Benchmark

non-incremental/QF_NRA/20220314-Uncu/Rational_Function_Proof_Calls_With_Disjunctive_Denominator_Simplifications/DDC_ProveIneq_Mitrinovic_4_22a.smt2

Translated to SMT-Lib by Maple SMTLIB package.

Application: Automated proof of (4.22) in 
D.S. Mitrinovic, Elementary Inequalities, P. Noordhoff ltd - Groningen, (1964)
("https://www.isinj.com/mt-usamo/Elementary%20Inequalities%20-%20Mitrinovic,%20et.%20al.%20(1964,%20Noordhoff).pdf")

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	1493
Compressed Size	788
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	2022-02-01 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	1467
Compressed Size	780
Max. Term Depth	8
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	2	and	5	+	7	-	14
*	22	<	10	<=	4

Evaluations

Evaluation	Rating	Solver	Variant	Result	Wallclock	CPU Time
SMT-COMP 2022		cvc5	cvc5-default-2022-07-02-b15e116-wrapped_sq	sat ✅	0.09772	0.09743
		MathSAT	MathSAT-5.6.8_default	sat ✅	0.02650	0.02647
		NRA-LS	NRA-LS-FINAL_default	sat ✅	0.03846	0.03850
		Par4	Par4-wrapped-sq_default	sat ✅	0.02224	0.00808
		SMT-RAT	SMT-RAT-MCSAT_default	sat ✅	0.01104	0.01102
		veriT	veriT+raSAT+Redlog_default	sat ✅	0.67057	0.67185
		Yices2	Yices 2.6.2 for SMTCOMP 2021_default	sat ✅	0.01389	0.01207
		Z3	z3-4.8.17_default	sat ✅	0.01923	0.02112
		Z3++	z3++0715_default	sat ✅	0.28167	0.28169