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: none
  observed: Z1=1, Z2=1, Y=1

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

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

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

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

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

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  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


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 Z2=1
  observed: Z1=0, Z2=1, Y=0

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

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

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

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

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

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


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: none
  observed: Z1=1, Z2=1, Y=1

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

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

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

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

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

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

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

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

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

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

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

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

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=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=1
  intervention: none
  observed: Z1=1, Z2=1, Y=0

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

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

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

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=0
  observed: Z1=0, Z2=0, Y=0

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

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

Experiment 3:
  inputs: X1=0, X2=1, X3=0
  intervention: none
  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


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: none
  observed: Z1=1, Z2=1, Y=1

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

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

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

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

Experiment 3:
  inputs: X1=1, X2=0, 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=1, Z2=0, Y=0

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

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

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

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

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

Experiment 4:
  inputs: X1=1, X2=0, X3=1
  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=0, Y=0

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

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

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

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

Experiment 3:
  inputs: X1=0, 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=1

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

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

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

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

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

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

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

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

Experiment 4:
  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=1
  intervention: none
  observed: Z1=1, Z2=1, Y=1

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

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

Experiment 4:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  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


{"agent": {}, "env_type": "causal_micro_lab", "max_commit": 1, "max_consecutive_invalid": 2, "max_steps": 1, "protocol": "single", "seed": 23, "task": {"state": {"available_experiment_ids": [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39], "metadata": {"evidence_size": 3, "family_bucket": "cross_family", "maximum_separation": 0.5405405405405406, "mean_separation": 0.3963963963963965, "minimum_separation": 0.10810810810810811, "normalized_mean_separation": 0.3963963963963965, "oracle_budget_representation_error": 0.0, "oracle_singleton_representation_error": 0.22972972972972974, "representative_budget": 4, "representative_coverage_opportunity": 0.22972972972972974, "separation_bucket": "continuous", "separation_definition": "full_outcome_disagreement_v3", "separation_targets": ["Z1", "Z2", "Y"], "valid_mode_count": 4}, "private": {"hidden_mode_id": "687000cb2bd94027bfa2fdff5c270fabbe8c010dc7c92a71a62b4cbaa61a4c08", "valid_mode_ids": ["502cba069b7f42fb980c2d116995da1d9ea4ad2dfaae28c3953e729cff5e98ac", "687000cb2bd94027bfa2fdff5c270fabbe8c010dc7c92a71a62b4cbaa61a4c08", "d1576b826d6eeb4ecd0420b50dfa54a4790c17250dabba7ac2c7d8eee4327754", "dfa11729d98cd1b355a4bdbc00a349e1bcf8845d352fc92189686ccb574cd4c9"]}, "state_id": "0481c074a983f1ed0c7c250b", "visible_experiments": [{"experiment_id": 0, "inputs": {"X1": 0, "X2": 0, "X3": 0}, "intervention": "OBSERVE", "observation": {"Y": 1, "Z1": 0, "Z2": 1}}, {"experiment_id": 10, "inputs": {"X1": 0, "X2": 1, "X3": 0}, "intervention": "OBSERVE", "observation": {"Y": 1, "Z1": 1, "Z2": 0}}, {"experiment_id": 30, "inputs": {"X1": 1, "X2": 1, "X3": 0}, "intervention": "OBSERVE", "observation": {"Y": 1, "Z1": 0, "Z2": 1}}]}}}

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=1

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

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

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

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

Experiment 4:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  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=1

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

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

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

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

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

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

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

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

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


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=1, Z2=1, Y=0

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

Experiment 3:
  inputs: X1=1, X2=0, X3=0
  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=1

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

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

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

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

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  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=1, Z2=1, Y=1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Experiment 4:
  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=1
  intervention: none
  observed: Z1=0, Z2=1, Y=0

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

Experiment 4:
  inputs: X1=1, X2=1, 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


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: none
  observed: Z1=0, Z2=0, Y=1

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

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

Experiment 4:
  inputs: X1=1, X2=1, X3=1
  intervention: none
  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


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=1
  observed: Z1=1, Z2=1, Y=0

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

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

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

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

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

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

Experiment 3:
  inputs: X1=1, X2=1, X3=1
  intervention: none
  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


{"agent": {}, "env_type": "causal_micro_lab", "max_commit": 1, "max_consecutive_invalid": 2, "max_steps": 1, "protocol": "single", "seed": 44, "task": {"state": {"available_experiment_ids": [0, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], "metadata": {"evidence_size": 4, "family_bucket": "within_family", "maximum_separation": 0.6666666666666666, "mean_separation": 0.5092592592592592, "minimum_separation": 0.3333333333333333, "normalized_mean_separation": 0.5092592592592592, "oracle_budget_representation_error": 0.0, "oracle_singleton_representation_error": 0.375, "representative_budget": 4, "representative_coverage_opportunity": 0.375, "separation_bucket": "continuous", "separation_definition": "full_outcome_disagreement_v3", "separation_targets": ["Z1", "Z2", "Y"], "valid_mode_count": 4}, "private": {"hidden_mode_id": "c9cfc51c17d0e672055a42e3b8c3ac7f8f3b83e18a5e47aad6a700f90e8b6579", "valid_mode_ids": ["2b81f1ce29dd6274ea3bfdcfcc9e13aeedf725ee492f601b85ddbf599be4bb50", "a40126323172b5213d29de657c193f8a1aa0b06c0f8c4d5e851e9abf9cc896f9", "a6432fbc3fd136cc540aa7b2a5e192a5e8e4de16b5cfc6646d66023ff4013446", "c9cfc51c17d0e672055a42e3b8c3ac7f8f3b83e18a5e47aad6a700f90e8b6579"]}, "state_id": "6d681851b32ab0efcd22a0d9", "visible_experiments": [{"experiment_id": 1, "inputs": {"X1": 0, "X2": 0, "X3": 0}, "intervention": "DO_Z1_0", "observation": {"Y": 0, "Z1": 0, "Z2": 0}}, {"experiment_id": 5, "inputs": {"X1": 0, "X2": 0, "X3": 1}, "intervention": "OBSERVE", "observation": {"Y": 1, "Z1": 1, "Z2": 0}}, {"experiment_id": 25, "inputs": {"X1": 1, "X2": 0, "X3": 1}, "intervention": "OBSERVE", "observation": {"Y": 1, "Z1": 0, "Z2": 0}}, {"experiment_id": 27, "inputs": {"X1": 1, "X2": 0, "X3": 1}, "intervention": "DO_Z1_1", "observation": {"Y": 0, "Z1": 1, "Z2": 1}}]}}}

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=0, Y=0

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

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

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

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

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

Experiment 4:
  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: set Z1=0
  observed: Z1=0, Z2=1, Y=0

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

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

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

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

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

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

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

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

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

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

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

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

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

Experiment 4:
  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=1
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

Experiment 3:
  inputs: X1=1, X2=0, X3=0
  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=0, Y=0

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

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

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

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

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=1
  intervention: none
  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: set Z1=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=0
  intervention: none
  observed: Z1=1, Z2=1, Y=1

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

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

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

Experiment 3:
  inputs: X1=0, X2=1, 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

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=0, Y=1

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=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


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=1, Z2=0, Y=0

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

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

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

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

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

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

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

Experiment 4:
  inputs: X1=1, X2=0, X3=0
  intervention: none
  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


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=0, Y=0

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

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

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

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

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

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

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

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

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

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

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

Experiment 4:
  inputs: X1=1, X2=1, 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


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: none
  observed: Z1=1, Z2=1, Y=0

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

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

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

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

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

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

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

Experiment 4:
  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=1
  intervention: none
  observed: Z1=1, Z2=0, Y=0

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

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

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

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

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

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

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

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

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

Experiment 4:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  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


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 Z1=0
  observed: Z1=0, Z2=1, Y=1

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

Experiment 3:
  inputs: X1=0, X2=1, X3=1
  intervention: none
  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


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=1, Z2=1, Y=0

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

Experiment 3:
  inputs: X1=1, X2=0, 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=0, Y=1

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

Experiment 3:
  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=1
  intervention: none
  observed: Z1=0, Z2=1, Y=0

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

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

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

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

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

Experiment 4:
  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: set Z1=1
  observed: Z1=1, Z2=0, Y=1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Experiment 3:
  inputs: X1=1, X2=0, X3=1
  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=1

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

Experiment 3:
  inputs: X1=1, X2=0, X3=1
  intervention: none
  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


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 Z2=1
  observed: Z1=0, Z2=1, Y=1

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

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

Experiment 4:
  inputs: X1=1, X2=1, X3=0
  intervention: none
  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=1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Experiment 3:
  inputs: X1=1, X2=1, 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