Benchmark
non-incremental/QF_NRA/20220314-Uncu/Rational_Function_Proof_Calls_With_Basic_Denominator_Simplifications/BDC_ProveIneq_ISSAC05_LevinLHS.smt2
Translated to SMT-Lib by Maple SMTLIB package.
Application: CAD calls of SUMCracker-ProveInequality to prove LHS of Levin's Inequality 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 in a simple way:
a/b == c/d --> a d==b c && b<>0 && d<>0
a/b > c/d --> a d^2 >=b^2 c && b<>0 && d<>0
| Benchmark |
|---|
| Size | 1422 |
| Compressed Size | 808 |
| 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 | 2022-02-03 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 | 1401 |
| Compressed Size | 805 |
| Max. Term Depth | 6 |
| 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
not | 2 |
and | 1 |
= | 2 |
+ | 11 |
* | 16 |
< | 2 |
<= | 4 |
| |
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 ✅
|
0.11960
|
0.12017
|
| |
MathSAT |
MathSAT-5.6.8_default |
unknown ❌
|
1200.02000
|
1199.83000
|
| |
NRA-LS |
NRA-LS-FINAL_default |
unsat ✅
|
0.10250
|
0.10244
|
| |
Par4 |
Par4-wrapped-sq_default |
unsat ✅
|
0.02621
|
0.01003
|
| |
SMT-RAT |
SMT-RAT-MCSAT_default |
unsat ✅
|
0.17204
|
0.17198
|
| |
veriT |
veriT+raSAT+Redlog_default |
unsat ✅
|
1.52992
|
1.53069
|
| |
Yices2 |
Yices 2.6.2 for SMTCOMP 2021_default |
unsat ✅
|
0.02786
|
0.02779
|
| |
Z3 |
z3-4.8.17_default |
unsat ✅
|
0.01938
|
0.02125
|
| |
Z3++ |
z3++0715_default |
unsat ✅
|
0.28770
|
0.28762
|
|
SMT-COMP 2023
|
|
cvc5 |
cvc5-default-2023-05-16-ea045f305_sq |
unsat ✅
|
0.08391
|
0.08432
|
| |
NRA-LS |
cvc5-NRA-LS-sq_default |
unsat ✅
|
0.10583
|
0.10588
|
| |
Par4 |
Par4-wrapped-sq_default |
unsat ✅
|
0.02230
|
0.00788
|
| |
SMT-RAT |
SMT-RAT-MCSAT_default |
unsat ✅
|
0.20928
|
0.20919
|
| |
Yices2 |
Yices 2 for SMTCOMP 2023_default |
unsat ✅
|
0.02351
|
0.02348
|
| |
Z3alpha |
z3alpha_default |
unsat ✅
|
0.02326
|
0.02350
|
| |
Z3++ |
z3++0715_default |
unsat ✅
|
0.29603
|
0.29610
|
| |
|
Z3++_sq_0526_default |
unsat ✅
|
0.29354
|
0.29358
|
|
SMT-COMP 2024
|
0.20 (4/5) |
cvc5 |
cvc5 |
unsat ✅
|
0.25800
|
0.15844
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.41665
|
0.43153
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
0.27116
|
0.17136
|
| |
Yices2 |
Yices2 |
unsat ✅
|
0.23255
|
0.13239
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.26621
|
0.16651
|
|
SMT-COMP 2025
|
0.17 (5/6) |
cvc5 |
cvc5 |
unsat ✅
|
0.30541
|
0.18688
|
| |
SMTInterpol |
SMTInterpol |
unknown ❌
|
0.44863
|
0.43384
|
| |
SMT-RAT |
SMT-RAT |
unsat ✅
|
0.30081
|
0.17524
|
| |
Yices2 |
Yices2 |
unsat ✅
|
0.30466
|
0.17537
|
| |
Z3alpha |
Z3-alpha |
unsat ✅
|
0.61575
|
0.49819
|
| |
Z3 |
Z3-alpha-base |
unsat ✅
|
0.31545
|
0.19008
|
| |
|
z3siri-base |
unsat ✅
|
0.29381
|
0.17283
|