Complex sentence: Through investigations, public statements and writings, protests, and livestock theft, DxE has alleged that such companies for lying about the actual conditions on their farms or suppliers farms and believing that it is impossible to raise and kill animals in a humane way.
Split into simpler sentences: Through investigations, public statements and writings, protests, and livestock theft, DxE has alleged in many cases that such companies are lying about the actual conditions on their farms and/or suppliers farms. DxE also believes that it is impossible to raise and kill animals in a humane way.