Benchmark

non-incremental/QF_NRA/20220314-Uncu/Rational_Function_Proof_Calls_With_Disjunctive_Denominator_Simplifications/DDC_ProveIneq_ISSAC10_ex3d.smt2

Translated to SMT-Lib by Maple SMTLIB package.

Application: CAD calls of SUMCracker-ProveInequality to prove Example 3 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	2272
Compressed Size	953
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	2244
Compressed Size	964
Max. Term Depth	8
Asserts	1
Declared Functions	0
Declared Constants	2
Declared Sorts	0
Defined Functions	0
Defined Recursive Functions	0
Defined Sorts	0
Constants	0
Declared Datatypes	0

Symbols

or	4	and	9	+	30	-	31
*	66	<	10	<=	12

Evaluations

Evaluation	Rating	Solver	Variant	Result	Wallclock	CPU Time
SMT-COMP 2023		cvc5	cvc5-default-2023-05-16-ea045f305_sq	sat ✅	0.05572	0.05626
		NRA-LS	cvc5-NRA-LS-sq_default	sat ✅	0.11914	0.11918
		Par4	Par4-wrapped-sq_default	sat ✅	0.02409	0.00639
		SMT-RAT	SMT-RAT-MCSAT_default	sat ✅	0.13709	0.13706
		Yices2	Yices 2 for SMTCOMP 2023_default	sat ✅	0.01448	0.01442
		Z3alpha	z3alpha_default	sat ✅	0.02906	0.02928
		Z3++	z3++0715_default	sat ✅	0.28935	0.28942
			Z3++_sq_0526_default	sat ✅	0.29624	0.29615