Argument from poor design
Judging the intelligence of a designer who created the natural world would not lead to the conclusion of a perfectly intelligent one. There are a large number of rather stunning defects in nature that a competent designer wouldn't make, the human eye for example certainly relies on the principles of optics, but the ganglion cells are situated such that the nerves and blood which feed the eye are backwards and run across the light sensing cells of the eye, then feed through a hole placed in the center such that humans and other mammals have a blind spot. Appendices serve no purpose and get infected and need to be removed. The human jaw is too small to properly fit wisdom teeth. Embryos sometimes implant themselves outside of the uterus and without abortion would kill the mother. If you were to conclude design, you would need to conclude an idiotic tinkerer rather than a divine perfect creator.
Examples of poor design
We conclude that this argument efficiently proves the non-existence of God. If the natural world is perfect then God exists. If it is imperfect then the the counter-argument- if it's bad design, it's a result of the Fall (Genesis 3:16 has God saying to Eve "I will increase your trouble in pregnancy")- leads to the unfalsifiability of ID theory.