Benchmark
non-incremental/QF_NRA/20220314-Uncu/Rational_Function_Proof_Calls_With_Disjunctive_Denominator_Simplifications/DDC_ProveIneq_ISSAC05_LevinRHSm.smt2
Translated to SMT-Lib by Maple SMTLIB package.
Application: CAD calls of SUMCracker-ProveInequality to prove RHS of Levin's Inequality (after multiplying both siides of the inequality with x^n) in
S. Gerhold and M. Kauers, A Procedure for Proving Special Function Inequalities Involving a Discrete Parameter.
ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computationJuly 2005 Pages 156-162.
(https://dl.acm.org/doi/10.1145/1073884.1073907)
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 | 1803 |
| Compressed Size | 907 |
| 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 |
| Status | unsat |
| Inferred Status | unsat |
| Size | 1778 |
| Compressed Size | 918 |
| Max. Term Depth | 11 |
| Asserts | 1 |
| Declared Functions | 0 |
| Declared Constants | 3 |
| Declared Sorts | 0 |
| Defined Functions | 0 |
| Defined Recursive Functions | 0 |
| Defined Sorts | 0 |
| Constants | 0 |
| Declared Datatypes | 0 |
Symbols
or | 2 |
and | 5 |
+ | 25 |
- | 10 |
* | 30 |
< | 7 |
<= | 5 |
| |
Evaluations
| Evaluation |
Rating |
Solver |
Variant |
Result |
Wallclock |
CPU Time |
|
SMT-COMP 2022
|
0.11 (8/9) |
cvc5 |
cvc5-default-2022-07-02-b15e116-wrapped_sq |
unsat ✅
|
0.68316
|
0.68368
|
| |
MathSAT |
MathSAT-5.6.8_default |
unknown ❌
|
1200.02000
|
1199.95000
|
| |
NRA-LS |
NRA-LS-FINAL_default |
unsat ✅
|
0.05952
|
0.05872
|
| |
Par4 |
Par4-wrapped-sq_default |
unsat ✅
|
0.02175
|
0.00700
|
| |
SMT-RAT |
SMT-RAT-MCSAT_default |
unsat ✅
|
0.06945
|
0.06942
|
| |
veriT |
veriT+raSAT+Redlog_default |
unsat ✅
|
4.14451
|
4.14547
|
| |
Yices2 |
Yices 2.6.2 for SMTCOMP 2021_default |
unsat ✅
|
0.01923
|
0.01919
|
| |
Z3 |
z3-4.8.17_default |
unsat ✅
|
0.01979
|
0.02171
|
| |
Z3++ |
z3++0715_default |
unsat ✅
|
0.28895
|
0.28884
|
|
SMT-COMP 2024
|
0.20 (4/5) |
cvc5 |
cvc5 |
unsat ✅
|
0.38910
|
0.28944
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.41840
|
0.43914
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
0.57009
|
0.46957
|
| |
Yices2 |
Yices2 |
unsat ✅
|
0.22632
|
0.12629
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.27386
|
0.17442
|
|
SMT-COMP 2025
|
0.17 (5/6) |
cvc5 |
cvc5 |
unsat ✅
|
1.91682
|
1.79800
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.43696
|
0.43005
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
0.30930
|
0.17951
|
| |
Yices2 |
Yices2 |
unsat ✅
|
0.29716
|
0.16987
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.57788
|
0.46710
|
| |
Z3 |
Z3-alpha-base |
unsat ✅
|
0.31538
|
0.18825
|
| |
|
z3siri-base |
unsat ✅
|
0.30772
|
0.17662
|