Skip to main content

Table 1. Description of our benchmark set of 120 new examples.

From: Integer Induction in Saturation

Set Variant tag Description
sum x / y \(\mathtt {sum}(x, y)\) for \(x>y\) defined as \(x + \mathtt {sum}(x+1, y)\) or \(y + \mathtt {sum}(x, y-1)\)
all / geq / leq the conjecture holds for all xy where \(x \le y\), or only for \(x \le y = c\), or only for \(c = x \le y\); where \(c\in \mathbb Z\) is an interpreted constant
val declared / defined \(\mathtt {val}\) was either not defined, only declared and axiomatized (as in (6)), or defined as a total computable function (as in (14))
inter / unint / mixed the axiom and conjecture use concrete interpreted constants, or uninterpreted constants, or a mix of both
ax-fin/ax-all/ ax-leq/ax-geq the axiom holds for integers in an interval \([c, c')\), or for all \(x\in \mathbb Z\), or only for \(x \le c\), or only for \(x \ge c\); where \(c, c'\in \mathbb Z\) are constants
conj-fin/conj-all/conj-leq /conj-geq the conjecture holds for integers in an interval \([c, c']\), or for all integers, or only for integers \(\le c\), or only for integers \(\ge c\); where \(c, c' \in \mathbb Z\) are constants
power 0 / 1 \(\mathtt {power}\) defined starting with \(\mathtt {power}(x, 0) = 1\) or \(\mathtt {power}(x, 1) = x\)
all / pos / neg the conjecture holds either for all xy, or only for \(x, y \ge 0\), or only for \(x, y \le 0\)