Phase description for a substance dissolved in a solvent other than water?
IUPAC “Green Book” recommends to use $\mathrm{sln}$ for denoting a solution in general [1, p. 54], referring to earlier Recommendations 1981. Appendix No. IV to Manual of Symbols and Terminology for Physicochemical Quantities and Units [2, pp. 1240–1242].
This has been extensively covered in the following posts:

What is the standard way to denote physical states in a chemical reaction? (Meta)
Phase abbreviations for non-aqueous solutions

On the contrary, abbreviation $\mathrm{sol}$ is used to denote a process (typically a sub- or superscript to a symbol for a thermodynamic quantity), not state of matter [1, pp. 59–60]:

2.11.1 Other symbols and conventions in chemical thermodynamics
(i) Symbols used as subscripts to denote a physical chemical process or reaction
These symbols should be printed in Roman (upright) type, without a full stop (period).
$$
\begin{array}{ll}
\ldots \\
\text{solution (of solute in solvent)} &amp; \mathrm{sol} \\ 
\ldots
\end{array}
$$

Another reason not to use $\mathrm{sol}$ for denoting a state of aggregation is its ambiguity: $\mathrm{sol}$ is often used as an abbreviation for “solid”, as listed in Appendix 10-2 Abbreviations, Acronyms, and Symbols in ACS Style Guide [3, p. 197]

$$
\begin{array}{ll}
\ldots \\
\text{sol} &amp; \text{solid} \\
\text{soln} &amp; \text{solution} \\
\ldots
\end{array}
$$

Also, specialized literature on electrochemistry of non-aqueous solutions uses $\mathrm{sv}$ to denote solvation process separately, see e.g. [4, p. 27]:

$ΔH^\circ_\mathrm{sv},$ $ΔS^\circ_\mathrm{sv},$ $ΔG^\circ_\mathrm{sv}$: Enthalpy, entropy, and Gibbs energy of solvation of the electrolyte

With this obligatory standardization part, the simplest reaction can be written as
$$\ce{CuI(s) -&gt;[CH3CN] Cu^+(sln) + I^-(sln)}$$
However, copper(I) is extremely stable in acetonitrile due to solvation [4, p. 33]:

Interactions by Back-Donation from $\mathrm{d^{10}}$-Cation to Solvent Molecules
Acetonitrile (AN) has relatively small DN and usually solvates rather weakly to
metal ions. However, it solvates very strongly to $\ce{Cu+},$ $\ce{Ag+}$ and $\ce{Au+},$ which are univalent $\mathrm{d^{10}}$-metal ions.
This is because these metal ions have an ability to back-donate their electrons into a π*-antibonding orbital of the $\ce{CN}$ group of AN, as shown by $\ce{CH3C#N\overleftarrow{\ce{:\bond{-&gt;}A}}g+}.$
As a result, $\ce{Cu+}$ and $\ce{Ag+}$ in AN are stable and not easily reduced to metal, while the weakly solvated $\ce{Cu^2+}$ is very easily reduced to $\ce{Cu+}$ … , making $\ce{Cu^2+}$ in AN a strong oxidizing agent.

and may theoretically be coordinated by up to five acetonitrile ligands [5] with C.N. 4 being the most common unless there are other ligands.
Copper(I) and iodide don't seem to form a complex in acetonitrile [6, p. 194]:

Also in tetraethyl­ ammonium iodide and thiocyanate solutions, the dissociation is seemingly complete, … while a slight association is indicated for bromide … and, especially, chloride.

To sum it up, upon dissolving of copper(I) iodide in acetnitrile the formation of tetrakis(acetonitrile-N)copper(I) is the most likely scenario so that the final reaction can be written as
$$\ce{CuI(s) + 4 CH3CN(l) -&gt;[CH3CN] [Cu(CH3CN)4]^+(sln) + I^-(sln)}$$
It should be noted that in a presence of better coordinating ligands $\ce{L}$ composition of the complex may, of course, vary $(\ce{[Cu(CH3CN)_xL_y]^z+}).$
Also, copper(I) iodide may form various coordination polymers based on $\ce{(CuI)_n}$ cluster core [7, 8, 9].
References

IUPAC “Green Book” Quantities, Units, and Symbols in Physical Chemistry, 3rd ed.; Cohen, R. E., Mills, I., Eds.; IUPAC Recommendations; RSC Pub: Cambridge, UK, 2007. ISBN 978-0-85404-433-7.
Cox, J. D. Notation for States and Processes, Significance of the Word Standard in Chemical Thermodynamics, and Remarks on Commonly Tabulated Forms of Thermodynamic Functions. Pure and Applied Chemistry 1982, 54 (6), 1239–1250. https://doi.org/10/d783th. (Free Access)
The ACS Style Guide: Effective Communication of Scientific Information, 3rd ed.; Coghill, A. M., Garson, L. R., Eds.; American Chemical Society; Oxford University Press: Washington, DC; Oxford; New York, 2006. ISBN 978-0-8412-3999-9.
Izutsu, K. Electrochemistry in Nonaqueous Solutions; John Wiley &amp; Sons, 2005. ISBN 978-3-527-60065-6.
Vitale, G.; Valina, A. B.; Huang, H.; Amunugama, R.; Rodgers, M. T. Solvation of Copper Ions by Acetonitrile. Structures and Sequential Binding Energies of $\ce{Cu + (CH3CN)_x},$ $x = 1−5,$ from Collision-Induced Dissociation and Theoretical Studies. J. Phys. Chem. A 2001, 105 (50), 11351–11364. https://doi.org/10/ckvsxw.
Ahrland, S.; Nilsson, K.; Tagesson, B.; Haaland, A.; Schilling, B. E. R.; Seip, R.; Taugbøl, K. Thermodynamics of the Copper(I) Halide and Thiocyanate Complex Formation in Acetonitrile. Acta Chem. Scand. 1983, 37a, 193–201. https://doi.org/10/bqvn5f.
Knorr, M.; Guyon, F.; Khatyr, A.; Strohmann, C.; Allain, M.; Aly, S. M.; Lapprand, A.; Fortin, D.; Harvey, P. D. Construction of $\ce{(CuX)_{2n}}$  Cluster-Containing ($\ce{X} = \ce{Br}, \ce{I}$; $n = 1, 2$) Coordination Polymers Assembled by Dithioethers $\ce{ArS(CH2)_mSAr}$ ($\ce{Ar} = \ce{Ph},$ $\ce{\textit{p-}Tol}$; $m = 3, 5$): Effect of the Spacer Length, Aryl Group, and Metal-to-Ligand Ratio on the Dimensionality, Cluster Nuclearity, and the Luminescence Properties of the Metal–Organic Frameworks. Inorg. Chem. 2012, 51 (18), 9917–9934. https://doi.org/10/f37kdx.
Knorr, M.; Khatyr, A.; Dini Aleo, A.; El Yaagoubi, A.; Strohmann, C.; Kubicki, M. M.; Rousselin, Y.; Aly, S. M.; Fortin, D.; Lapprand, A.; et al. Copper(I) Halides $(\ce{X} = \ce{Br}, \ce{I})$ Coordinated to Bis(Arylthio)Methane Ligands: Aryl Substitution and Halide Effects on the Dimensionality, Cluster Size, and Luminescence Properties of the Coordination Polymers. Crystal Growth &amp; Design 2014, 14 (11), 5373–5387. https://doi.org/10/f6pnff.
Knorr, M.; Bonnot, A.; Lapprand, A.; Khatyr, A.; Strohmann, C.; Kubicki, M. M.; Rousselin, Y.; Harvey, P. D. Reactivity of $\ce{CuI}$ and $\ce{CuBr}$ toward Dialkyl Sulfides RSR: From Discrete Molecular $\ce{Cu4I4S4}$ and $\ce{Cu8I8S6}$ Clusters to Luminescent Copper(I) Coordination Polymers. Inorg. Chem. 2015, 54 (8), 4076–4093. https://doi.org/10/f7cjk2.