What is Z3 automated theorem prover?

Z3 is a state-of-the art theorem prover from Microsoft Research . It can be used to check the satisfiability of logical formulas over one or more theories. Z3 offers a compelling match for software analysis and verification tools, since several common software constructs map directly into supported theories.

What can Z3 be used for?

Z3 supports arithmetic, fixed-size bit-vectors, extensional arrays, datatypes, uninterpreted functions, and quantifiers. Its main applications are extended static checking, test case generation, and predicate abstraction .

Z3 is much more than a simple SAT solver , but we will not use any of its SMT solving or theorem proving capabilities for now. >>> x_or_y_iff_not_x = x_and_y == not_x # This is the formula (x_or_y <=> not_x) not a boolean! And that is all you need for this tutorial, as well as for the assignment.

Z3 Theorem Prover Benchmark - OpenBenchmarking.org (2024)

The Z3 Theorem Prover / SMT solver is developed by Microsoft Research under the MIT license.

To run this test with the Phoronix Test Suite, the basic command is: phoronix-test-suite benchmark z3.

Project Site

github.com

Source Repository

github.com

Test Created

5 May 2023

Last Updated

16 July 2024

Test Maintainer

Lucian Popescu

Test Type

Processor

Average Install Time

2 Minutes, 28 Seconds

Average Run Time

4 Minutes, 14 Seconds

Test Dependencies

C/C++ Compiler Toolchain + Python + CMake

Accolades

5k+ Downloads + Recently Updated Test Profile

Supported Platforms

Supported Architectures

x86_64 + aarch64

* Uploading of benchmark result data to OpenBenchmarking.org is always optional (opt-in) via the Phoronix Test Suite for users wishing to share their results publicly.
** Data based on those opting to upload their test results to OpenBenchmarking.org and users enabling the opt-in anonymous statistics reporting while running benchmarks from an Internet-connected platform.
Data updated weekly as of 28 July 2024.

Revision History

pts/z3-1.0.1 [View Source] Tue, 16 Jul 2024 12:59:39 GMT
Enable AArch64 support, change broken download URLs. Closes: https://github.com/phoronix-test-suite/test-profiles/issues/295

pts/z3-1.0.0 [View Source] Fri, 05 May 2023 12:58:31 GMT
Upload Z3 theorem prover test profile from https://github.com/phoronix-test-suite/test-profiles/pull/273 with various cleanups/improvements. Closes: https://github.com/phoronix-test-suite/test-profiles/pull/273

Performance Metrics

Analyze Test Configuration:

Z3 Theorem Prover 4.12.1

SMT File: 2.smt2

OpenBenchmarking.org metrics for this test profile configuration based on 569 public results since 5 May 2023 with the latest data as of 2 August 2024.

Below is an overview of the generalized performance for components where there is sufficient statistically significant data based upon user-uploaded results. It is important to keep in mind particularly in the Linux/open-source space there can be vastly different OS configurations, with this overview intended to offer just general guidance as to the performance expectations.

Component

Percentile Rank

# Compatible Public Results

Seconds (Average)

AMD Ryzen 7 7700X 8-Core

95th

45 ^{+/- 1}

AMD Ryzen 9 7950X 16-Core

95th

46 ^{+/- 1}

AMD Ryzen 9 7900X 12-Core

92nd

47 ^{+/- 1}

AMD Ryzen 7 7700 8-Core

92nd

47 ^{+/- 1}

AMD Ryzen 7 7800X3D 8-Core

90th

47 ^{+/- 1}

2 x AMD EPYC 9J14 96-Core

89th

47 ^{+/- 1}

AMD EPYC 4484PX 12-Core

88th

AMD Ryzen 9 7900 12-Core

87th

47 ^{+/- 2}

AMD EPYC 4584PX 16-Core

85th

AMD EPYC 4344P 8-Core

83rd

AMD Ryzen 5 7600 6-Core

82nd

48 ^{+/- 1}

AMD Ryzen 5 7600X 6-Core

81st

48 ^{+/- 2}

AMD EPYC 4364P 8-Core

81st

AMD Ryzen 9 7950X3D 16-Core

81st

49 ^{+/- 4}

AMD Ryzen Threadripper PRO 7995WX 96-Cores

80th

49 ^{+/- 1}

AMD EPYC 4564P 16-Core

78th

AMD Ryzen 9 7900X3D 12-Core

76th

49 ^{+/- 4}

Does It Scale Well With Increasing Cores?

No, based on the automated analysis of the collected public benchmark data, this test / test settings does not generally scale well with increasing CPU core counts. Data based on publicly available results for this test / test settings, separated by vendor, result divided by the reference CPU clock speed, grouped by matching physical CPU core count, and normalized against the smallest core count tested from each vendor for each CPU having a sufficient number of test samples and statistically significant data.

Notable Instruction Set Usage

Notable instruction set extensions supported by this test, based on an automatic analysis by the Phoronix Test Suite / OpenBenchmarking.org analytics engine.

Instruction Set

Support

Instructions Detected

SSE2 (SSE2)

Used by default on supported hardware.

MOVDQA MOVDQU CVTSI2SD DIVSD PUNPCKLQDQ MOVD SUBSD UNPCKLPD MOVAPD COMISD XORPD ADDSD SHUFPD MULSD CVTTSD2SI CVTSD2SS UCOMISD PSHUFD CVTSS2SD PSRLDQ MAXSD CVTDQ2PD CMPLTPD ANDPD ADDPD MOVUPD DIVPD SQRTSD MINSD PADDQ PUNPCKHQDQ MULPD CVTDQ2PS ANDNPD CMPNLESD ORPD PMULUDQ UNPCKHPD CMPLTSD MOVHPD MOVLPD CMPLESD SUBPD SQRTPD

SSE 4.2 (SSE4_2)

Requires passing a supported compiler/build flag (verified with targets: sandybridge, skylake, tigerlake, cascadelake, sapphirerapids, alderlake, znver2, znver3).
Found on Intel processors since at least 2010.
Found on AMD processors since Bulldozer (2011).

POPCNT

Advanced Vector Extensions (AVX)

Requires passing a supported compiler/build flag (verified with targets: sandybridge, skylake, tigerlake, cascadelake, sapphirerapids, alderlake, znver2, znver3).
Found on Intel processors since Sandy Bridge (2011).
Found on AMD processors since Bulldozer (2011).

VZEROUPPER VEXTRACTF128 VINSERTF128 VBROADCASTSD VBROADCASTSS VPERM2F128 VPERMILPD

Advanced Vector Extensions 2 (AVX2)

Requires passing a supported compiler/build flag (verified with targets: skylake, tigerlake, cascadelake, sapphirerapids, alderlake, znver2, znver3).
Found on Intel processors since Haswell (2013).
Found on AMD processors since Excavator (2016).

VINSERTI128 VEXTRACTI128 VPBROADCASTQ VPBROADCASTD VPERM2I128 VPSLLVD VPSRLVD VPGATHERQD VPGATHERQQ VPERMQ VPMASKMOVQ VPERMPD VPERMD VPMASKMOVD VPBROADCASTB VPBROADCASTW

FMA (FMA)

VFMADD231SD VFMADD132SD VFMADD213SD VFNMADD231SD VFMSUB132SD VFNMADD132SD VFNMADD213SD VFMSUB231SD

Advanced Vector Extensions 512 (AVX512)

Requires passing a supported compiler/build flag (verified with targets: cascadelake, sapphirerapids).

(ZMM REGISTER USE)

The test / benchmark does honor compiler flag changes.

Last automated analysis: 25 June 2023

This test profile binary relies on the shared libraries libm.so.6, libc.so.6.

Tested CPU Architectures

This benchmark has been successfully tested on the below mentioned architectures. The CPU architectures listed is where successful OpenBenchmarking.org result uploads occurred, namely for helping to determine if a given test is compatible with various alternative CPU architectures.

CPU Architecture

Kernel Identifier

Verified On

Intel / AMD x86 64-bit

x86_64

(Many Processors)

ARMv8 64-bit

aarch64

ARMv8 Neoverse-N1 160-Core

Recent Test Results

Compare

z3-1.0.0-Xclang-no-enable-noundef-analysis 1 System - 2 Benchmark Results	ARMv8 Neoverse-N1 - Oracle TLA MB TRAY A1-2c - 1008GB Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-all 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fdrop-deref-attr 1 System - 2 Benchmark Results	ARMv8 Neoverse-N1 - Oracle TLA MB TRAY A1-2c - 1008GB Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
TIGERLAKE Intel Linux Laptop 2 Systems - 413 Benchmark Results	Intel Core i7-1185G7 - Dell XPS 13 9310 0DXP1F - Intel Tiger Lake-LP Ubuntu 24.04 - 6.10.0-061000rc4daily20240621-generic - GNOME Shell 46.0
z3-1.0.0-fdrop-align-attr 1 System - 2 Benchmark Results	ARMv8 Neoverse-N1 - Oracle TLA MB TRAY A1-2c - 1008GB Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fdrop-ub-builtins 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fdrop-noalias-restrict-attr 1 System - 2 Benchmark Results	ARMv8 Neoverse-N1 - Oracle TLA MB TRAY A1-2c - 1008GB Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-Xclang-no-enable-noundef-analysis 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fdrop-deref-attr 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fcheck-div-rem-overflow 1 System - 2 Benchmark Results	ARMv8 Neoverse-N1 - Oracle TLA MB TRAY A1-2c - 1008GB Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fdrop-align-attr 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-mllvm-disable-object-based-analysis 1 System - 2 Benchmark Results	ARMv8 Neoverse-N1 - Oracle TLA MB TRAY A1-2c - 1008GB Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fdrop-noalias-restrict-attr 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-fcheck-div-rem-overflow 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255
z3-1.0.0-mllvm-disable-object-based-analysis 1 System - 2 Benchmark Results	2 x AMD EPYC 9J14 96-Core - Oracle Asm MB+Tray E5-2c - AMD Device 14a4 Ubuntu 22.04 - 6.5.0-1025-oracle - 1.3.255

Compare

AMD EPYC 9684X 2P Genoa-X Benchmarks 12 Systems - 69 Benchmark Results	2 x AMD EPYC 9654 96-Core - AMD Titanite_4G - AMD Device 14a4 Ubuntu 23.04 - 6.2.0-23-generic - GNOME Shell 44.0
AMD Ryzen 5000 Series Linux Performance Featured Processor Comparison	AMD Ryzen 9 5900X 12-Core - ASUS ROG CROSSHAIR VIII HERO - AMD Starship Ubuntu 22.04 - 5.19.0-46-generic - GNOME Shell 42.5
AMD Ryzen 5000 Series Linux Performance 10 Systems - 272 Benchmark Results	AMD Ryzen 7 5800X3D 8-Core - ASUS ROG CROSSHAIR VIII HERO - AMD Starship Ubuntu 22.04 - 5.19.0-46-generic - GNOME Shell 42.5
AMD Ryzen 5000 Series Linux Performance 8 Systems - 271 Benchmark Results	AMD Ryzen 7 7800X3D 8-Core - ASUS PRIME X670-P - AMD Device 14d8 Ubuntu 22.04 - 6.2.0-26-generic - MATE 1.26.0
Intel Core Ultra 7 155H vs. AMD Ryzen 7 7840U Linux Benchmarks 2 Systems - 831 Benchmark Results	Intel Core Ultra 7 155H - MTL Coral_MTH - Intel Device 7e7f Ubuntu 23.10 - 6.7.0-060700rc5-generic - GNOME Shell 45.1
7950x3d may 2 Systems - 35 Benchmark Results	AMD Ryzen 9 7950X3D 16-Core - ASRock X670E PG Lightning - AMD Device 14d8 Ubuntu 22.10 - 5.19.0-23-generic - GNOME Shell 43.0
new new 2 Systems - 191 Benchmark Results	AMD Ryzen Z1 Extreme - ASUS RC71L v1.0 - AMD Device 14e8 Ubuntu 23.04 - 6.4.0-060400rc6-generic - GNOME Shell 44.2
Framework 13 AMD Ryzen 7 7840U Linux Benchmarks 7 Systems - 223 Benchmark Results	AMD Ryzen 7 7840U - PHX Ray_PEU - AMD Device 14e8 Ubuntu 23.10 - 6.3.0-7-generic - GNOME Shell
AMD Ryzen 5000 Series Linux Performance 8 Systems - 271 Benchmark Results	AMD Ryzen 9 5900X 12-Core - ASUS ROG CROSSHAIR VIII HERO - AMD Starship Ubuntu 22.04 - 5.19.0-46-generic - GNOME Shell 42.5
ssa 3 Systems - 22 Benchmark Results	AMD Ryzen 5 5500U - NB01 NL5xNU - AMD Renoir Tuxedo 22.04 - 6.0.0-1010-oem - KDE Plasma 5.26.5
dddas 2 Systems - 234 Benchmark Results	AMD Ryzen Threadripper 3970X 32-Core - ASUS ROG ZENITH II EXTREME - AMD Starship Ubuntu 22.04 - 5.19.0-051900rc7-generic - GNOME Shell 42.2
dddas 2 Systems - 234 Benchmark Results	AMD Ryzen Threadripper 3970X 32-Core - ASUS ROG ZENITH II EXTREME - AMD Starship Ubuntu 22.04 - 5.19.0-051900rc7-generic - GNOME Shell 42.2
sdmay 3 Systems - 49 Benchmark Results	AMD Ryzen 5 4500U - LENOVO LNVNB161216 - AMD Renoir Pop 22.04 - 5.17.5-76051705-generic - GNOME Shell 42.1
icy may 3 Systems - 37 Benchmark Results	Intel Core i7-1065G7 - Dell 06CDVY - Intel Ice Lake-LP DRAM Ubuntu 22.04 - 5.19.0-38-generic - GNOME Shell 42.2
7950x3d may 2 Systems - 35 Benchmark Results	AMD Ryzen 9 7950X3D 16-Core - ASRock X670E PG Lightning - AMD Device 14d8 Ubuntu 22.10 - 5.19.0-23-generic - GNOME Shell 43.0

Z3 Theorem Prover Benchmark - OpenBenchmarking.org (2024)

Project Site

Source Repository

Test Created

Last Updated

Test Maintainer

Test Type

Average Install Time

Average Run Time

Test Dependencies

Accolades

Supported Platforms

Supported Architectures

Revision History

Performance Metrics

Z3 Theorem Prover 4.12.1

SMT File: 2.smt2

Does It Scale Well With Increasing Cores?

Notable Instruction Set Usage

Tested CPU Architectures

Recent Test Results

Compare

z3-1.0.0-Xclang-no-enable-noundef-analysis

z3-1.0.0-all

z3-1.0.0-fdrop-deref-attr

TIGERLAKE Intel Linux Laptop

z3-1.0.0-fdrop-align-attr

z3-1.0.0-fdrop-ub-builtins

z3-1.0.0-fdrop-noalias-restrict-attr

z3-1.0.0-Xclang-no-enable-noundef-analysis

z3-1.0.0-fdrop-deref-attr

z3-1.0.0-fcheck-div-rem-overflow

z3-1.0.0-fdrop-align-attr

z3-1.0.0-mllvm-disable-object-based-analysis

z3-1.0.0-fdrop-noalias-restrict-attr

z3-1.0.0-fcheck-div-rem-overflow

z3-1.0.0-mllvm-disable-object-based-analysis

Most Popular Test Results

Compare

AMD EPYC 9684X 2P Genoa-X Benchmarks

AMD Ryzen 5000 Series Linux Performance

AMD Ryzen 5000 Series Linux Performance

AMD Ryzen 5000 Series Linux Performance

Intel Core Ultra 7 155H vs. AMD Ryzen 7 7840U Linux Benchmarks

7950x3d may

new new

Framework 13 AMD Ryzen 7 7840U Linux Benchmarks

AMD Ryzen 5000 Series Linux Performance

ssa

dddas

dddas

sdmay

icy may

7950x3d may

FAQs

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