Another way of getting the same results is simply to break down (decompose) each string, remembering to negate the original conclusion, and decide how many branches are created by the different strings. Then prepare a line for all the original strings that did not branch and check for any contradiction there. If there is none, then cross out any branched string that has its negation either in the line of non-branching strings or in some other branched string. If any branched strings remain, the argument pattern is invalid.

EXAMPLES:
(1) PQORC, RN |- PN
PQON / R...RN...P
PN+QN / R.....RN...P

RN+P

PN+QN / R
.......X......X .... valid
In the example above, note that in any conjoined strings (represented with +) a contradiction of one is a contradiction of the entire group.

(2) PQARC, RN |- PN
PQAN / R...RN...P
PN / QN / R ... RN ... P

RN+P

PN / QN / R
. X......0.....X .... invalid

(3) FGD, GHE |- FHE
FNa/Ga.......Ga+Ha.......FNa/HNa

Fa+Ga
FNa / Ga / FNa / HNa
..X.......0......X.........X ....invalid

(4) FGE, GHD |- FHE
Fa+Ga....GNa/Ha....FNa/HNa

Fa+Ga

GNa / Ha / FNa / HNa
..X.......X.......X........X .... valid

(5) FGD, FW | GV
FNa/Ga...Fa...GNb..(think of why we must apply the new name rule)

Fa+GNb

FNa / Ga
..X.......O .... invalid

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