query: Herbrand Theorem and Clauses
positive_passages.docid: 151938
positive_passages.text: Intuition about Herbrand Models.
negative_passages.docid: 75625
negative_passages.text: Complete residue system proof
negative_passages.docid: 9158
negative_passages.text: Proving that a propositional theory of any cardinality has an independent set of axioms
negative_passages.docid: 79328
negative_passages.text: Proposition 5.15 from Atiyah and Macdonald: Integral Closure and Minimal Polynomial
negative_passages.docid: 152856
negative_passages.text: Using $p\supset q$ instead of $p\implies q$
negative_passages.docid: 104771
negative_passages.text: Dedekind's cut and axioms
negative_passages.docid: 148790
negative_passages.text: Basic question about proofs with the goal $\exists x P(x)$
negative_passages.docid: 102824
negative_passages.text: Countable set of truth assignments satisfying set of well formed formulas
negative_passages.docid: 139064
negative_passages.text: Show by using logical connectives laws that $(P\to Q) \land (Q \to R) $ is equivalent to $(P \to R) \land [(P \iff Q) \lor (R \iff Q)]$
negative_passages.docid: 156850
negative_passages.text: Fix-Point Theorem Proof.
negative_passages.docid: 34938
negative_passages.text: Recalling a theorem
negative_passages.docid: 17786
negative_passages.text: Existence of Consecutive Quadratic residues
negative_passages.docid: 157924
negative_passages.text: $\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
negative_passages.docid: 117005
negative_passages.text: Rules in the ring with coefficients in finite field $\mathbb{F}_p$
negative_passages.docid: 102042
negative_passages.text: If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
negative_passages.docid: 135267
negative_passages.text: Predicate Logic and Inference
negative_passages.docid: 21250
negative_passages.text: Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$