.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r213",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 0, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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:**\\nTriple (-6, 0, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, -8, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r213.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r223",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -2, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-5, 0, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, 9, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r223.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r235",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, 7, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -8, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (3, -5, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r235.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r237",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 8, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, -4, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, -8, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r237.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r259",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 1, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, 0, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, -6, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r259.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r26",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -1, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 4, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, 1, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r26.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r261",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 10, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 10, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, 3, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r261.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r271",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 6, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-3, -7, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, -3, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r271.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r275",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 2, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 10, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, 10, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r275.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r281",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, -2, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, -10, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, -10, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r281.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r294",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 4, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (8, 8, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, 4, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r294.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r296",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 5, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (9, 5, -10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, 2, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r296.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r305",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, -4, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 10, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, -6, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r305.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r315",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 10, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (3, 1, -10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-2, 0, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r315.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r322",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 2, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-8, -7, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, 8, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r322.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r330",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 6, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-4, -10, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, -1, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r330.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r335",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, -4, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-10, -1, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, 10, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r335.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r336",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, -8, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-6, -3, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, 9, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r336.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r350",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -4, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, -1, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, -10, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r350.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r366",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, 9, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (9, 10, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, -1, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r366.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r400",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 8, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, 1, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, 2, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r400.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r403",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 7, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (4, -7, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, 4, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r403.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r409",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-4, -3, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, 0, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -2, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r409.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r423",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -8, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-4, 10, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, 5, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r423.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r439",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 5, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 10, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -5, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r439.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r449",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -6, 6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, -9, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, 7, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r449.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r451",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -1, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-6, 6, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, 0, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r451.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r461",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -10, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (7, -1, 1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 9, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r461.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r465",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 5, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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:**\\nTriple (-6, -5, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, -10, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r465.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r474",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, 2, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-3, 3, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, 4, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r474.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r499",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 8, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (3, 8, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, -5, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r499.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r505",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -1, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, 2, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 0, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r505.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r516",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -8, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-6, -3, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, 8, 6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r516.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r530",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 0, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-2, -1, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, -5, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r530.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r533",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 7, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (7, -7, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, 10, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r533.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r537",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-4, 0, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-2, -4, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, 7, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r537.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r556",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -9, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, 4, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, 8, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r556.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r570",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 4, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, -10, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, -1, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r570.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r574",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 4, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 0, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, 9, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r574.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r587",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 6, 6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending �� NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 0, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, -6, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r587.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r609",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, 1, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -6, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, -5, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r609.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r620",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -3, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, 8, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, 2, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r620.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r626",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -3, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -5, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 3, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r626.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r634",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, -1, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-9, -2, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-5, 5, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r634.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r645",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, 2, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (6, 8, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, 7, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r645.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r660",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -4, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 2, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, 0, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r660.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r678",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 0, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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:**\\nTriple (5, 4, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, 0, 3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r678.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r695",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, -3, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (8, 3, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 10, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r695.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r702",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-4, 5, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, 5, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, 0, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r702.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r706",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -9, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-8, -3, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -1, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r706.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r714",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 3, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (4, 8, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, -7, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r714.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r724",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, -1, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (3, 7, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, 3, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r724.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r738",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 0, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, -2, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, 2, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r738.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r742",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 1, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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:**\\nTriple (4, 0, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, 7, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r742.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r743",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 7, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (3, 3, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (6, -10, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r743.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r744",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, -9, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, 3, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, -1, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r744.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r748",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, -6, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, 7, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, -9, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r748.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r750",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, -4, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-4, -6, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (8, -2, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r750.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r767",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -9, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, 1, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, -1, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r767.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r768",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, -7, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-2, -8, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-8, 5, 6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r768.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r770",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -1, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, 10, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 5, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r770.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r772",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -5, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (3, 1, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-3, -4, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r772.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r788",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, 10, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (1, 6, 1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (0, -1, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r788.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r789",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -5, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (4, 10, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, 2, 1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r789.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r8",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, 3, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, -5, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, -3, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r8.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r816",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, -2, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 1, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (1, 6, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r816.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r819",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -3, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (0, 2, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 2, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r819.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r830",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, 8, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (5, 9, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-2, 8, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r830.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r836",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -8, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-2, 2, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-2, -3, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r836.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r842",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 7, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (5, 0, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 6, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r842.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r843",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 4, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 0, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-4, 1, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r843.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r847",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, -10, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-8, 8, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (7, 3, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r847.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r85",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, -8, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, 5, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-6, -7, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r85.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r855",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, 0, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-10, -7, 6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-9, 6, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r855.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r860",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -2, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, 10, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (10, -10, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r860.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r877",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 3, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (7, 0, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 7, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r877.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r898",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 3, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (0, 6, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (9, -5, -3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r898.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r903",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, -8, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, 0, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-7, 1, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r903.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r937",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-4, 3, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-4, 0, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (4, 5, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r937.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r944",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -2, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-9, 6, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-1, -4, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r944.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r982",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, -6, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-8, -5, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (-10, -3, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r982.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r985",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, -1, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -5, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (2, -1, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r985.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_stay_failed_stay_mountain_or_valley_r989",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_stay",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -9, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (3, 5, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"mountain_or_valley\"]}, {\"prompt\": \"**Turn 2 evidence:**\\nTriple (5, -5, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_stay/failed_stay_mountain_or_valley_r989.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r109",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (6, -4, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-4, 0, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-4, 0, -9) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r109.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r131",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, 0, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (4, 3, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (4, 3, 7) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r131.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r132",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, -4, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, -5, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, -5, 4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r132.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r14",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, -4, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, -7, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-1, -7, 4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r14.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r157",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 3, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, 4, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-1, 4, -8) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r157.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r160",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, 6, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-8, 0, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-8, 0, 0) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r160.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r166",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -8, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (9, -5, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (9, -5, 4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r166.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r17",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, -3, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (4, -3, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (4, -3, 10) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r17.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r174",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, -3, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 5, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, 5, 6) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r174.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r182",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, 3, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, -3, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-2, -3, 9) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r182.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r184",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, -2, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-3, -10, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-3, -10, 0) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r184.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r215",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, -8, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (6, -8, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, -8, 9) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r215.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r236",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, 4, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-1, 9, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-1, 9, 7) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r236.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r242",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 3, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, 9, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, 9, 0) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r242.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r259",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, 9, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-3, -5, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-3, -5, -7) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r259.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r272",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 3, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, -7, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, -7, -6) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r272.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r274",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -9, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, -10, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, -10, -10) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r274.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r287",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 2, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 7, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (2, 7, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r287.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r309",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 5, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 5, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (2, 5, -8) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r309.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r330",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, 7, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 3, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, 3, 8) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r330.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r335",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -8, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, -8, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, -8, 8) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r335.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r337",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (1, -3, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-5, -10, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-5, -10, -9) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r337.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r341",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -8, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, -1, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, -1, 0) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r341.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r352",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-4, 0, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-10, 1, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-10, 1, 2) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r352.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r353",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -10, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-9, 6, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-9, 6, 8) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r353.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r37",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 9, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-9, -3, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-9, -3, 4) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r37.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r377",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, -7, 1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, -3, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-1, -3, -1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r377.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r398",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 4, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (1, -10, 8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (1, -10, 8) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r398.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r4",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, -2, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (2, 5, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (2, 5, -7) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r4.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r401",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, 1, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (9, -8, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (9, -8, 10) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r401.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r405",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 1, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (10, -4, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (10, -4, -8) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r405.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r42",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, 7, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-6, -4, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-6, -4, 8) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r42.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r423",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 7, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (0, -3, -9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (0, -3, -9) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r423.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r431",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -8, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-7, 9, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-7, 9, 9) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r431.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r433",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -6, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-7, -2, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-7, -2, 5) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r433.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r436",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, -6, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 8, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, 8, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r436.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r44",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 0, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-10, -5, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-10, -5, 5) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r44.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r453",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -6, -10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, -4, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (9, -4, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r453.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r456",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 3, -6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, -7, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (9, -7, 9) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r456.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r467",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, -6, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-5, -3, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-5, -3, 0) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r467.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r470",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -9, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -1, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (8, -1, 4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r470.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r474",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, -3, 3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, -2, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (8, -2, -8) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r474.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r478",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, 9, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-5, -4, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-5, -4, -7) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r478.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r482",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 9, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (3, -10, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (3, -10, -10) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r482.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r534",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -6, 5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 8, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-7, 8, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r534.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r54",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, -4, -9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, -5, 1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-3, -5, 1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r54.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r549",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, -5, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -5, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-6, -5, -5) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r549.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r555",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, 2, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-5, 7, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-5, 7, -4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r555.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r556",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 7, 1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 10, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-2, 10, 4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r556.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r56",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, 6, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 8, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (2, 8, -4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r56.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r561",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -6, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (1, 8, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (1, 8, 4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r561.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r575",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 1, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, -3, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-9, -3, 10) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r575.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r59",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -1, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, -6, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, -6, 0) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r59.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r595",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 0, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-8, 8, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-8, 8, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r595.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r596",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -5, -2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-10, 5, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-10, 5, 4) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r596.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r602",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 3, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-2, 10, 6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-2, 10, 6) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r602.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r608",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -7, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-6, 7, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-6, 7, 9) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r608.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r611",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, -2, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-10, 5, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-10, 5, -7) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r611.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r612",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -2, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-3, -1, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-3, -1, -8) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r612.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r613",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -6, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, -7, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (7, -7, -1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r613.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r629",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 6, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, 0, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-3, 0, -1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r629.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r651",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 1, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-7, 9, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-7, 9, 5) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r651.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r666",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, -1, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, 5, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (2, 5, -1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r666.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r674",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 0, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (7, 4, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (7, 4, -10) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r674.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r677",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, 9, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (9, 3, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (9, 3, 5) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r677.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r678",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 1, 1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, 10, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (9, 10, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r678.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r69",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, 7, 1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (5, 3, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, 3, 9) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r69.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r695",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, -6, -7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (9, 6, -4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (9, 6, -4) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r695.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r701",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 3, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-3, -10, 6): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-3, -10, 6) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r701.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r712",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, 4, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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:**\\nTriple (6, 0, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, 0, 2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r712.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r715",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 8, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, -2, 1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (2, -2, 1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r715.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r733",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, -7, -4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, -10, -10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, -10, -10) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r733.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r741",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -10, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 6, 9): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, 6, 9) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r741.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r750",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-5, -9, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (3, -9, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (3, -9, 2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r750.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r756",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, -8, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-8, 9, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-8, 9, 2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r756.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r757",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (0, -3, -8): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (6, -10, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, -10, -1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r757.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r759",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -8, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-1, 1, 10): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-1, 1, 10) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r759.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r766",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 2, -10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (3, 1, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (3, 1, 5) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r766.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r787",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-3, -5, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (0, 1, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (0, 1, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r787.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r788",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (7, 10, 3): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, -3, 7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-6, -3, 7) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r788.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r790",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, -9, -6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (5, -8, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, -8, 10) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r790.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r797",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 9, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-7, 6, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-7, 6, -3) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r797.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r806",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-9, -10, -8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (8, -7, 1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (8, -7, 1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r806.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r812",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-8, 1, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-3, 8, -10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-3, 8, -10) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r812.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r817",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, 7, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, -5, 4): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-9, -5, 4) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r817.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r834",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (3, 5, 10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-6, 6, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-6, 6, 5) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r834.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r85",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-7, -5, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-1, -3, -1): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-1, -3, -1) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r85.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r865",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (5, -2, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-4, -8, 5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-4, -8, 5) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r865.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r897",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (2, 6, 2): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (5, 1, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (5, 1, 7) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r897.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r909",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, -10, 4): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-7, 9, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-7, 9, -5) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r909.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r921",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, -5, 6): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → YES (consistent)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (6, 7, 2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (6, 7, 2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r921.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r934",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (10, 6, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, -5, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (7, -5, -7) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r934.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r935",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (9, -6, -1): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-9, 9, -3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-9, 9, -3) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r935.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r948",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (8, 7, 3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (-4, -10, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\", \"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-4, -10, 0) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r948.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r97",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-2, -1, -5): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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:**\\nTriple (-8, 3, -5): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"sum_even_xnor_product_negative\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-8, 3, -5) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r97.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r970",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, 6, 7): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (8, 2, 3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (8, 2, 3) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r970.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r978",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-10, 5, -7): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (1, 2, 0): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (1, 2, 0) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r978.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r98",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-1, -5, 0): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (consistent)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\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:**\\nTriple (-10, 7, 8): **YES**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (-10, 7, 8) → YES) was wrong.\\nThe correct result for that same triple is **NO**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → NO (consistent)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"endpoints_ascending_xor_middle_between\", \"mountain_or_valley\"]}]",
+    "messages_json": "[]",
+    "gt_survivors_json": "[]",
+    "selected_prompt": "",
+    "selected_turn": -1,
+    "train_kind": "",
+    "source_category": "belief_failure",
+    "source_file": "task_a/outputs/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r98.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r980",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (-6, 9, 9): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → YES (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"distinct_xor_same_parity\", \"mountain_or_valley\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (7, 1, 3): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → NO (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"distinct_xor_same_parity\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (7, 1, 3) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → NO (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r980.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  },
+  {
+    "case_id": "failed_update_failed_update_mountain_or_valley_r994",
+    "task": "task_a",
+    "task_name": "Rule Discovery",
+    "model_setting": "7B",
+    "split": "test",
+    "cbm_challenge_type": "failed_update",
+    "oracle": "mountain_or_valley",
+    "target_set_json": "[\"mountain_or_valley\"]",
+    "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. What each candidate rule predicts for that triple.\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- \"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):\n<hypothesis>rule_id_1, rule_id_2</hypothesis>\n\n- Inside `<hypothesis>`: comma-separated rule IDs that are still consistent with ALL active evidence.\n- Do not output anything outside the `<hypothesis>` tag.\n",
+    "turns_json": "[{\"prompt\": \"Let's begin.\\n\\n**Turn 0 evidence:**\\nTriple (4, -7, -10): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → NO (consistent)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses based on this evidence.\", \"golden\": [\"mountain_or_valley\", \"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 1 evidence:**\\nTriple (2, -3, -2): **NO**\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (CONTRADICTS evidence → eliminated)\\n  - one_negative_xor_ascending → NO (consistent)\\n  - distinct_xor_same_parity → YES (CONTRADICTS evidence → eliminated)\\n  - endpoints_ascending_xor_middle_between → NO (consistent)\\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\\n\\nPlease update your hypotheses using all currently active evidence.\", \"golden\": [\"one_negative_xor_ascending\"]}, {\"prompt\": \"**Turn 2 evidence:**\\n⚠️ CORRECTION: The recorded result from Turn 1 (triple (2, -3, -2) → NO) was wrong.\\nThe correct result for that same triple is **YES**.\\n\\nRule predictions for this triple:\\n  - mountain_or_valley → YES (consistent)\\n  - one_negative_xor_ascending → NO (CONTRADICTS evidence → eliminated)\\n  - distinct_xor_same_parity → YES (consistent)\\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\\n  - sum_even_xnor_product_negative → YES (consistent)\\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/task_a_cases_7B_valid/target_mountain_or_valley/failed_update/failed_update_mountain_or_valley_r994.json",
+    "source_repeat_index": -1,
+    "source_repeat_count": 5
+  }
+]