処分 and 廃棄: handling unwanted goods and discarding them
Compare dealing with unused furniture with discarding materials. 処分 of goods alone does not identify disposal by discarding as the exact method.
Deal with unwanted goods
処分, read しょぶん, means disposal or handling in this goods context. 使わない家具を相談して処分した。 says that the unused furniture was dealt with after discussion.
Discussion and handling the furniture are reported. Whether it was discarded or passed to another person requires more context.
Focus on discarding the goods
廃棄, read はいき, means disposal by discarding. 期限を過ぎた材料を規則に従って廃棄した。 says that expired materials were discarded according to the rules.
The example identifies the discarded materials and reports that rules were followed. It does not specify the rules; read how discarding relates to the broader handling of unwanted goods.
Other contexts and the scope of negation
規則に違反した選手への処分が決まった。 says that disciplinary action was decided for the athlete who broke the rules. This is a different context from handling unwanted goods.
まだ使える品を廃棄しない方法を考えた。 says that someone considered a way not to discard items that can still be used. Thinking is completed, but actual disposal or implementation of the method is not reported.
Does 家具を処分した。 alone establish that the furniture was 廃棄?
Show the answer and why
No. It reports dealing with the unwanted furniture. Discarding or passing it on needs an accompanying statement.