As per the rules of this debate, round one is for arguments only. I will respond to Pro’s arguments in the next round.
The question at hand in this debate is whether the constitution requires the defendant of a Senate impeachment trial to be in office at the time of the trial and subsequent vote. I will begin by providing some background and then move on to how it applies to the texts of the constitution.
Over the years there has been much debate over various passages of the constitution with regards to its meaning and application within our society. Opposing sides of this debate are normally categorized into one of two camps; originalism, in which the meaning of the Constitution is interpreted as fixed as of the time it was enacted vs. non-originalism, in which the meaning of the Constitution is viewed as evolving with changes in society and culture.
When the constitutionality of any law or action is contentiously litigated, the ultimate ruling often comes down to which of these approaches is applied by the majority. Because the issue being debated has little to do with changes in society or culture, non-originalism has no real application here. Therefore, it seems clear that we are working within the “originalist” framework, meaning that we are looking at what the framers intended at the time the constitution was written.
Origins of Impeachment
To understand the framer’s viewpoint on impeachment it is important to begin by understanding that this concept did not originate with them. Rather, this was a concept barrowed from England where impeachment was not only regularly used against former officials, but there was even a closely followed impeachment trial in progress in England during the drafting of the constitution and cited at the Philadelphia debates. Impeachment proceedings against Warren Hastings began in 1785 upon his return to England after having resigned as an officer serving overseas .
This fact demonstrates that the understanding the framers had of the concept of impeachment prior to writing the constitution was in no way no way limited to serving officials. Thus, for any argument that the framer’s intended to limit impeachment to serving officers only to be considered logically valid, it must be supported with explicit examples of such intentions. It defies Occam’s razor to presume that they intended for impeachment to apply differently than what was universally understood at the time and yet never bothered to make such intentions clear.
Purpose of Impeachment
Few people will challenge the notion that the primary concern of the framers was to ensure a check on the power of the sitting president. But the fact that disqualification was also provided as an option for the Senate tells us that sitting presidents were not their only concern. The founders could have decided that they would designate elections be the sole process determining whether any individual should hold public office, but they granted the Senate the power to make this decision upon a guilty verdict. We don’t need a history lesson to understand what this tells us; the framers were very concerned about the prospect of a dangerous former official running for public office.
Impacts of the Resolution
The notion that an impeached President whose time in office runs out before his Senate trial can be completed contradicts everything we know about what the framers intended and frankly, defies common sense.
Impeachment is the political version of an indictment. That is, this is where charges are brought. Once an individual has been charged, the trial is where Congress makes its determination as to the defendant’s guilt. Pro’s position is that a charged individual escapes the consequences of conviction if his time in office runs out. If this is the case then the below necessarily follows;
1. Officials who abuse their office at the end of their term cannot be held politically liable
2. Any office holder can escape disqualification from holding future office if they resign prior to the Senate vote to convict
Both of these facts fly in the face of everything we know about the framers intent regarding impeachment and defending against the prospect of a dangerous candidate who threatens to destabilize our democracy.
Interpreting the Texts
Article I, Section 3, Clause 6:
The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present. 
Once the House has impeached the President the articles move to the Senate where the constitution gives the Senate “the sole Power to try all Impeachments”. This alone affirms the resolution. If the charges brought to the Senate are constitutional, and the Senate has the power to try “all” charges, then by extension the Senate has the power to try the charges brought. To argue otherwise is to argue that “all” in this passage actually means “all… except in a specific case which we never mentioned”. Such an argument would be a complete absurdity.
Article I, Section 3, Clause 7:
Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law. 
This passage makes very clear that an officer being tried and convicted in an impeachment trial is no substitute for being legally prosecuted, highlighting the fact that these are two entirely separate processes and thus one cannot be used as a means of dismissing the other.
Article II, Section 4:
The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors. 
There is much contained within this passage, as this is the only passage anywhere in the constitution that mentions government officials subject to impeachment, any requirements of conviction, and what constitutes an impeachable offense, all in 31 words.
The vagueness of this passage is particularly notable, as one of the most contested phrases in the constitution is with regards to what the framers meant by “high crimes and misdemeanors”. Gerald Ford famously defined this term as “whatever a majority of the House of Representatives considers them to be at a moment in history.”
The claim that this impeachment trial is unconstitutional goes against everything we know about what the framers intended and any logical inference from the passages themselves. Other than two passages I did not cite (one stating that the House has sole power of impeachment, the other stating that presidential pardons do not apply to impeachment) everything else the constitution says about impeachment was cited above.
Pro’s position in this debate amounts to the framers understanding that impeachment had historically been used against former officials and yet decided to change this while making no mention of it anywhere, that they expressly gave the Senate the power to try “all impeachments” while really meaning “only impeachments on officials actively serving at the time of trial”, and they intended to give the Senate the power to disqualify former officials from running again while providing those officials a clear loophole to evade any such disqualification.
Any attempt to argue that all of this is true is merely an exercise of ascribing meaning to the passages that are not there.