Benchmark

non-incremental/QF_NRA/20220314-Uncu/Rational_Function_Proof_Calls_With_Disjunctive_Denominator_Simplifications/DDC_ProveIneq_ISSAC10_ex1c.smt2

Translated to SMT-Lib by Maple SMTLIB package.

Application: CAD calls of SUMCracker-ProveInequality to prove Example 1 in
M. Kauers and V. Pillwein, When can we detect that a P-finite sequence is positive?
ISSAC '10: Proceedings of the 2010 International Symposium on Symbolic and Algebraic ComputationJuly 2010 Pages 195–201
(https://doi.org/10.1145/1837934.1837974)

All denominators in the original CAD call got cleared by introducing disjunctions with sign conditions:
a/b == c/d --> a d==b c && b<>0 && d<>0
a/b >= c  --> a >=b c && b >0  or ( a <= b c && b < 0)

Benchmark
Size	1479
Compressed Size	835
License	Creative Commons Attribution 4.0 International (CC-BY-4.0)
Category	industrial
First Occurrence	2022-08-10
Generated By	Ali K. Uncu, Matthew England, and James H. Davenport
Generated On	2022-01-06 00:00:00
Generator	SUMCracker-ProveInequality function by Manuel Kauers ("https://www3.risc.jku.at/research/combinat/software/ergosum/RISC/SumCracker.html")
Dolmen OK	1
strict Dolmen OK	1
check-sat calls	1

Query 1

Status	sat
Inferred Status	sat
Size	1455
Compressed Size	827
Max. Term Depth	9
Asserts	1
Declared Functions	0
Declared Constants	4
Declared Sorts	0
Defined Functions	0
Defined Recursive Functions	0
Defined Sorts	0
Constants	0
Declared Datatypes	0

Symbols

or	1	and	3	+	11	-	3
*	16	<	4	<=	7

Evaluations

Evaluation	Rating	Solver	Variant	Result	Wallclock	CPU Time
SMT-COMP 2025	0.17 (5/6)	cvc5	cvc5	sat ✅	0.29796	0.17039
		SMTInterpol	SMTInterpol	unknown ❌	0.41821	0.40758
		SMT-RAT	SMT-RAT	sat ✅	0.29664	0.16629
		Yices2	Yices2	sat ✅	0.29472	0.16525
		Z3alpha	Z3-alpha	sat ✅	0.60673	0.48425
		Z3	Z3-alpha-base	sat ✅	0.30194	0.18153
			z3siri-base	sat ✅	0.29956	0.17253