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\begin{document}
Derivation of $(A\supset B)^p,(A\lor C)^t$:
\[
\infer{(A\supset B)^p,(A\lor C)^t}%
{\infer{A^p,B^p,(A\lor C)^t}%
{\deduce{A^p,A^t,B^p,C^t}%
{\mbox{hypothesis}}
}
&
\infer{A^t,B^f,(A\lor C)^t}%
{\deduce{A^t,B^f,C^t}%
{\mbox{hypothesis}}
}
}
\]
List of hypotheses:
\[\begin{array}{l}
A^p,A^t,B^p,C^t\\
A^t,B^f,C^t
  \end{array}
\]
Derivation of $(A\supset B)^p,(A\lor C)^t$:
\[
\infer{1}%
{\infer{2}%
{\deduce{3}%
{}
}
&
\infer{4}%
{\deduce{5}%
{}
}
}
\]
Table of sequents:
\[\begin{array}{rl}
1{:} & (A\supset B)^p,(A\lor C)^t\\
2{:} & A^p,B^p,(A\lor C)^t\\
3{:} & A^p,A^t,B^p,C^t\\
4{:} & A^t,B^f,(A\lor C)^t\\
5{:} & A^t,B^f,C^t
  \end{array}
\]
\end{document}