\section{end_of_file} \begin{tabular}{|r||c|c|} \hline \hline \# & EBL ? ROTE \\ \hline 2.06 > @{P orsign Q} bar orsign ( {{Q} bar orsign R} bar orsign ( P orsign R ) )@ @P/{p} bar, Q/q, R/r, @ 2.08 = @P implies P@ @@ 2.11 = @P orsign {P} bar@ @@ 2.14 = @{{P} bar} bar implies P@ @@ 2.16 > @P orsign Q implies {{Q} bar} bar orsign P@ @P/{p} bar, Q/q, @ 2.17 > @{{P} bar} bar orsign Q implies Q orsign P@ @P/p, Q/{q} bar, @ 2.18 = @( {P} bar implies P ) implies P@ @@ 2.2 = @P implies P orsign Q@ @@ 2.24 > @P orsign ( {P} bar orsign Q )@ @P/{p} bar, Q/q, @ 2.25 = @P orsign ( P orsign Q implies Q )@ @@ 2.3 = @P orsign ( Q orsign R ) implies P orsign ( R orsign Q )@ @@ 2.31 = @P orsign ( Q orsign R ) implies ( P orsign Q ) orsign R@ @@ 2.32 = @( P orsign Q ) orsign R implies P orsign ( Q orsign R )@ @@ 2.36 = @( P implies Q ) implies ( R orsign P implies Q orsign R )@ @@ 2.37 = @( P implies Q ) implies ( P orsign R implies R orsign Q )@ @@ 2.38 = @( P implies Q ) implies ( P orsign R implies Q orsign R )@ @@ 2.4 = @P orsign ( P orsign Q ) implies P orsign Q@ @@ 2.41 = @P orsign ( Q orsign P ) implies Q orsign P@ @@ 2.45 = @{P orsign Q} bar implies {P} bar@ @@ 2.46 = @{P orsign Q} bar implies {Q} bar@ @@ 2.47 > @{P orsign Q} bar implies {P} bar orsign R@ @P/p, Q/q, R/q, @ 2.48 > @{P orsign Q} bar implies R orsign {Q} bar@ @P/p, Q/q, R/p, @ 2.521 > @{{P orsign Q} bar} bar orsign ( {Q} bar orsign R )@ @P/{p} bar, Q/q, R/p, @ 2.53 = @P orsign Q implies ( {P} bar implies Q )@ @@ 2.54 = @( {P} bar implies Q ) implies P orsign Q@ @@ 2.55 = @{P} bar implies ( P orsign Q implies Q )@ @@ 2.56 = @{P} bar implies ( Q orsign P implies Q )@ @@ 2.6 > @P orsign ( {Q} bar orsign ( R orsign Q ) )@ @P/{{p} bar} bar, Q/q, R/{{p} bar orsign q} bar, @ 2.61 > @P orsign Q implies {{P} bar orsign Q} bar orsign Q@ @P/{p} bar, Q/q, @ 2.621 = @( P implies Q ) implies ( P orsign Q implies Q )@ @@ 2.64 = @P orsign Q implies ( P orsign {Q} bar implies P )@ @@ 2.67 > @{{P orsign Q} bar orsign R} bar orsign ( {P} bar orsign R )@ @P/p, Q/q, R/q, @ 2.68 > @{{{P} bar orsign Q} bar orsign R} bar orsign ( P orsign R )@ @P/p, Q/q, R/q, @ 2.69 > @{{P} bar orsign Q} bar orsign R implies {{R} bar orsign P} bar orsign P@ @P/p, Q/q, R/q, @ 2.73 = @( P implies Q ) implies ( ( P orsign Q ) orsign R implies Q orsign R )@ @@ 2.76 = @P orsign ( Q implies R ) implies ( P orsign Q implies P orsign R )@ @@ 2.81 = @( P implies ( Q implies R ) ) implies ( S orsign P implies ( S orsign Q implies S orsign R ) )@ @@ 2.83 > @{P orsign ( Q orsign R )} bar orsign ( {P orsign ( {R} bar orsign S )} bar orsign ( P orsign ( Q orsign S ) ) )@ @P/{p} bar, Q/{q} bar, R/r, S/s, @ 2.85 > @{P orsign Q} bar orsign ( R orsign S ) implies R orsign ( {Q} bar orsign S )@ @P/p, Q/q, R/p, S/r, @ 3.12 > @P orsign ( Q orsign {P orsign Q} bar )@ @P/{p} bar, Q/{q} bar, @ 3.21 > @P orsign ( Q orsign {Q orsign P} bar )@ @P/{p} bar, Q/{q} bar, @ 3.22 > @{{P orsign Q} bar} bar orsign {Q orsign P} bar@ @P/{p} bar, Q/{q} bar, @ 3.24 > @{{P orsign {P} bar} bar} bar@ @P/{p} bar, @ 3.26 > @{{{P} bar orsign Q} bar} bar orsign P@ @P/p, Q/{q} bar, @ 3.27 > @{{P orsign {Q} bar} bar} bar orsign Q@ @P/{p} bar, Q/q, @ 3.3 > @{{P orsign Q} bar} bar orsign R implies P orsign ( Q orsign R )@ @P/{p} bar, Q/{q} bar, R/r, @ 3.31 > @P orsign ( Q orsign R ) implies {{P orsign Q} bar} bar orsign R@ @P/{p} bar, Q/{q} bar, R/r, @ 3.33 > @{{{P orsign Q} bar orsign {{Q} bar orsign R} bar} bar} bar orsign ( P orsign R )@ @P/{p} bar, Q/q, R/r, @ 3.34 > @{{{{P} bar orsign Q} bar orsign {R orsign P} bar} bar} bar orsign ( R orsign Q )@ @P/p, Q/q, R/{r} bar, @ 3.35 > @{{P orsign {P orsign Q} bar} bar} bar orsign Q@ @P/{p} bar, Q/q, @ 3.37 > @{{P orsign Q} bar} bar orsign R implies {{P orsign {{R} bar} bar} bar} bar orsign Q@ @P/{p} bar, Q/{q} bar, R/r, @ 3.4 > @{{P orsign {Q} bar} bar} bar orsign ( R orsign Q )@ @P/{p} bar, Q/q, R/{p} bar, @ 3.41 > @{{P} bar orsign Q} bar orsign ( {{{P} bar orsign R} bar} bar orsign Q )@ @P/p, Q/q, R/{r} bar, @ 3.42 > @{{P} bar orsign Q} bar orsign ( {{R orsign {P} bar} bar} bar orsign Q )@ @P/p, Q/q, R/{r} bar, @ 3.43 > @{{{P orsign Q} bar orsign {P orsign R} bar} bar} bar orsign ( P orsign {{Q} bar orsign {R} bar} bar )@ @P/{p} bar, Q/q, R/r, @ 3.45 > @P orsign Q implies {{P orsign R} bar} bar orsign {{Q} bar orsign R} bar@ @P/{p} bar, Q/q, R/{r} bar, @ \hline \end{tabular}