Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 7:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Experiment 5:
  inputs: X1=1, X2=0, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


{"agent": {"length_penalty_max": -0.2, "length_penalty_start": 3072.0, "mask_truncated": true}, "env_type": "causal_micro_lab", "max_commit": 1, "max_consecutive_invalid": 2, "max_steps": 1, "protocol": "single", "seed": 87, "task": {"evidence_consistent_reward": 0.0, "nonempty_output_reward": 0.0, "parse_valid_reward": 0.0, "rule_marker_reward": 0.0, "state": {"available_experiment_ids": [0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39], "metadata": {"evidence_size": 4, "family_bucket": "within_family", "maximum_separation": 0.0, "mean_separation": 0.0, "minimum_separation": 0.0, "normalized_mean_separation": 0.0, "separation_bucket": "low", "separation_definition": "predictive_target_disagreement_v2", "separation_targets": ["Y"], "valid_mode_count": 4}, "private": {"hidden_mode_id": "d426363a002681ff4034d9a81c270d2660a3fa8ab8d4df02b16dc13ca2338608", "valid_mode_ids": ["3a099a698aef9c7630b55036b74a0e9bafbaf5d2ccf7da9408676ac8c9877d4a", "4b281f0c85cad823411a5d6de1bc6db816afdc489e91292954ff40507b2939da", "c3298509ca1b2c95a8f3198e58d2d27fddd21c3e91675bbb6fb18adf6a3478cd", "d426363a002681ff4034d9a81c270d2660a3fa8ab8d4df02b16dc13ca2338608"]}, "state_id": "05cc4dfc936107686f0e4885", "visible_experiments": [{"experiment_id": 9, "inputs": {"X1": 0, "X2": 0, "X3": 1}, "intervention": "DO_Z2_1", "observation": {"Y": 0, "Z1": 1, "Z2": 1}}, {"experiment_id": 10, "inputs": {"X1": 0, "X2": 1, "X3": 0}, "intervention": "OBSERVE", "observation": {"Y": 0, "Z1": 1, "Z2": 1}}, {"experiment_id": 25, "inputs": {"X1": 1, "X2": 0, "X3": 1}, "intervention": "OBSERVE", "observation": {"Y": 1, "Z1": 1, "Z2": 0}}, {"experiment_id": 30, "inputs": {"X1": 1, "X2": 1, "X3": 0}, "intervention": "OBSERVE", "observation": {"Y": 0, "Z1": 1, "Z2": 0}}]}, "syntax_valid_reward": 0.2, "valid_hypothesis_reward": 1.0}}

Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 7:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 8:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


{"agent": {"length_penalty_max": -0.2, "length_penalty_start": 3072.0, "mask_truncated": true}, "env_type": "causal_micro_lab", "max_commit": 1, "max_consecutive_invalid": 2, "max_steps": 1, "protocol": "single", "seed": 96, "task": {"evidence_consistent_reward": 0.0, "nonempty_output_reward": 0.0, "parse_valid_reward": 0.0, "rule_marker_reward": 0.0, "state": {"available_experiment_ids": [1, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], "metadata": {"evidence_size": 6, "family_bucket": "within_family", "maximum_separation": 0.0, "mean_separation": 0.0, "minimum_separation": 0.0, "normalized_mean_separation": 0.0, "separation_bucket": "low", "separation_definition": "predictive_target_disagreement_v2", "separation_targets": ["Y"], "valid_mode_count": 4}, "private": {"hidden_mode_id": "d426363a002681ff4034d9a81c270d2660a3fa8ab8d4df02b16dc13ca2338608", "valid_mode_ids": ["3a099a698aef9c7630b55036b74a0e9bafbaf5d2ccf7da9408676ac8c9877d4a", "46c15e618ecd7be92a4e0571deb8d0fa01e1aaf6001108a62243649984c3f2e8", "9c6f88852c2770107b4b64ca0e0e154859ea1b0d1270a20079680054b13b93f1", "d426363a002681ff4034d9a81c270d2660a3fa8ab8d4df02b16dc13ca2338608"]}, "state_id": "016edb8924a9b558f0da4c47", "visible_experiments": [{"experiment_id": 0, "inputs": {"X1": 0, "X2": 0, "X3": 0}, "intervention": "OBSERVE", "observation": {"Y": 0, "Z1": 0, "Z2": 1}}, {"experiment_id": 2, "inputs": {"X1": 0, "X2": 0, "X3": 0}, "intervention": "DO_Z1_1", "observation": {"Y": 0, "Z1": 1, "Z2": 1}}, {"experiment_id": 5, "inputs": {"X1": 0, "X2": 0, "X3": 1}, "intervention": "OBSERVE", "observation": {"Y": 0, "Z1": 1, "Z2": 1}}, {"experiment_id": 12, "inputs": {"X1": 0, "X2": 1, "X3": 0}, "intervention": "DO_Z1_1", "observation": {"Y": 0, "Z1": 1, "Z2": 1}}, {"experiment_id": 22, "inputs": {"X1": 1, "X2": 0, "X3": 0}, "intervention": "DO_Z1_1", "observation": {"Y": 0, "Z1": 1, "Z2": 0}}, {"experiment_id": 25, "inputs": {"X1": 1, "X2": 0, "X3": 1}, "intervention": "OBSERVE", "observation": {"Y": 1, "Z1": 1, "Z2": 0}}]}, "syntax_valid_reward": 0.2, "valid_hypothesis_reward": 1.0}}

Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 7:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=1

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=1

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 7:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 7:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 8:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 7:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=1

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 7:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 8:
  inputs: X1=1, X2=0, X3=1
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Experiment 7:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=0, Y=0

Experiment 8:
  inputs: X1=1, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 7:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=0, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 7:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

Experiment 8:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 5:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=1
  observed: Z1=1, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=0, Y=0

Experiment 5:
  inputs: X1=1, X2=1, X3=0
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=1, X3=1
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=1

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1


Prompt:
Infer one Boolean causal program consistent with the evidence.

Variables: inputs X1,X2,X3; intermediates Z1,Z2; output Y.
Rules: exactly one shallow rule for each target Z1, Z2, Y.
Operators: COPY(A), NOT(A), AND(A,B), OR(A,B), XOR(A,B).
Available inputs:
- Z1 rule can use: X1, X2, X3
- Z2 rule can use: X1, X2, X3, Z1
- Y rule can use: X1, X2, X3, Z1, Z2
For AND/OR/XOR, use two different inputs. Do not nest operators.

Evidence:

Experiment 1:
  inputs: X1=0, X2=0, X3=0
  intervention: none
  observed: Z1=0, Z2=1, Y=0

Experiment 2:
  inputs: X1=0, X2=0, X3=0
  intervention: set Z1=0
  observed: Z1=0, Z2=1, Y=0

Experiment 3:
  inputs: X1=0, X2=1, X3=0
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 4:
  inputs: X1=0, X2=1, X3=0
  intervention: set Z2=0
  observed: Z1=1, Z2=0, Y=0

Experiment 5:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

Experiment 6:
  inputs: X1=1, X2=0, X3=0
  intervention: set Z2=1
  observed: Z1=0, Z2=1, Y=0

Return exactly three lines, no extra text.
Use this flat format:
Z1: OP input [input]
Z2: OP input [input]
Y: OP input [input]
Example:
Z1: AND X1 X2
Z2: OR X2 Z1
Y: XOR X3 Z1