Source
This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a "posthuman" stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation.
As written, the conclusion doesn't follow from these premises.
Steps marked ‘assumed’ state what you'd have to assume to reach the conclusion.
Nick Bostrom, "Are You Living in a Computer Simulation?", Philosophical Quarterly 53(211), 2003
As written, before the assumed premise
This paper argues that at least one of the following propositions is true.
The human species is very likely to go extinct before reaching a 'posthuman' stage.
Any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof).
We are almost certainly living in a computer simulation.
Therefore, the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. [1,2,3,4]
What's missing
The conclusion introduces the concept 'the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation.' This evaluative/conditional claim about a belief being false under certain conditions is not directly contained in the cited premises. Premises 1-4 state three disjunctive propositions and a meta-claim that at least one is true, but the conclusion reframes these as a conditional falsity of a belief about future posthuman ancestor-simulations. The concept 'ancestor-simulations' does not appear in the cited premises (premise 3 says 'simulations of their evolutionary history'), and the logical structure connecting the disjunction to the falsity of the belief requires an unstated bridge premise. However, a true bridge premise (that if at least one of these three propositions holds, then the belief in a significant chance of becoming posthumans who run ancestor-simulations is false unless we are in a simulation) could make the conclusion follow, so this is valid with unstated reasoning rather than invalid.