If we looked at the peak strength feat for new 52 Superman, he bench pressed the weight of the planet Earth for 5 days straight. So this illustrates that his strength is at least sufficient to support the weight of the Earth and may be in fact higher, considering he supported this weight for 5 days.
Now a consideration of what force Superman could apply to the bars should be modified by his positioning. He could apply more force by using a dead lift stance (grip a bar and lift, as he braces his feet against another). Typically (by looking at weights that have be lifted) a dead lift form can produce weights approx 40% higher than a bench press. A typical weights bar is 25 - 28mm diameter (so approx 1 - 1.1"), which matches well with the bars of the cage.
So based on this Superman might be able to lift 40% more than the weight of the Earth (that calculates out to 8,360,800,000,000,000,000,000 tonnes).
Now the question I then have is this - Can a 1" diameter bar of Adamantium hold up the weight of the planet Earth or even 1.4x the weight of the planet Earth?
If it can, it would make Adamantium 141,490,000,000,000,000,000 times stronger than high tensile steel.
Based on these factors, I can actually believe that Superman could break the 1" diameter Adamantium bar.
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