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

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

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

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

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

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

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


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=0, X3=1
  intervention: set Z2=1
  observed: Z1=1, Z2=1, Y=0

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

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

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

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

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

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

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

Experiment 3:
  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=1, 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=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=1, Y=0

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

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

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

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

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

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

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

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=1, Z2=0, Y=1

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

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

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=0, Z2=1, Y=1

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

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

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

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=0
  intervention: set Z2=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=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=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=1, Z2=1, Y=0

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

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

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

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

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

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

Experiment 3:
  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=1
  intervention: set Z1=1
  observed: Z1=1, Z2=0, Y=0

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

Experiment 3:
  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=0, Z2=0, Y=1

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

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

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

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

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

Experiment 3:
  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=1, Y=1

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

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=0, Z2=1, Y=1

Experiment 3:
  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=1
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=0

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

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

Experiment 3:
  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=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=0, Y=1

Experiment 3:
  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: 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=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=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=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=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=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: set Z2=1
  observed: Z1=1, Z2=1, Y=0

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

Experiment 3:
  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=0
  intervention: set Z2=0
  observed: Z1=0, Z2=0, Y=1

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

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

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

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

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=1, Z2=1, Y=1

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

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

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

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

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

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

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

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

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

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

Experiment 3:
  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=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=1, Y=1

Experiment 3:
  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=1
  intervention: set Z1=1
  observed: Z1=1, 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=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=0
  observed: Z1=0, Z2=0, Y=1

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

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

Experiment 3:
  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: set Z1=0
  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=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=1, Y=0

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


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

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

Evidence:

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

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

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

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


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

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

Evidence:

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

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=1, Z2=0, Y=0

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


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

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

Evidence:

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

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

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

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

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

Experiment 3:
  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=1, 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=0

Experiment 3:
  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=1, Y=0

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

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 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=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=1

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

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

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


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

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

Evidence:

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

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

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

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

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

Experiment 3:
  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: 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=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=0, Z2=1, Y=1

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

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

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=0, Y=1

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

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

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

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

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=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=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=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=0, Y=1

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

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

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

Experiment 3:
  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