Upload raw JSON dataset

.gitattributes

@@ -62,3 +62,5 @@ task_a_9b/train.jsonl filter=lfs diff=lfs merge=lfs -text
 task_b_9b/train.jsonl filter=lfs diff=lfs merge=lfs -text
 task_a_9b/train.json filter=lfs diff=lfs merge=lfs -text
 task_b_9b/train.json filter=lfs diff=lfs merge=lfs -text
+Task_A/9B/train/train_cases_9B_thinking.json filter=lfs diff=lfs merge=lfs -text
+Task_B/9B/train/train_cases_9B_thinking.json filter=lfs diff=lfs merge=lfs -text

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r101.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r101",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-1, 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 → 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, 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 → 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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (10, -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 → NO (consistent)\n  - endpoints_ascending_xor_middle_between → YES (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → NO (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: `sum_even_xnor_product_negative` seems likely from the evidence so far.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r101.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r106.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r106",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-1, 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 → 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",
+        "one_negative_xor_ascending"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (7, 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 → 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\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (0, 4, 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 → NO (consistent)\n  - sum_even_xnor_product_negative → NO (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Right now, `mountain_or_valley` appears comparatively unlikely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r106.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r111.json

@@ -0,0 +1,35 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r111",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (8, 4, 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 → YES (consistent)\n\nPlease update your hypotheses based on this evidence.",
+      "golden": [
+        "distinct_xor_same_parity",
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (3, 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 → 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\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (2, 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 → NO (CONTRADICTS evidence → eliminated)\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Given the current evidence, `mountain_or_valley` doesn't look like the best fit.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r111.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r117.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r117",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-8, -7, 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, 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 → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (0, -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 → YES (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → NO (consistent)\n\nPrevious hypothesis: mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: `mountain_or_valley` seems less likely at the moment.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r117.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r12.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r12",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (3, -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 → 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, 5, 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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (4, -5, 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 → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `sum_even_xnor_product_negative`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r12.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r124.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r124",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-7, 1, 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 based on this evidence.",
+      "golden": [
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley",
+        "one_negative_xor_ascending"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (7, 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 → YES (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (1, -1, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Right now, `mountain_or_valley` appears comparatively unlikely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r124.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r127.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r127",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 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 → 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 (3, 4, 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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-6, -6, -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 → NO (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Numbers like these usually mean the rule is probably `one_negative_xor_ascending`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r127.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r13.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r13",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "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 (-9, -9, 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\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (2, -4, 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 → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: `mountain_or_valley` seems less likely at the moment.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r13.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r131.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r131",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (6, 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 based on this evidence.",
+      "golden": [
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (3, 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 → 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\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-8, -6, 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 → NO (consistent)\n  - endpoints_ascending_xor_middle_between → NO (consistent)\n  - sum_even_xnor_product_negative → NO (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'd currently lean toward `endpoints_ascending_xor_middle_between`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r131.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r133.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r133",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "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 (5, -3, 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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-1, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Right now, `mountain_or_valley` appears comparatively unlikely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r133.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r156.json

@@ -0,0 +1,35 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r156",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 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 based on this evidence.",
+      "golden": [
+        "distinct_xor_same_parity",
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (4, 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\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (0, -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 → YES (consistent)\n  - endpoints_ascending_xor_middle_between → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: So far, `sum_even_xnor_product_negative` remains a plausible explanation.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r156.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r179.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r179",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-4, 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 → 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",
+        "one_negative_xor_ascending"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (-5, 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\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (1, 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 → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: From what we've seen so far, `mountain_or_valley` is probably not the answer.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r179.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r180.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r180",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-2, 2, -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 (10, 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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-2, 6, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: `mountain_or_valley` seems less likely at the moment.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r180.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r185.json

@@ -0,0 +1,35 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r185",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "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 → YES (consistent)\n  - sum_even_xnor_product_negative → YES (consistent)\n\nPlease update your hypotheses based on this evidence.",
+      "golden": [
+        "distinct_xor_same_parity",
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (5, 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 → YES (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-4, 1, 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 → NO (consistent)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `endpoints_ascending_xor_middle_between`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r185.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r2.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r2",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (9, 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 → 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, -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 → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (6, -4, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'd be cautious about `mountain_or_valley` for now.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r2.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r21.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r21",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (5, 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 based on this evidence.",
+      "golden": [
+        "distinct_xor_same_parity",
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (-6, 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 → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (8, -2, 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 → NO (CONTRADICTS evidence → eliminated)\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `sum_even_xnor_product_negative`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r21.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r211.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r211",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (8, -2, 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 (-9, -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 → NO (CONTRADICTS evidence → eliminated)\n  - endpoints_ascending_xor_middle_between → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (3, -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 → NO (CONTRADICTS evidence → eliminated)\n  - endpoints_ascending_xor_middle_between → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'd tentatively deprioritize `mountain_or_valley`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r211.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r218.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r218",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-7, -6, -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 based on this evidence.",
+      "golden": [
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (-2, 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 → 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\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (9, -4, 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 → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: At this point, `sum_even_xnor_product_negative` still feels like a strong candidate.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r218.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r221.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r221",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-4, -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 → 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, 4, -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\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-5, 8, 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 → YES (consistent)\n  - sum_even_xnor_product_negative → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'd currently lean toward `endpoints_ascending_xor_middle_between`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r221.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r226.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r226",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 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 → 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, 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 → 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\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-9, 4, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Numbers like these usually mean the rule is probably `one_negative_xor_ascending`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r226.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r228.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r228",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (4, 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 → 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 (7, 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 → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-6, -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 → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: So far, `sum_even_xnor_product_negative` remains a plausible explanation.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r228.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r229.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r229",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 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 → 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 (-6, -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 → YES (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (8, -1, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'd be cautious about `mountain_or_valley` for now.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r229.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r23.json

@@ -0,0 +1,35 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r23",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (0, 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 based on this evidence.",
+      "golden": [
+        "distinct_xor_same_parity",
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "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 → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (8, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `endpoints_ascending_xor_middle_between`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r23.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r237.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r237",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (1, 7, 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 (4, 0, -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 → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 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 → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: So far, `sum_even_xnor_product_negative` remains a plausible explanation.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r237.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r240.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r240",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-7, 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 → 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, 8, 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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (0, 0, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: At this point, `sum_even_xnor_product_negative` still feels like a strong candidate.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r240.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r244.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r244",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (4, 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 based on this evidence.",
+      "golden": [
+        "distinct_xor_same_parity",
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (2, 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 → NO (consistent)\n\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (8, 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 → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Numbers like these usually mean the rule is probably `one_negative_xor_ascending`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r244.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r246.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r246",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-3, 6, -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 based on this evidence.",
+      "golden": [
+        "distinct_xor_same_parity",
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (-10, 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 → NO (CONTRADICTS evidence → eliminated)\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (consistent)\n\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-5, -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 → YES (consistent)\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: So far, `sum_even_xnor_product_negative` remains a plausible explanation.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r246.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r26.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r26",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-5, -9, -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 (-5, -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 → NO (consistent)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (1, -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 → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'm pretty sure `endpoints_ascending_xor_middle_between` is still likely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r26.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r263.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r263",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-5, 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 → 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, 2, -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\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-10, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: At this point, `sum_even_xnor_product_negative` still feels like a strong candidate.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r263.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r274.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r274",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-1, 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 → 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, -4, -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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-5, 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 → YES (CONTRADICTS evidence → eliminated)\n  - endpoints_ascending_xor_middle_between → NO (consistent)\n  - sum_even_xnor_product_negative → NO (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'd be cautious about `mountain_or_valley` for now.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r274.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r276.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r276",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-3, -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 (9, 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 → 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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-7, 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 → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `sum_even_xnor_product_negative`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r276.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r28.json

@@ -0,0 +1,35 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r28",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (3, 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 → YES (consistent)\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": [
+        "distinct_xor_same_parity",
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 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 → YES (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-10, -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\nPrevious hypothesis: mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Numbers like these usually mean the rule is probably `distinct_xor_same_parity`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r28.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r285.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r285",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-2, 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 → 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, 2, 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\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-2, -4, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `sum_even_xnor_product_negative`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r285.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r287.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r287",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "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 → 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, 7, -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\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-10, 5, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: From what we've seen so far, `mountain_or_valley` is probably not the answer.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r287.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r288.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r288",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (0, 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 → 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 (-10, 6, -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 → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (0, 4, -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 → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Given the current evidence, `mountain_or_valley` doesn't look like the best fit.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r288.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r290.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r290",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-2, -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 → 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",
+        "one_negative_xor_ascending"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (1, -7, -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\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\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 → 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: At this point, `sum_even_xnor_product_negative` still feels like a strong candidate.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r290.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r291.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r291",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (7, 5, 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 → 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",
+        "one_negative_xor_ascending"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (9, -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\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (5, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: So far, `sum_even_xnor_product_negative` remains a plausible explanation.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r291.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r299.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r299",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "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 → 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, 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 → NO (CONTRADICTS evidence → eliminated)\n  - endpoints_ascending_xor_middle_between → NO (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (consistent)\n\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-8, 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 → NO (consistent)\n  - sum_even_xnor_product_negative → NO (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: `sum_even_xnor_product_negative` seems likely from the evidence so far.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r299.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r303.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r303",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (10, 9, 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 → 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, -2, 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 → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-1, 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 → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: At this point, `sum_even_xnor_product_negative` still feels like a strong candidate.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r303.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r304.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r304",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (5, 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 → 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 (-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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-10, -4, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Right now, `mountain_or_valley` appears comparatively unlikely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r304.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r313.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r313",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (10, 8, -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 → 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 (-1, 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\nPrevious hypothesis: mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (10, -3, 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 → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Right now, `mountain_or_valley` appears comparatively unlikely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r313.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r32.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r32",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-8, -5, -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 (0, 10, -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 → 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\nPrevious hypothesis: endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-3, 10, 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 → YES (consistent)\n  - sum_even_xnor_product_negative → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `endpoints_ascending_xor_middle_between`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r32.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r322.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r322",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (3, 2, 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 → 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, 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\nPrevious hypothesis: mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (10, -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 → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Right now, `mountain_or_valley` appears comparatively unlikely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r322.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r329.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r329",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-9, 7, -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 (-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 → YES (CONTRADICTS evidence → eliminated)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-4, 5, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `endpoints_ascending_xor_middle_between`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r329.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r34.json

@@ -0,0 +1,35 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r34",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (0, 4, 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 → NO (consistent)\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": [
+        "distinct_xor_same_parity",
+        "endpoints_ascending_xor_middle_between",
+        "mountain_or_valley",
+        "sum_even_xnor_product_negative"
+      ]
+    },
+    {
+      "prompt": "**Turn 1 evidence:**\nTriple (-2, 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\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley, sum_even_xnor_product_negative\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (6, -6, 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 → YES (consistent)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: I'm pretty sure `distinct_xor_same_parity` is still likely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r34.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r340.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r340",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "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, -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 → NO (consistent)\n  - sum_even_xnor_product_negative → YES (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (3, -10, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, distinct_xor_same_parity, endpoints_ascending_xor_middle_between, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: Right now, `mountain_or_valley` appears comparatively unlikely.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r340.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r353.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r353",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (3, 5, -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 (-7, 9, -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\nPrevious hypothesis: mountain_or_valley, one_negative_xor_ascending\nCurrent matching rule IDs: mountain_or_valley, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (10, -1, -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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, sum_even_xnor_product_negative\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: At this point, `sum_even_xnor_product_negative` still feels like a strong candidate.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r353.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r363.json

@@ -0,0 +1,33 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r363",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-8, 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 → 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, 0, -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\nPrevious hypothesis: distinct_xor_same_parity, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (-6, -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 → YES (consistent)\n  - sum_even_xnor_product_negative → NO (CONTRADICTS evidence → eliminated)\n\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, distinct_xor_same_parity, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: So far, `sum_even_xnor_product_negative` remains a plausible explanation.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r363.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}

Task_A/7B/test/failed_isolation/failed_isolation_failed_isolation_mountain_or_valley_r366.json

@@ -0,0 +1,34 @@
+{
+  "case_id": "failed_isolation_failed_isolation_mountain_or_valley_r366",
+  "cbm_challenge_type": "failed_isolation",
+  "oracle": "mountain_or_valley",
+  "target_set": [
+    "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. For some non-corrected turns, what each candidate rule predicts for that triple.\nIf rule predictions are omitted, use the rule definitions and all active evidence directly.\n\nSometimes the host may correct an earlier recorded result.\nWhen that happens, the old record becomes inactive and the corrected one replaces it.\nDo not revise old evidence unless the host explicitly issues a correction.\n\nYour job is to maintain the set of rule IDs that are still consistent with all currently active recorded evidence.\nA rule is contradicted if its prediction differs from the currently recorded result for any active evidence item.\n\nFor later turns, use set intersection:\n- Previous hypothesis: rule_a, rule_b; Current matching rule IDs: rule_b, rule_c; next output is <hypothesis>rule_b</hypothesis>.\n- Previous hypothesis: rule_a, rule_b, rule_c; Current matching rule IDs: rule_c, rule_d; next output is <hypothesis>rule_c</hypothesis>.\n- Never add a rule ID only because it matches the current triple; it must also be in the previous hypothesis.\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.",
+  "turns": [
+    {
+      "prompt": "Let's begin.\n\n**Turn 0 evidence:**\nTriple (-3, -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 → 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, -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\nPrevious hypothesis: distinct_xor_same_parity, endpoints_ascending_xor_middle_between, mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    },
+    {
+      "prompt": "**Turn 2 evidence:**\nTriple (7, -9, 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\nPrevious hypothesis: mountain_or_valley\nCurrent matching rule IDs: mountain_or_valley, one_negative_xor_ascending, endpoints_ascending_xor_middle_between\nUpdate rule: keep only rule IDs that are in BOTH lists above. Do not add new rule IDs.\n\nPlease update your hypotheses using all currently active evidence.\nHost comment: This triple looks especially diagnostic for `sum_even_xnor_product_negative`.",
+      "golden": [
+        "mountain_or_valley"
+      ]
+    }
+  ],
+  "source_file": "data/raw_data/task_a/7B/task_a_cases_7B_valid/target_mountain_or_valley/failed_isolation/failed_isolation_mountain_or_valley_r366.json",
+  "source_category": "belief_failure",
+  "source_repeat_count": 3
+}