SAT means at least one full assignment makes every clause true. This is CP-SAT-style exhaustive search on tiny data; real solvers use propagation and clause learning.
Search and Optimization
Example
SAT means at least one full assignment makes every clause true. This is an exhaustive-search view on tiny data; unlike a real CP-SAT solver, it does not propagate constraints or learn clauses.
highlighted = computed this step
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 \begin{array}{c|c}\text{A=0 B=0 C=0}&\hlmath{\text{c1=0 c2=1 c3=1 SAT=0}}\end{array} A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\hlmath{\text{c1=0 c2=1 c3=1 SAT=0}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 A=0 B=1 C=0 c1=1 c2=1 c3=0 SAT=0 \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=1 C=0}&\hlmath{\text{c1=1 c2=1 c3=0 SAT=0}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 A=0 B=1 C=0 c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0 c1=1 c2=1 c3=0 SAT=0
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 A=0 B=1 C=0 c1=1 c2=1 c3=0 SAT=0 A=0 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=1 C=0}&\text{c1=1 c2=1 c3=0 SAT=0}\\\text{A=0 B=1 C=1}&\hlmath{\text{c1=1 c2=1 c3=1 SAT=1}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 A=0 B=1 C=0 A=0 B=1 C=1 c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0 c1=1 c2=1 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 A=0 B=1 C=0 c1=1 c2=1 c3=0 SAT=0 A=0 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=0 C=0 c1=1 c2=0 c3=1 SAT=0 \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=1 C=0}&\text{c1=1 c2=1 c3=0 SAT=0}\\\text{A=0 B=1 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=0 C=0}&\hlmath{\text{c1=1 c2=0 c3=1 SAT=0}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 A=0 B=1 C=0 A=0 B=1 C=1 A=1 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0 c1=1 c2=1 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=1 SAT=0
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 A=0 B=1 C=0 c1=1 c2=1 c3=0 SAT=0 A=0 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=0 C=0 c1=1 c2=0 c3=1 SAT=0 A=1 B=0 C=1 c1=1 c2=1 c3=1 SAT=1 \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=1 C=0}&\text{c1=1 c2=1 c3=0 SAT=0}\\\text{A=0 B=1 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=0 C=0}&\text{c1=1 c2=0 c3=1 SAT=0}\\\text{A=1 B=0 C=1}&\hlmath{\text{c1=1 c2=1 c3=1 SAT=1}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 A=0 B=1 C=0 A=0 B=1 C=1 A=1 B=0 C=0 A=1 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0 c1=1 c2=1 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=1 SAT=0 c1=1 c2=1 c3=1 SAT=1
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 A=0 B=1 C=0 c1=1 c2=1 c3=0 SAT=0 A=0 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=0 C=0 c1=1 c2=0 c3=1 SAT=0 A=1 B=0 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=1 C=0 c1=1 c2=0 c3=0 SAT=0 \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=1 C=0}&\text{c1=1 c2=1 c3=0 SAT=0}\\\text{A=0 B=1 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=0 C=0}&\text{c1=1 c2=0 c3=1 SAT=0}\\\text{A=1 B=0 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=1 C=0}&\hlmath{\text{c1=1 c2=0 c3=0 SAT=0}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 A=0 B=1 C=0 A=0 B=1 C=1 A=1 B=0 C=0 A=1 B=0 C=1 A=1 B=1 C=0 c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0 c1=1 c2=1 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=1 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=0 SAT=0
Build the concrete table
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 A=0 B=1 C=0 c1=1 c2=1 c3=0 SAT=0 A=0 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=0 C=0 c1=1 c2=0 c3=1 SAT=0 A=1 B=0 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=1 C=0 c1=1 c2=0 c3=0 SAT=0 A=1 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=1 C=0}&\text{c1=1 c2=1 c3=0 SAT=0}\\\text{A=0 B=1 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=0 C=0}&\text{c1=1 c2=0 c3=1 SAT=0}\\\text{A=1 B=0 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=1 C=0}&\text{c1=1 c2=0 c3=0 SAT=0}\\\text{A=1 B=1 C=1}&\hlmath{\text{c1=1 c2=1 c3=1 SAT=1}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 A=0 B=1 C=0 A=0 B=1 C=1 A=1 B=0 C=0 A=1 B=0 C=1 A=1 B=1 C=0 A=1 B=1 C=1 c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0 c1=1 c2=1 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=1 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1
Read the table verdict
Compute the highlighted logic-table value.
A=0 B=0 C=0 c1=0 c2=1 c3=1 SAT=0 A=0 B=0 C=1 c1=0 c2=1 c3=1 SAT=0 A=0 B=1 C=0 c1=1 c2=1 c3=0 SAT=0 A=0 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=0 C=0 c1=1 c2=0 c3=1 SAT=0 A=1 B=0 C=1 c1=1 c2=1 c3=1 SAT=1 A=1 B=1 C=0 c1=1 c2=0 c3=0 SAT=0 A=1 B=1 C=1 c1=1 c2=1 c3=1 SAT=1 verdict satisfiable \begin{array}{c|c}\text{A=0 B=0 C=0}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=0 C=1}&\text{c1=0 c2=1 c3=1 SAT=0}\\\text{A=0 B=1 C=0}&\text{c1=1 c2=1 c3=0 SAT=0}\\\text{A=0 B=1 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=0 C=0}&\text{c1=1 c2=0 c3=1 SAT=0}\\\text{A=1 B=0 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{A=1 B=1 C=0}&\text{c1=1 c2=0 c3=0 SAT=0}\\\text{A=1 B=1 C=1}&\text{c1=1 c2=1 c3=1 SAT=1}\\\text{verdict}&\hlmath{\text{satisfiable}}\end{array} A=0 B=0 C=0 A=0 B=0 C=1 A=0 B=1 C=0 A=0 B=1 C=1 A=1 B=0 C=0 A=1 B=0 C=1 A=1 B=1 C=0 A=1 B=1 C=1 verdict c1=0 c2=1 c3=1 SAT=0 c1=0 c2=1 c3=1 SAT=0 c1=1 c2=1 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=1 SAT=0 c1=1 c2=1 c3=1 SAT=1 c1=1 c2=0 c3=0 SAT=0 c1=1 c2=1 c3=1 SAT=1 satisfiable
logic-computation
Every row is intentionally ordered and pinned to the lesson specification.