2:15 We are Jews by birth and not Gentile sinners, that no one is justified by the works of the law but by the faithfulness of Jesus Christ. And we have come to believe in Christ Jesus, so that we may be justified by the faithfulness of Christ and not by the works of the law, because by the works of the law no one will be justified. 2:17 But if while seeking to be justified in Christ we ourselves have also been found to be sinners, is Christ then one who encourages sin? Absolutely not! I demonstrate that I am one who breaks God’s law. 2:19 For through the law I died to the law so that I may live to God. and it is no longer I who live, but Christ lives in me. So the life I now live in the body, I live because of the faithfulness of the Son of God, who loved me and gave himself for me. God’s grace, because if righteousness could come through the law, then Christ died for nothing! (NET)
This passage was posted and the suggestion made it conflicts with the Salvation Formula. But just exactly how it conflicts was not explained.
Paul, born of Jewish parents, declares no one is justified by the works of the Law, but instead we are justified by the faithfulness (sacrifice) of Jesus Christ. What "the works of the Law" refers to may be keeping the Law, which is a works based salvation effort. But no one is justified by "the works of the Law."
Next, Paul says they have been justified by believing in the faithfulness of Christ. Again the Salvation Formula presents this truth.
Next, Paul offers a hypothetical, if while seeking to be justified, and therefore not yet chosen and placed in Christ, does that mean Christ encourages sin? Absolutely not. Rather it means that I (Paul) am the one who breaks the law.
Next Paul returns to His actual, in Christ and saved, status, so His physical life after being put into Christ and indwelt with Christ, should be to live for Christ. Thus keeping the Law, is something Paul should strive to do, while knowing that righteousness comes not through his effort, but through Christ. And not eating the right foods or getting circumcised does not diminish the righteousness that comes through Christ.
Paul makes a similar argument that after we are saved, we should not sin so that grace may abound.
We should strive to be faithful like Jesus was, doing our best to keep in the center of God's will.
Nothing in this passage, or anywhere else in scripture that I am aware of, does the Salvation Formula conflict.