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README.html
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<!DOCTYPE html>
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<meta charset="UTF-8">
<title>README</title>
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<body><div class="markdown-container ltr"><div id="readme"><article class="container-lg"><img src="icon/icon-readme.png" alt="icon" style="float: left; padding-right: 20px; margin-top: -24px;">
<h1 id="xamidipmgenerator">@xamidi/pmGenerator</h1>
<p><a href="https://doi.org/10.5281/zenodo.10931360"><img src="svg/zenodo.10931360.svg" alt="DOI"></a></p>
<p>This tool can collect exhaustive sets of <a href="https://en.wikipedia.org/wiki/Condensed_detachment">condensed detachment</a> proofs in D-N-notation and has various functions to display, analyze and utilize them. It can, for example, be used to generate improved versions of Metamath's <a href="https://us.metamath.org/mmsolitaire/pmproofs.txt" title="us.metamath.org/mmsolitaire/pmproofs.txt">“Shortest known proofs of the propositional calculus theorems from Principia Mathematica”</a> collection.<br>The D-rule combines unification with <a href="https://en.wikipedia.org/wiki/Modus_ponens">modus ponens</a> (⊢p,⊢Cpq ⇒ ⊢q), and there is an option to enable the N-rule (rule of necessitation; ⊢p ⇒ ⊢Lp), thus <em>pmGenerator</em> covers all <a href="https://en.wikipedia.org/wiki/Logical_consequence#Syntactic_consequence">syntactic consequences</a> within <a href="https://en.wikipedia.org/wiki/Hilbert_system">Hilbert systems</a> based on modus ponens and necessitation, each with a minimal proof, limited only by computing power.<br>There is a <a href="https://github.com/xamidi/pmGenerator/discussions">discussion forum</a> for questions, ideas, challenges, and related information.</p>
<p>Eligible for high-performance computing. If you have access to a powerful computer, you may use <em>pmGenerator</em> to further contribute to our knowledge regarding the <a href="https://en.wikipedia.org/wiki/Proof_complexity">complexity of proof systems</a>. Progress that has already been made is exemplarily shown below.</p>
<h6 id="freges-calculus-simplified-by-łukasiewicz-cpcqpccpcqrccpqcprccnpnqcqp-top1000-cardinalities-db-customization-info">Frege's calculus simplified by Łukasiewicz (<a href="svg/frege-1.svg">CpCqp</a>,<a href="svg/frege-2.svg">CCpCqrCCpqCpr</a>,<a href="svg/lukasiewicz-3.svg">CCNpNqCqp</a>) <small>[<a href="data/top1000SmallestConclusions_1to39Steps.txt">top1000</a>] [<a href="data/cardinalities.txt">cardinalities</a>] [<a href="https://us.metamath.org/mmsolitaire/pmproofs.txt">db</a>] [<a href="data/52436f9e87daeb2c361a73a9f389b061258328e641f750b1767addf7/!.def">customization info</a>]</small></h6>
<details open><summary>Behavioral Graph <small>[<a href="svg/plot/default-bgraph_grayscale.svg">grayscale</a>] [<a href="data/plot/default-plot_data_x500.txt">raw</a>]</small></summary>
<a href="https://xamidi.github.io/pmGenerator/svg/plot/default-bgraph.svg"><img src="svg/plot/default-bgraph.svg" width="700"></a></details>
<details open><summary>Data</summary>
<table>
<thead>
<tr>
<th>Files up to..</th>
<th style="text-align:center">Paths</th>
<th style="text-align:right"> Size of Files <br>[B] </th>
<th style="text-align:right">+Costs <br>[≈core‑h]</th>
<th style="text-align:right">RAM (load)<br>[≈GiB] </th>
<th style="text-align:right">RAM (gen.)<br>[≈GiB] </th>
<th style="text-align:right">Recent <br>Growth</th>
</tr>
</thead>
<tbody>
<tr>
<td><small><a href="https://github.com/xamidi/pmGenerator/tree/master/data/dProofs-withConclusions" title="735'676'962 bytes compressed into 41'959'698 bytes (ratio approx. 17.5329)">dProofs29.txt</a></small></td>
<td style="text-align:center"><img src="svg/markers.svg#7" alt="111"></td>
<td style="text-align:right">735 676 962</td>
<td style="text-align:right"><a href="log/dProofs29_6node_288cpu.log">1276.72</a></td>
<td style="text-align:right"><a href="log/utilization/29.log">2.16</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L1-L9">3.22</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=516720692%2F153725015" title="size(dProofs29.txt) / size(dProofs27.txt)">3.3613...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/G18AWIpC#B04xOdtQj_2PJJP0yNQxbim7pOgd-hwv1i1EVU6ZsTM" title="2'161'632'450 bytes compressed into 112'364'583 bytes (ratio approx. 19.2377)">dProofs31‑unfiltered31+.txt</a></small></td>
<td style="text-align:center"><img src="svg/markers.svg#4" alt="100"></td>
<td style="text-align:right">2 897 309 412</td>
<td style="text-align:right"><a href="log/dProofs31-unfiltered31+_48cpu.log">23.19</a></td>
<td style="text-align:right"><a href="log/utilization/31-31.log">5.78</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L11-L18">12.54</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=2161632450%2F516720692" title="size(dProofs31-unfiltered31+.txt) / size(dProofs29.txt)">4.1833...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/P1ki0IKQ#mb0QCboSu0Ofgr9nxspZTdcGUaAHPLzt-rQ8y0TN27k" title="1'741'338'664 bytes compressed into 89'327'496 bytes (ratio approx. 19.4939)">dProofs31.txt</a></small><sup>✻</sup></td>
<td style="text-align:center"><img src="svg/markers.svg#3" alt="011"></td>
<td style="text-align:right">2 477 015 626</td>
<td style="text-align:right"><a href="log/dProofs31_6node_288cpu.log">12681.68</a></td>
<td style="text-align:right"><a href="log/utilization/31.log">5.00</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L20-L28">12.51</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=1741338664%2F516720692" title="size(dProofs31.txt) / size(dProofs29.txt)">3.3699...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/3gVQSIJL#Qfa9CoUwsHWYYNHXYaP1mg61QQSJ1NSl1CHudK4g7BA" title="8'349'023'875 bytes compressed into 402'886'507 bytes (ratio approx. 20.7230)">dProofs33‑unfiltered31+.txt</a></small></td>
<td style="text-align:center"><img src="svg/markers.svg#4" alt="100"></td>
<td style="text-align:right">11 246 333 287</td>
<td style="text-align:right"><a href="log/dProofs33-unfiltered31+_48cpu.log">86.59</a></td>
<td style="text-align:right"><a href="log/utilization/33-31.log">19.49</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L30-L37">43.73</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=8349023875%2F2161632450" title="size(dProofs33-unfiltered31+.txt) / size(dProofs31-unfiltered31+.txt)">3.8623...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/ixshHB7S#ktigbEzeOvCvFP8pruhC0NFfeK91p__eS_uZxBtIy0w" title="7'295'621'951 bytes compressed into 352'588'174 bytes (ratio approx. 20.6916)">dProofs33‑unfiltered33+.txt</a></small></td>
<td style="text-align:center"><img src="svg/markers.svg#2" alt="010"></td>
<td style="text-align:right">10 192 931 363</td>
<td style="text-align:right"><a href="log/dProofs33-unfiltered33+_48cpu.log">92.19</a></td>
<td style="text-align:right"><a href="log/utilization/33-33.log">17.04</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L39-L46">39.42</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=7295621951%2F1741338664" title="size(dProofs33-unfiltered33+.txt) / size(dProofs31.txt)">4.1896...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/S5tDkSCC#WKEWeT7Niaj9ZVWrqiy-FGPI8ACGsd2H7mA3ZWUITFY" title="5'876'664'090 bytes compressed into 279'929'404 bytes (ratio approx. 20.9934)">dProofs33.txt</a></small><sup>✻</sup></td>
<td style="text-align:center"><img src="svg/markers.svg#1" alt="001"></td>
<td style="text-align:right">8 353 679 716</td>
<td style="text-align:right"><a href="log/dProofs33_60node_2880cpu.log">110356.00</a></td>
<td style="text-align:right"><a href="log/utilization/33.log">14.67</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L48-L56">39.20</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=5876664090%2F1741338664" title="size(dProofs33.txt) / size(dProofs31.txt)">3.3747...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/2893yZ7S#JlCHv4uOajgBJPPE2W87F_LAPzkH0-FlF4_2OrccuC4" title="30'717'801'573 bytes compressed into 1'400'853'331 bytes (ratio approx. 21.9279)">dProofs35‑unfiltered31+.txt</a></small></td>
<td style="text-align:center"><img src="svg/markers.svg#4" alt="100"></td>
<td style="text-align:right">41 964 134 860</td>
<td style="text-align:right"><a href="log/dProofs35-unfiltered31+_48cpu.log">366.69</a></td>
<td style="text-align:right"><a href="log/utilization/35-31.log">67.74</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L58-L65">154.60</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=30717801573%2F8349023875" title="size(dProofs35-unfiltered31+.txt) / size(dProofs33-unfiltered31+.txt)">3.6792...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/WwNViKRa#UBiPOFN4wRkMgetY60eAQi1oXVQ3fQdkcg7hFxB-Dfk" title="28'223'320'428 bytes compressed into 1'290'589'236 bytes (ratio approx. 21.8686)">dProofs35‑unfiltered33+.txt</a></small></td>
<td style="text-align:center"><img src="svg/markers.svg#2" alt="010"></td>
<td style="text-align:right">38 416 251 791</td>
<td style="text-align:right"><a href="log/dProofs35-unfiltered33+_48cpu.log">329.08</a></td>
<td style="text-align:right"><a href="log/utilization/35-33.log">61.41</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L67-L74">137.87</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=28223320428%2F7295621951" title="size(dProofs35-unfiltered33+.txt) / size(dProofs33-unfiltered33+.txt)">3.8685...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/b0t1xbKI#6sjAICTTNMfQ2VO5kyVMpxVHSQNZzxWPktOEGJkberk" title="24'669'947'024 bytes compressed into 1'121'466'816 bytes (ratio approx. 21.9979)">dProofs35‑unfiltered35+.txt</a></small></td>
<td style="text-align:center"><img src="svg/markers.svg#1" alt="001"></td>
<td style="text-align:right">33 023 626 740</td>
<td style="text-align:right"><a href="log/dProofs35-unfiltered35+_48cpu.log">307.16</a></td>
<td style="text-align:right"><a href="log/utilization/35-35.log">53.49</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L76-L83">124.14</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=24669947024%2F5876664090" title="size(dProofs35-unfiltered35+.txt) / size(dProofs33.txt)">4.1979...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/6wUyDQzT#DQIJOLd5dCn-6V9sJWiJXeGRPUTUaA-7LqbGfLStjV0" title="113'174'356'461 bytes compressed into 4'897'020'927 bytes (ratio approx. 23.1109)">dProofs37‑unfiltered31+.txt</a></small><sup>✻</sup></td>
<td style="text-align:center"><img src="svg/markers.svg#4" alt="100"></td>
<td style="text-align:right">155 138 491 321</td>
<td style="text-align:right"><a href="log/dProofs37-unfiltered31+_144cpu.log">18975.40</a></td>
<td style="text-align:right"><a href="log/utilization/37-31.log">238.30</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L85-L92">485.12</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=113174356461%2F30717801573" title="size(dProofs37-unfiltered31+.txt) / size(dProofs35-unfiltered31+.txt)">3.6843...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/q1txWSZA#P_HoU6_4_fCYd_1Zw7Y5UG7R4UWdlVm4_s9xG6pzsoY" title="103'965'043'304 bytes compressed into 4'479'575'346 bytes (ratio approx. 23.2087)">dProofs37‑unfiltered33+.txt</a></small><sup>✻</sup></td>
<td style="text-align:center"><img src="svg/markers.svg#2" alt="010"></td>
<td style="text-align:right">142 381 295 095</td>
<td style="text-align:right"><a href="log/dProofs37-unfiltered33+_144cpu.log">14331.28</a></td>
<td style="text-align:right"><a href="log/utilization/37-33.log">217.76</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L94-L101">446.50</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=103965043304%2F28223320428" title="size(dProofs37-unfiltered33+.txt) / size(dProofs35-unfiltered33+.txt)">3.6836...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/Pg0STDYL#YZF0i4i6AcLP2_gZQuHNb40ajbspYC8wOFsK7fmKQTw" title="95'571'571'048 bytes compressed into 4'105'722'124 bytes (ratio approx. 23.2777)">dProofs37‑unfiltered35+.txt</a></small><sup>✻</sup></td>
<td style="text-align:center"><img src="svg/markers.svg#1" alt="001"></td>
<td style="text-align:right">128 595 197 788</td>
<td style="text-align:right"><a href="log/dProofs37-unfiltered35+_144cpu.log">14740.88</a></td>
<td style="text-align:right"><a href="log/utilization/37-35.log">197.08</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L103-L110">408.38</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=95571571048%2F24669947024" title="size(dProofs37-unfiltered35+.txt) / size(dProofs35-unfiltered35+.txt)">3.8740...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/WwEgwITB#Fk145eaRsw7S3IFpuxwcbeyYi4IwNatrxF7SWnZwvIo" title="352'398'833'029 bytes compressed into 14'265'852'732 bytes (ratio approx. 24.7023)">dProofs39‑unfiltered35+.txt</a></small><sup>✻</sup></td>
<td style="text-align:center"><img src="svg/markers.svg#1" alt="001"></td>
<td style="text-align:right">480 994 030 817</td>
<td style="text-align:right"><a href="log/dProofs39-unfiltered35+_64cpu.log">4566.99</a></td>
<td style="text-align:right"><a href="log/utilization/39-35.log">1301.97</a></td>
<td style="text-align:right"><a href="log/jobsRSS.txt#L112-L119">1768.07</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=352398833029%2F95571571048" title="size(dProofs39-unfiltered35+.txt) / size(dProofs37-unfiltered35+.txt)">3.6872...</a></td>
</tr>
</tbody>
</table>
</details>
<p>Measured RAM requirements correspond to the maximum resident set size according to <a href="https://slurm.schedmd.com/documentation.html">Slurm</a>, i.e. <code>MaxRSS</code> of <a href="https://slurm.schedmd.com/sacct.html">sacct</a>.<br>Required resources vary based on implementation and environment; numbers are to illustrate orders of magnitude.<br>Some more – and very special – proof systems are illustrated <a href="#custom-proof-systems">further down below</a>.</p>
<h4 id="usage">Usage</h4>
<pre><code>pmGenerator ( <configuring command> | <composable command> )+ | <configuring command>* <standalone command>
Configuring:
-c [-i <file>] [-s <string>] [-n] [-N <limit or -1>] [-l] [-e <id>] [-d]
Proof system customization ; Generates a SHA-512/224 hash to identify the system, sets the effective data location to "<data location>/<hash>", and (if nonexisting) creates the !.def file.
-i: specify axioms by input file path (where a LF-separated string of axioms is stored), ignoring lines that are empty or starting with '%'
-s: specify axioms by comma-separated string ; used only when '-i' unspecified ; default: "C0C1.0,CC0C1.2CC0.1C0.2,CCN0N1C1.0"
-n: specify formulas in normal Polish notation (e.g. "CpCqp"), not with numeric variables (e.g. "C0C1.0")
-N: enable necessitation rule "N" for the given system with unlimited (-N 0) or limited (-N <positive amount>) consecutive necessitation steps allowed
-l: disable lazy N-rule parsing ; parse proofs Nα:Lβ despite knowing α:β (requires more time but less memory)
-e: specify extracted system with the given identifier
-d: default system ; ignore all other arguments except '-e'
Composable:
-g <limit or -1> [-u] [-q <limit>] [-s] [-l <limit or -1>]
Generate proof files ; at ./data/[<hash>/]/dProofs-withConclusions/ when '-s' unspecified ; otherwise at ./data/[<hash>/]/dProofs-withoutConclusions/
-u: unfiltered (significantly faster, but generates redundant proofs)
-q: limit number of proof candidate strings queued per worker thread (may lower memory requirements for systems with low acceptance rates)
-s: proof files without conclusions, requires additional parsing
-l: limit symbolic length of generated conclusions to at most the given number ; works only in extracted environments ; recommended to use in combination with '-q' to save memory
-r <D-proof database> <output file> [-l <path>] [-i <prefix>] [-s] [-d]
Replacements file creation based on proof files
-l: customize data location path ; default: "data"
-i: customize input file path prefix in data location ; default: "dProofs-withConclusions/dProofs"
-s: proof files without conclusions, requires additional parsing ; sets default input file path prefix to "dProofs-withoutConclusions/dProofs"
-d: print debug information
-a <initials> <replacements file> <D-proof database> <output file> [-s] [-l] [-w] [-d]
Apply replacements file
-s: style all proofs (replace proofs with alphanumerically smaller variants)
-l: list all proofs (i.e. not only modified proofs)
-w: wrap results
-d: print debug information
--parse <string> [-n] [-u] [-j <limit or -1>] [-b] [-s] [-e] [-f] [-o <output file>] [-d]
Parse and print proofs given by a comma-separated string
-n: print formulas in normal Polish notation (e.g. "CpCqp"), not with numeric variables (e.g. "C0C1.0")
-u: print formulas in infix notation with operators as Unicode characters ; used only when '-n' unspecified
-j: join common subproofs together when they are used at least a given amount of times ; default: 2
-b: only print conclusions of the given proofs ; sets default of '-j' to 1
-s: only print summary with conclusions and abstract condensed detachment proofs ; used only when '-b' unspecified
-e: keep expanded proof strings ; show fully detailed condensed detachment proofs rather than allowing them to contain references ; used only when '-b' unspecified
-f: proofs are given by input file path (where a comma-separated string is stored), ignoring all CR, LF, whitespace, and lines starting with '%'
-o: redirect the result's output to the specified file
-d: print debug information
--transform <string> [-s <string>] [-j <limit or -1>] [-p <limit or -1>] [-n] [-u] [-t <string>] [-e] [-i <limit or -1>] [-l <limit or -1>] [-z] [-f] [-o <output file>] [-d]
Transform proof summary (as by '--parse [...] -s') into recombined variant ; ignores configured system (proof summaries provide their own axioms) ; "," represents LF
-s: list a subproof with its conclusion if it occurs in the given comma-separated list of conclusions
-j: join common subproofs together when they are used at least a given amount of times ; default: 2
-p: only keep subproofs with primitive lengths not exceeding the given limit ; default: -1
-n: specify and print formulas in normal Polish notation (e.g. "CpCqp"), not with numeric variables (e.g. "C0C1.0")
-u: print formulas in infix notation with operators as Unicode characters ; does not affect input format (for which '-n' can still be specified)
-t: only transform proofs of specified theorems (proven by subsequences of the input), given by a comma-separated string ; "." to keep all conclusions ; default: final theorem only
-e: keep expanded proof strings ; show fully detailed condensed detachment proofs rather than allowing them to contain references
-i: decrease memory requirements but increase time consumption by not storing intermediate unfoldings that exceed a certain length ; default: -1
-l: abort computation when combined requested proof sequences exceed the given limit in bytes ; default: 134217728 (i.e. 128 MiB)
-z: proof compression ; find and remove internal redundancies (e.g. non-trivial parts not affecting intermediate theorems) by attempting to use shorter owned subproofs at all positions
-f: proof summary is given by input file path ; ignores lines that are empty or starting with '%'
-o: redirect the result's output to the specified file
-d: print debug information
--unfold <string> [-n] [-t <string>] [-i <limit or -1>] [-l <limit or -1>] [-w] [-f] [-o <output file>] [-d]
Break down proof summary (as by '--parse [...] -s') into primitive steps ; ignores configured system (proof summaries provide their own axioms) ; "," represents LF
-n: specify formulas in normal Polish notation (e.g. "CpCqp"), not with numeric variables (e.g. "C0C1.0")
-t: obtain proofs of specified theorems (proven by subsequences of the input), given by a comma-separated string ; "." to obtain a proof for each conclusion ; default: final theorem only
-i: decrease memory requirements but increase time consumption by not storing intermediate unfoldings that exceed a certain length ; default: -1
-l: abort computation when combined requested proof sequences exceed the given limit in bytes ; default: 134217728 (i.e. 128 MiB)
-w: wrap results
-f: proof summary is given by input file path ; ignores lines that are empty or starting with '%'
-o: redirect the result's output to the specified file
-d: print debug information
--search <string> [-n] [-s] [-w] [-p] [-f] [-d]
Search in proof files at ./data/[<hash>/]/dProofs-withConclusions/ via comma-separated string of full formulas or full proofs ; [Hint: Generate missing files with '--variate 1 -s'.]
-n: specify formulas in normal Polish notation (e.g. "CpCqp"), not with numeric variables (e.g. "C0C1.0")
-s: search for schemas of the given formulas
-w: search whole collections of schemas (i.e. enable multiple results per term) ; entails '-s'
-p: search proofs (rather than conclusions) ; used only when '-n' and '-s' unspecified
-f: search terms are given by input file path (where a comma-separated string is stored), ignoring all CR, LF, whitespace, and lines starting with '%'
-d: print debug information
--extract [-t <limit or -1>] [-o <output file>] [-s] [-# <amount up to 35>] [-h <string>] [-l <limit or -1>] [-f] [-d]
Various options to extract information from proof files ; [Hint: Generate missing files with '--variate 1 -s'.]
-t: compose file with up to the given amount of smallest conclusions that occur in proof files ; includes origins, symbolic lengths, proofs, and formulas in normal Polish notation
-o: specify output file path for '-t' ; relative to effective data location ; default: "top<amount>SmallestConclusions_<min proof length>to<max proof length>Steps<unfiltered info>.txt"
-s: redundant schema removal for '-t' ; very time-intensive for requesting huge collections from unfiltered proof files - better pre-filter via '-g' or '-m' instead ; default: false
-#: initialize proof system at ./data/[<hash>/]/extraction-<id>/ with the given amount of smallest filtered conclusions that occur in proof files ; specify with '-c <parent system> -e <id>'
-h: similar to '-#' ; hand-pick conclusions with a comma-separated string of proofs ; "." to not modify axioms
-l: similar to '-#' (but creates identical system with prebuilt proof files) ; copy proofs with conclusions that have a symbolic length of at most the given number
-f: proofs for '-h' are given by input file path (where a comma-separated string is stored), ignoring all CR, LF, whitespace, and lines starting with '%'
-d: print debug information
--iterate [-u] [-s]
Iterate proof candidates currently next up for generation and print (and store for custom proof systems) their amount for prediction purposes
-u: use unfiltered proof files
-s: use proof files without conclusions
--variate ( 0 | 1 ) [-l <path>] [-i <prefix>] [-o <prefix>] [-s] [-d]
Create proof files with removed (--variate 0) or added (--variate 1) conclusions from in-memory data and proof files of the other variant
-l: customize data location path ; default: "data"
-i: customize input file path prefix in data location ; default: "dProofs-withConclusions/dProofs" or "dProofs-withoutConclusions/dProofs"
-o: customize output file path prefix in data location ; default: "dProofs-withoutConclusions/dProofs" or "dProofs-withConclusions/dProofs"
-s: only use data stored in-memory
-d: print debug information
--plot [-l <path>] [-i <prefix>] [-s] [-t] [-x <limit or -1>] [-y <limit or -1>] [-o <output file>] [-d]
Print conclusion length plot data
-l: customize data location path ; default: "data"
-i: customize input file path prefix in data location ; requires files with conclusions ; default: "dProofs-withConclusions/dProofs"
-s: measure symbolic length (in contrast to conclusion representation length)
-u: include unfiltered proof files
-t: table arrangement, one data point per row
-x: upper horizontal limit
-y: upper vertical limit
-o: print to given output file
-d: print debug information
Standalone:
-m <limit> [-s]
MPI-based multi-node filtering (-m <n>) of a first unfiltered proof file (with conclusions) at ./data/[<hash>/]dProofs-withConclusions/dProofs<n>-unfiltered<n>+.txt. Creates dProofs<n>.txt.
-s: disable smooth progress mode (lowers memory requirements, but makes terrible progress predictions)
</code></pre><h4 id="examples">Examples</h4>
<pre><code>pmGenerator -g -1 -q 50
pmGenerator -g 19 -g 21 -u -r data/pmproofs-old.txt data/pmproofs-reducer.txt -d -a SD data/pmproofs-reducer.txt data/pmproofs-old.txt data/pmproofs-result-styleAll-modifiedOnly.txt -s -w -d
pmGenerator --variate 0 -l data/ -o "dProofs-withoutConclusions (all)/dProofs" -d
pmGenerator --variate 1 -s --search CNpCCNpqNp -n -d --search CNpCCNpqNp -n -s
pmGenerator --variate 1 -s --search CCNpCpqCNpCpq,CCCCppCppCCCppCppCNCCqqCqqCCCqqCqqCCqqCqqCCCppCppCNCCqqCqqCCCqqCqqCCqqCqq -n -w -d
pmGenerator --plot -s -d --plot -s -t -x 50 -y 100 -o data/plot_data_x50_y100.txt
pmGenerator -c -N -1 -n -s CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,CLpp,CLCpqCLpLq,CNLNpLNLNp --parse DD2D16DD2DD2D13DD2D1D2DD2D1D2D1DD2DD2D13D1DD2DD2D13DD2D13114DD2D13DD2D1311D3DD2DD2D13DD2D1311 -j 2 -n
pmGenerator --parse DD2D11DD2D13DD2D1DD22D11DD2D11DD2D131 -n -s -o data/CNCpNqCrCsq.txt --transform data/CNCpNqCrCsq.txt -f -n -j 1 -e --transform data/CNCpNqCrCsq.txt -f -n -t CNCpNqCrq -d
pmGenerator --unfold CpCqp=1,CCpCqrCCpqCpr=2,CCNpNqCqp=3,[0]CCpCNqNrCpCrq:D2D13,[1]Cpp:DD211,[2]NCCppNCqq:DD3DD2DD2D[0]D[0]11D1[1][1] -n -t CNNpp,NCCppNCqq
pmGenerator --transform data/m.txt -f -n -t CpCqp,CCpCqrCCpqCpr,CCNpNqCqp,Cpp,CCpqCCqrCpr,CCNppp,CpCNpq -j -1 -p -2 -d
pmGenerator -c -s CCCCC0.1CN2N3.2.4CC4.0C3.0 -g 35 --plot -s -t -x 50 -y 100 -o data/478804cd4793bc7f87041d99326aff4595662146d8a68175dda22bed/plot_data_x50_y100.txt
pmGenerator -c -n -s CCCCCpqCNrNsrtCCtpCsp --search CpCqp,CCpCqrCCpqCpr,CCNpNqCqp -n
pmGenerator --variate 1 -s --extract -t 1000 -s -d
pmGenerator --variate 1 -s --extract -# 35 -d -c -d -e 0
pmGenerator -m 17 -s
</code></pre><h4 id="multi-node-computing">Multi-node Computing</h4>
<p>For MPI-based filtering, each spawned process is multithreaded and attempts to use as many threads as the hardware specifies as concurrent. Therefore, it is ideal to spawn the same amount of processes and nodes.<br>The following exemplary <a href="https://slurm.schedmd.com/documentation.html">Slurm</a> batch script has been used via <a href="https://slurm.schedmd.com/sbatch.html">sbatch</a> in order to reduce <code>dProofs31‑unfiltered31+.txt</code> to <code>dProofs31.txt</code>.</p>
<pre><code>#!/bin/zsh
#SBATCH --job-name=pmGen-20
#SBATCH --output=output_%J.txt
#SBATCH --partition=c18m
#SBATCH --account=rwth1392
#SBATCH --time=3-00:00:00
#SBATCH --mem-per-cpu=3900M
#SBATCH --cpus-per-task=48
#SBATCH --mail-user=<email>
#SBATCH --mail-type=END,FAIL,TIME_LIMIT
## Number of nodes to use ; Also update #processes (via srun)!
#SBATCH --nodes=6
srun -n 6 ./pmGenerator -m 31
</code></pre><p>A subsequent query with <a href="https://slurm.schedmd.com/squeue.html">squeue</a> would then reveal the following information:</p>
<pre><code>$ squeue -o "%.9i %.8j %.9P %.11a %.8u %.5C %.5D %.10T %.10M %.10l %.19S %R" -u <userID>
JOBID NAME PARTITION ACCOUNT USER CPUS NODES STATE TIME TIME_LIMIT START_TIME NODELIST(REASON)
34762453 pmGen-20 c18m rwth1392 <userID> 288 6 RUNNING 3:34 3-00:00:00 2023-05-04T07:52:24 ncm[0297,0306-0307,0315,0320-0321]
</code></pre><p>You may have a look at the <a href="log/dProofs31_6node_288cpu.log">log file</a> generated by that computation.</p>
<h4 id="navigation">Navigation</h4>
<ul>
<li><a href="https://github.com/xamidi/pmGenerator/tree/c++11">C++11 branch</a> (version 1.2.0, discontinued)</li>
<li><a href="https://github.com/xamidi/pmGenerator/tree/master">C++20 branch</a></li>
</ul>
<h4 id="custom-proof-systems">Custom Proof Systems</h4>
<p>There are illustrated seven proof systems in the following which according to <a href="http://fitelson.org/walsh.pdf">M. Walsh and B. Fitelson</a> are minimal 1-bases (i.e. generators consisting of shortest single axioms) for propositional logic.
Their only remaining candidate CCCpqCCrNsCtNtCCtpCrp can be refuted since <code>pmGenerator -c -n -s CCCpqCCrNsCtNtCCtpCrp -g -1</code> produces only 9 more representatives (1.<code>D11:CCpCNpqCrCNpq</code>, 2.<code>D1D11:CCNppCqp</code>, 3.<code>D1D1D11:CCpNCpNpCqNCpNp</code>, 4.<code>DD11D11:CpCNCqCNqrCNqr</code>, 5.<code>DD11D1D11:CpCNCNqqq</code>, 6.<code>DDD11D111:CNCpCNpqCNpq</code>, 7.<code>DD11D1D1D11:CpCNCqNCqNqNCqNq</code>, 8.<code>DDD11D1D111:CNCNppp</code>, 9.<code>DDD11D1D1D111:CNCpNCpNpNCpNp</code>).<br>Therefore, these systems are implied to be the only minimal 1-bases for C-N propositional calculus.</p>
<p>Target files are distinguished using a hexadecimal SHA-512/224 digest as a folder name for each proof system.<br>For user identification of hash folders, I recommend to use custom icons, such as illustrated below.<br> <sub><img src="png/customIconPreview.png" alt="Icon-Preview" title="Hash folders with icons under Windows 7"></sub><br>For this purpose, a favicon database (<code>ico.dll</code>) is included in the release files, as well as an archive (<code>ico.7z</code>) with all the <code>.ico</code> files for usability with non-Windows operating systems.</p>
<h6 id="merediths-axiom-1-basis-cccccpqcnrnsrtcctpcsp-top1000-cardinalities-sample-info">Meredith's Axiom; 1-basis (<a href="svg/meredith.svg">CCCCCpqCNrNsrtCCtpCsp</a>) <small>[<a href="data/478804cd4793bc7f87041d99326aff4595662146d8a68175dda22bed/top1000SmallestConclusions_1to83Steps.txt">top1000</a>] [<a href="data/478804cd4793bc7f87041d99326aff4595662146d8a68175dda22bed/cardinalities.txt">cardinalities</a>] [<a href="data/m.txt">sample</a>] [<a href="data/478804cd4793bc7f87041d99326aff4595662146d8a68175dda22bed/!.def">info</a>]</small></h6>
<details open><summary>Behavioral Graph <small>[<a href="svg/plot/m-bgraph_grayscale.svg">grayscale</a>] [<a href="data/plot/m-plot_data_x200.txt">raw</a>]</small></summary>
<a href="https://xamidi.github.io/pmGenerator/svg/plot/m-bgraph.svg"><img src="svg/plot/m-bgraph.svg" width="700"></a></details>
<details open><summary>Data</summary>
<table>
<thead>
<tr>
<th>Files up to..</th>
<th style="text-align:right"> Size of Files <br>[B] </th>
<th style="text-align:right">+Costs <br>[≈core‑h]</th>
<th style="text-align:right">RAM (load)<br>[≈GiB] </th>
<th style="text-align:right">RAM (gen.)<br>[≈GiB] </th>
<th style="text-align:right">Recent <br>Growth</th>
</tr>
</thead>
<tbody>
<tr>
<td><small><a href="https://mega.nz/file/XkUgRB4J#iK3tk82M-QdI5dBJbuLgN21PFrHHKDKE9gVYdwaBvz0" title="2'422'110'008 bytes compressed into 108'455'851 bytes (ratio approx. 22.3327)">dProofs67.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">2 422 110 008</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs67_24node_1152cpu.log">5500.48</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/67.log">7.77</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L1-L9">10.00</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=996579205%2F586496233" title="size(dProofs67.txt) / size(dProofs65.txt)">1.6992...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/T501SRaY#aAB8wnSt2OEQ7WBPM_ceo44Gwu_ZY28v7g-y_xXWMAg" title="1'692'424'708 bytes compressed into 70'022'956 bytes (ratio approx. 24.1696)">dProofs69.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">4 114 534 716</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs69_72node_3456cpu.log">15432.96</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/69.log">12.79</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L11-L19">17.07</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=1692424708%2F996579205" title="size(dProofs69.txt) / size(dProofs67.txt)">1.6982...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/vgM2VQ6L#9CepsGbebmnqlSdXlgsjL4PmoU8kmcB9vJiBFDCj3XE" title="4'269'010'294 bytes compressed into 174'601'845 bytes (ratio approx. 24.4500)">dProofs71‑unfiltered71+.txt</a></small></td>
<td style="text-align:right">8 383 545 010</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs71-unfiltered71+_48cpu.log">148.71</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/71-71.log">25.06</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L21-L28">47.19</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=4269010294%2F1692424708" title="size(dProofs71-unfiltered71+.txt) / size(dProofs69.txt)">2.5224...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/HsUwiaBI#Lr9dg_vkkl5LDniDbhoajaoUf5DMrSuhOLWs7AVtsZo" title="8'690'446'595 bytes compressed into 350'352'093 bytes (ratio approx. 24.8049)">dProofs73‑unfiltered71+.txt</a></small></td>
<td style="text-align:right">17 073 991 605</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs73-unfiltered71+_48cpu.log">254.48</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/73-71.log">50.85</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L30-L37">93.84</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=8690446595%2F4269010294" title="size(dProofs73-unfiltered71+.txt) / size(dProofs71-unfiltered71+.txt)">2.0357...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/G8klVCKA#vrclPrG9dTd7JuyKt3YoBCipmOyJh5WAGXi4A4qQH00" title="15'912'038'278 bytes compressed into 627'204'237 bytes (ratio approx. 25.3698)">dProofs75‑unfiltered71+.txt</a></small></td>
<td style="text-align:right">32 986 029 883</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs75-unfiltered71+_48cpu.log">372.08</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/75-71.log">97.22</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L39-L46">172.29</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=15912038278%2F8690446595" title="size(dProofs75-unfiltered71+.txt) / size(dProofs73-unfiltered71+.txt)">1.8309...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/W00zQRSS#pgCUAfcqdq6MqqaQ5tKLn7CQ_PsclH6_WKELo_FBA4k" title="29'440'512'597 bytes compressed into 1'137'980'567 bytes (ratio approx. 25.8708)">dProofs77‑unfiltered71+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">62 426 542 480</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs77-unfiltered71+_64cpu.log">742.28</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/77-71.log">181.43</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L48-L55">304.37</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=29440512597%2F15912038278" title="size(dProofs77-unfiltered71+.txt) / size(dProofs75-unfiltered71+.txt)">1.8502...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/vNC7xWrPSneFbn7" title="56'177'510'817 bytes compressed into 2'123'231'985 bytes (ratio approx. 26.4585)">dProofs79‑unfiltered71+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">118 604 053 297</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs79-unfiltered71+_64cpu.log">1578.13</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/79-71.log">339.19</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L57-L64">550.39</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=56177510817%2F29440512597" title="size(dProofs79-unfiltered71+.txt) / size(dProofs77-unfiltered71+.txt)">1.9081...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/xiKTUrcNNECfWJ2" title="108'323'290'318 bytes compressed into 4'002'658'331 bytes (ratio approx. 27.0628)">dProofs81‑unfiltered71+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">226 927 343 615</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs81-unfiltered71+_64cpu.log">2896.16</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/81-71.log">635.64</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L66-L73">1003.84</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=108323290318%2F56177510817" title="size(dProofs81-unfiltered71+.txt) / size(dProofs79-unfiltered71+.txt)">1.9282...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/Sy4u4kFrpBvXxYP" title="207'577'506'070 bytes compressed into 7'501'303'661 bytes (ratio approx. 27.6722)">dProofs83‑unfiltered71+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">434 504 849 685</td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/dProofs83-unfiltered71+_64cpu.log">5380.80</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/utilization/83-71.log">1196.78</a></td>
<td style="text-align:right"><a href="log/custom/meredith-CCCCCpqCNrNsrtCCtpCsp/jobsRSS.txt#L75-L82">1846.46</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=207577506070%2F108323290318" title="size(dProofs83-unfiltered71+.txt) / size(dProofs81-unfiltered71+.txt)">1.9162...</a></td>
</tr>
</tbody>
</table>
</details>
<h6 id="walshs-1st-axiom-1-basis-ccpccnpqrcsccntcrtcpt-top1000-cardinalities-sample-info">Walsh's 1st Axiom; 1-basis (<a href="svg/walsh1st.svg">CCpCCNpqrCsCCNtCrtCpt</a>) <small>[<a href="data/02974777ff5f71e12ef58ccebedeef133584aad66e06a2a13b2b4b2c/top1000SmallestConclusions_1to161Steps.txt">top1000</a>] [<a href="data/02974777ff5f71e12ef58ccebedeef133584aad66e06a2a13b2b4b2c/cardinalities.txt">cardinalities</a>] [<a href="data/w1.txt">sample</a>] [<a href="data/02974777ff5f71e12ef58ccebedeef133584aad66e06a2a13b2b4b2c/!.def">info</a>]</small></h6>
<details open><summary>Behavioral Graph <small>[<a href="svg/plot/w1-bgraph_grayscale.svg">grayscale</a>] [<a href="data/plot/w1-plot_data_x400.txt">raw</a>]</small></summary>
<a href="https://xamidi.github.io/pmGenerator/svg/plot/w1-bgraph.svg"><img src="svg/plot/w1-bgraph.svg" width="700"></a></details>
<details open><summary>Data</summary>
<table>
<thead>
<tr>
<th>Files up to..</th>
<th style="text-align:right"> Size of Files <br>[B] </th>
<th style="text-align:right">+Costs <br>[≈core‑h]</th>
<th style="text-align:right">RAM (load)<br>[≈GiB] </th>
<th style="text-align:right">RAM (gen.)<br>[≈GiB] </th>
<th style="text-align:right">Recent <br>Growth</th>
</tr>
</thead>
<tbody>
<tr>
<td><small><a href="https://mega.nz/file/utFBXQoL#Om9V_K5VP65ggMDeJJ7L389oXcpFtfaBduNyzCCF_0s" title="5'371'226'962 bytes compressed into 164'113'739 bytes (ratio approx. 32.7287)">dProofs137.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">5 371 226 962</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs137_48node_2304cpu.log">6707.84</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/137.log">14.01</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L1-L9">20.56</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=1235762264%2F954016122" title="size(dProofs137.txt) / size(dProofs135.txt)">1.2953...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/u0cnxDDJ#2GZAd2TC7bDiNivMBcj6Q20ls8qOottXK-NnGM0XEMM" title="1'602'917'394 bytes compressed into 46'630'892 bytes (ratio approx. 34.3746)">dProofs139.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">6 974 144 356</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs139_72node_3456cpu.log">11663.04</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/139.log">18.06</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L11-L19">25.23</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=1602917394%2F1235762264" title="size(dProofs139.txt) / size(dProofs137.txt)">1.2971...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/L5sgkQ4J#PfkvYUDrVs-kC_e96LRCWHGulBywbLcTgDGqdrYCPLA" title="5'160'630'061 bytes compressed into 144'705'625 bytes (ratio approx. 35.6630)">dProofs141‑unfiltered141+.txt</a></small></td>
<td style="text-align:right">12 134 774 417</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs141-unfiltered141+_48cpu.log">121.87</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/141-141.log">31.18</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L21-L28">53.15</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=5160630061%2F1602917394" title="size(dProofs141-unfiltered141+.txt) / size(dProofs139.txt)">3.2195...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/v8ckRSTT#oqzUYIBn7JpCVuIWucRWnrDHd3QR8zcY3nkcAxvBqXk" title="8'473'778'240 bytes compressed into 236'694'201 bytes (ratio approx. 35.8005)">dProofs143‑unfiltered141+.txt</a></small></td>
<td style="text-align:right">20 608 552 657</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs143-unfiltered141+_48cpu.log">167.89</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/143-141.log">52.28</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L30-L37">83.02</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=8473778240%2F5160630061" title="size(dProofs143-unfiltered141+.txt) / size(dProofs141-unfiltered141+.txt)">1.6420...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/uwlhXCZL#WOjPacTW0IOP4Faw5Y5PcnQMsjEPkf36lXcMvZpgfDo" title="12'166'973'212 bytes compressed into 335'810'389 bytes (ratio approx. 36.2317)">dProofs145‑unfiltered141+.txt</a></small></td>
<td style="text-align:right">32 775 525 869</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs145-unfiltered141+_48cpu.log">281.73</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/145-141.log">82.13</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L39-L46">126.35</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=12166973212%2F8473778240" title="size(dProofs145-unfiltered141+.txt) / size(dProofs143-unfiltered141+.txt)">1.4358...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/7t0AEZBZ#yJRMROkE6QVRlg2xJx3KK2VWxN2ibSMXBrDF8VC-UQY" title="16'130'023'412 bytes compressed into 440'582'939 bytes (ratio approx. 36.6106)">dProofs147‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">48 905 549 281</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs147-unfiltered141+_64cpu.log">376.27</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/147-141.log">121.50</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L48-L55">185.33</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=16130023412%2F12166973212" title="size(dProofs147-unfiltered141+.txt) / size(dProofs145-unfiltered141+.txt)">1.3257...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/yxdCXKwL#SfnM2LGuViJ3lIQQyrXskTu6ObGZuYfOltmYTV4zqNw" title="21'575'998'815 bytes compressed into 582'486'170 bytes (ratio approx. 37.0412)">dProofs149‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">70 481 548 096</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs149-unfiltered141+_64cpu.log">564.46</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/149-141.log">173.34</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L57-L64">264.17</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=21575998815%2F16130023412" title="size(dProofs149-unfiltered141+.txt) / size(dProofs147-unfiltered141+.txt)">1.3376...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/kyJbalQmwpsBxIZ" title="29'138'591'117 bytes compressed into 779'973'708 bytes (ratio approx. 37.3584)">dProofs151‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">99 620 139 213</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs151-unfiltered141+_64cpu.log">825.12</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/151-141.log">243.11</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L66-L73">371.22</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=29138591117%2F21575998815" title="size(dProofs151-unfiltered141+.txt) / size(dProofs149-unfiltered141+.txt)">1.3505...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/n9ccdaAHt2YgyBO" title="39'867'127'446 bytes compressed into 1'058'080'615 bytes (ratio approx. 37.6787)">dProofs153‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">139 487 266 659</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs153-unfiltered141+_64cpu.log">1169.19</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/153-141.log">340.40</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L75-L82">520.65</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=39867127446%2F29138591117" title="size(dProofs153-unfiltered141+.txt) / size(dProofs151-unfiltered141+.txt)">1.3681...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/iw4tK8bBsjWldVW" title="53'770'763'259 bytes compressed into 1'413'419'788 bytes (ratio approx. 38.0430)">dProofs155‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">193 258 029 918</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs155-unfiltered141+_64cpu.log">1610.97</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/155-141.log">471.06</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L84-L91">708.37</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=53770763259%2F39867127446" title="size(dProofs155-unfiltered141+.txt) / size(dProofs153-unfiltered141+.txt)">1.3487...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/YWjWeIZ6ms6dPZf" title="73'644'408'291 bytes compressed into 1'913'276'599 bytes (ratio approx. 38.4913)">dProofs157‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">266 902 438 209</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs157-unfiltered141+_64cpu.log">2178.79</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/157-141.log">647.45</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L93-L100">965.41</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=73644408291%2F53770763259" title="size(dProofs157-unfiltered141+.txt) / size(dProofs155-unfiltered141+.txt)">1.3695...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/5gJDQbZdgszCFE7" title="98'773'762'822 bytes compressed into 2'541'220'153 bytes (ratio approx. 38.8686)">dProofs159‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">365 676 201 031</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs159-unfiltered141+_64cpu.log">3099.95</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/159-141.log">881.28</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L102-L109">1307.16</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=98773762822%2F73644408291" title="size(dProofs159-unfiltered141+.txt) / size(dProofs157-unfiltered141+.txt)">1.3412...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/JH7S80qFOdcIfT6" title="133'862'174'308 bytes compressed into 3'408'096'122 bytes (ratio approx. 39.2777)">dProofs161‑unfiltered141+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">499 538 375 339</td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/dProofs161-unfiltered141+_64cpu.log">4419.27</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/utilization/161-141.log">1198.88</a></td>
<td style="text-align:right"><a href="log/custom/walsh1-CCpCCNpqrCsCCNtCrtCpt/jobsRSS.txt#L111-L118">1789.96</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=133862174308%2F98773762822" title="size(dProofs161-unfiltered141+.txt) / size(dProofs159-unfiltered141+.txt)">1.3552...</a></td>
</tr>
</tbody>
</table>
</details>
<h6 id="walshs-2nd-axiom-1-basis-cpccqcprccnrccnstqcsr-top1000-cardinalities-sample-info">Walsh's 2nd Axiom; 1-basis (<a href="svg/walsh2nd.svg">CpCCqCprCCNrCCNstqCsr</a>) <small>[<a href="data/db25c49b13fec26ecf32e40bde65e4e2273f23b3c022cfd0fa986cff/top1000SmallestConclusions_1to43Steps.txt">top1000</a>] [<a href="data/db25c49b13fec26ecf32e40bde65e4e2273f23b3c022cfd0fa986cff/cardinalities.txt">cardinalities</a>] [<a href="data/w2.txt">sample</a>] [<a href="data/db25c49b13fec26ecf32e40bde65e4e2273f23b3c022cfd0fa986cff/!.def">info</a>]</small></h6>
<details open><summary>Behavioral Graph <small>[<a href="svg/plot/w2-bgraph_grayscale.svg">grayscale</a>] [<a href="data/plot/w2-plot_data_x6000.txt">raw</a>]</small></summary>
<a href="https://xamidi.github.io/pmGenerator/svg/plot/w2-bgraph.svg"><img src="svg/plot/w2-bgraph.svg" width="700"></a></details>
<details open><summary>Data</summary>
<table>
<thead>
<tr>
<th>Files up to..</th>
<th style="text-align:right"> Size of Files <br>[B] </th>
<th style="text-align:right">+Costs <br>[≈core‑h]</th>
<th style="text-align:right">RAM (load)<br>[≈GiB] </th>
<th style="text-align:right">RAM (gen.)<br>[≈GiB] </th>
<th style="text-align:right">Recent <br>Growth</th>
</tr>
</thead>
<tbody>
<tr>
<td><small><a href="https://mega.nz/file/qkVhAYgZ#dgBiQbhJswQegZH4-fMHtxgPgnsLIJEgi1wvUMouYAw" title="4'428'081'090 bytes compressed into 48'240'683 bytes (ratio approx. 91.7914)">dProofs35.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">4 428 081 090</td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/dProofs35_24node_1152cpu.log">1335.68</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/utilization/35.log">8.56</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/jobsRSS.txt#L1-L9">12.14</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=2972554245%2F977151740" title="size(dProofs35.txt) / size(dProofs33.txt)">3.0420...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/CptW2J5J#XkOBO_cZMSyupCdrZ8ozbDHcrQzUURpALBHbKV01VM8" title="9'046'645'168 bytes compressed into 87'167'665 bytes (ratio approx. 103.7844)">dProofs37.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">13 474 726 258</td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/dProofs37_72node_3456cpu.log">11637.12</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/utilization/37.log">26.82</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/jobsRSS.txt#L11-L19">36.16</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=9046645168%2F2972554245" title="size(dProofs37.txt) / size(dProofs35.txt)">3.0433...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/jtliXJLZ#F14xQkIYPPY9U8FDcM_N_3DRoCx8u9j4J_aIMLcoAPY" title="27'702'180'806 bytes compressed into 250'367'939 bytes (ratio approx. 110.6459)">dProofs39‑unfiltered39+.txt</a></small></td>
<td style="text-align:right">41 176 907 064</td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/dProofs39-unfiltered39+_48cpu.log">139.36</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/utilization/39-39.log">81.00</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/jobsRSS.txt#L21-L28">99.42</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=27702180806%2F9046645168" title="size(dProofs39-unfiltered39+.txt) / size(dProofs37.txt)">3.0621...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/zwkHEaBb#3zHOZVNSnnDPRFTf2WzYaZBiKmo7s8I9hp6BssrItjM" title="84'489'763'512 bytes compressed into 714'705'708 bytes (ratio approx. 118.2162)">dProofs41‑unfiltered39+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">125 666 670 576</td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/dProofs41-unfiltered39+_64cpu.log">476.43</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/utilization/41-39.log">246.33</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/jobsRSS.txt#L30-L37">291.86</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=84489763512%2F27702180806" title="size(dProofs41-unfiltered39+.txt) / size(dProofs39-unfiltered39+.txt)">3.0499...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/f1P2wTUMf3nId0g" title="257'774'107'632 bytes compressed into 2'041'458'453 bytes (ratio approx. 126.2696)">dProofs43‑unfiltered39+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">383 440 778 208</td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/dProofs43-unfiltered39+_64cpu.log">1881.40</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/utilization/43-39.log">748.02</a></td>
<td style="text-align:right"><a href="log/custom/walsh2-CpCCqCprCCNrCCNstqCsr/jobsRSS.txt#L39-L46">888.57</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=257774107632%2F84489763512" title="size(dProofs43-unfiltered39+.txt) / size(dProofs41-unfiltered39+.txt)">3.0509...</a></td>
</tr>
</tbody>
</table>
</details>
<h6 id="walshs-3rd-axiom-1-basis-cpccnqccnrscptcctqcrq-top1000-cardinalities-sample-info">Walsh's 3rd Axiom; 1-basis (<a href="svg/walsh3rd.svg">CpCCNqCCNrsCptCCtqCrq</a>) <small>[<a href="data/0df075acc552c62513b49b6ed674bfcde1c1b018e532c665be229314/top1000SmallestConclusions_1to73Steps.txt">top1000</a>] [<a href="data/0df075acc552c62513b49b6ed674bfcde1c1b018e532c665be229314/cardinalities.txt">cardinalities</a>] [<a href="data/w3.txt">sample</a>] [<a href="data/0df075acc552c62513b49b6ed674bfcde1c1b018e532c665be229314/!.def">info</a>]</small></h6>
<details open><summary>Behavioral Graph <small>[<a href="svg/plot/w3-bgraph_grayscale.svg">grayscale</a>] [<a href="data/plot/w3-plot_data_x1000.txt">raw</a>]</small></summary>
<a href="https://xamidi.github.io/pmGenerator/svg/plot/w3-bgraph.svg"><img src="svg/plot/w3-bgraph.svg" width="700"></a></details>
<details open><summary>Data</summary>
<table>
<thead>
<tr>
<th>Files up to..</th>
<th style="text-align:right"> Size of Files <br>[B] </th>
<th style="text-align:right">+Costs <br>[≈core‑h]</th>
<th style="text-align:right">RAM (load)<br>[≈GiB] </th>
<th style="text-align:right">RAM (gen.)<br>[≈GiB] </th>
<th style="text-align:right">Recent <br>Growth</th>
</tr>
</thead>
<tbody>
<tr>
<td><small><a href="https://mega.nz/file/61sCyYIb#MoxnnjaHKxvT6d4pJCbZZs3Z52ufUx9ARAc5LNJjnMk" title="4'295'581'846 bytes compressed into 77'688'599 bytes (ratio approx. 55.2923)">dProofs61.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">4 295 581 846</td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/dProofs61_72node_3456cpu.log">3908.16</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/utilization/61.log">10.14</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/jobsRSS.txt#L1-L9">13.43</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=1786902420%2F1044902840" title="size(dProofs61.txt) / size(dProofs59.txt)">1.7101...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/WkMVkQbb#YEZX-szEMXLyaZW2a37D39FoXdNiQivXXOAS7d3Nb5M" title="3'053'239'506 bytes compressed into 49'574'609 bytes (ratio approx. 61.5888)">dProofs63.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">7 348 821 352</td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/dProofs63_72node_3456cpu.log">10532.16</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/utilization/63.log">16.96</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/jobsRSS.txt#L11-L19">26.15</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=3053239506%2F1786902420" title="size(dProofs63.txt) / size(dProofs61.txt)">1.7086...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/f41EjDiS#E7prfzRMDCzTw4kXcVf-En7tOMUZ0o1X1QrZ3Utw1sU" title="9'415'171'948 bytes compressed into 159'435'383 bytes (ratio approx. 59.0532)">dProofs65‑unfiltered65+.txt</a></small></td>
<td style="text-align:right">16 763 993 300</td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/dProofs65-unfiltered65+_48cpu.log">352.47</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/utilization/65-65.log">37.46</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/jobsRSS.txt#L21-L28">59.38</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=9415171948%2F3053239506" title="size(dProofs65-unfiltered65+.txt) / size(dProofs63.txt)">3.0836...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/j8NxySjQ#1sMFi4YPBJZzDYslYKan53VPSwUGWdVt9m78hM67k4s" title="22'771'527'998 bytes compressed into 382'594'819 bytes (ratio approx. 59.5187)">dProofs67‑unfiltered65+.txt</a></small></td>
<td style="text-align:right">39 535 521 298</td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/dProofs67-unfiltered65+_48cpu.log">711.19</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/utilization/67-65.log">86.14</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/jobsRSS.txt#L30-L37">124.11</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=22771527998%2F9415171948" title="size(dProofs67-unfiltered65+.txt) / size(dProofs65-unfiltered65+.txt)">2.4185...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/mlEwBbhZ#KBH21b6120HB2zqo0Cs8OWZYfjCUoWK6AeS75BtNdgY" title="49'180'529'600 bytes compressed into 801'720'838 bytes (ratio approx. 61.3437)">dProofs69‑unfiltered65+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">88 716 050 898</td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/dProofs69-unfiltered65+_64cpu.log">1222.77</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/utilization/69-65.log">189.80</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/jobsRSS.txt#L39-L46">251.38</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=49180529600%2F22771527998" title="size(dProofs69-unfiltered65+.txt) / size(dProofs67-unfiltered65+.txt)">2.1597...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/iDMtDYEdBpHTLRz" title="103'402'476'250 bytes compressed into 1'635'136'468 bytes (ratio approx. 63.2378)">dProofs71‑unfiltered65+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">192 118 527 148</td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/dProofs71-unfiltered65+_64cpu.log">2507.20</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/utilization/71-65.log">405.23</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/jobsRSS.txt#L48-L55">524.03</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=103402476250%2F49180529600" title="size(dProofs71-unfiltered65+.txt) / size(dProofs69-unfiltered65+.txt)">2.1025...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/rrZNVCfUpai5ZQC" title="220'718'480'631 bytes compressed into 3'365'806'262 bytes (ratio approx. 65.5767)">dProofs73‑unfiltered65+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">412 837 007 779</td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/dProofs73-unfiltered65+_64cpu.log">5133.48</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/utilization/73-65.log">867.31</a></td>
<td style="text-align:right"><a href="log/custom/walsh3-CpCCNqCCNrsCptCCtqCrq/jobsRSS.txt#L57-L64">1098.91</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=220718480631%2F103402476250" title="size(dProofs73-unfiltered65+.txt) / size(dProofs71-unfiltered65+.txt)">2.1345...</a></td>
</tr>
</tbody>
</table>
</details>
<h6 id="walshs-4th-axiom-1-basis-cpccnqccnrsctqccrtcrq-top1000-cardinalities-sample-info">Walsh's 4th Axiom; 1-basis (<a href="svg/walsh4th.svg">CpCCNqCCNrsCtqCCrtCrq</a>) <small>[<a href="data/fe7117b8aad7634fae344172b9fee05f77e5e23b035276b17d8c6ec9/top1000SmallestConclusions_1to169Steps.txt">top1000</a>] [<a href="data/fe7117b8aad7634fae344172b9fee05f77e5e23b035276b17d8c6ec9/cardinalities.txt">cardinalities</a>] [<a href="data/w4.txt">sample</a>] [<a href="data/fe7117b8aad7634fae344172b9fee05f77e5e23b035276b17d8c6ec9/!.def">info</a>]</small></h6>
<details open><summary>Behavioral Graph <small>[<a href="svg/plot/w4-bgraph_grayscale.svg">grayscale</a>] [<a href="data/plot/w4-plot_data_x1250.txt">raw</a>]</small></summary>
<a href="https://xamidi.github.io/pmGenerator/svg/plot/w4-bgraph.svg"><img src="svg/plot/w4-bgraph.svg" width="700"></a></details>
<details open><summary>Data</summary>
<table>
<thead>
<tr>
<th>Files up to..</th>
<th style="text-align:right"> Size of Files <br>[B] </th>
<th style="text-align:right">+Costs <br>[≈core‑h]</th>
<th style="text-align:right">RAM (load)<br>[≈GiB] </th>
<th style="text-align:right">RAM (gen.)<br>[≈GiB] </th>
<th style="text-align:right">Recent <br>Growth</th>
</tr>
</thead>
<tbody>
<tr>
<td><small><a href="https://mega.nz/file/Wld2zSQJ#6teaby3Dz71_kEjVDGJR3DPq2aR0aERqzi9j0NKNsT0" title="9'131'925'110 bytes compressed into 182'531'802 bytes (ratio approx. 50.0292)">dProofs149.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">9 131 925 110</td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/dProofs149_24node_1152cpu.log">6302.40</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/utilization/149.log">21.12</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/jobsRSS.txt#L1-L9">36.33</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=1898469358%2F1504178093" title="size(dProofs149.txt) / size(dProofs147.txt)">1.2621...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/epNS1KJI#o546RRx4JG-pp5VxSCrp7P2ousuuy6SuLWMZ6wCB2Ok" title="2'394'008'601 bytes compressed into 43'962'661 bytes (ratio approx. 54.4555)">dProofs151.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">11 525 933 711</td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/dProofs151_72node_3456cpu.log">10297.92</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/utilization/151.log">26.43</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/jobsRSS.txt#L11-L19">45.07</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=2394008601%2F1898469358" title="size(dProofs151.txt) / size(dProofs149.txt)">1.2610...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/a9dG1TZK#ULVpQWaIMuhFkov8ozfyAscNEkSTQFeG4P8_4DUHpVU" title="13'257'500'572 bytes compressed into 259'889'811 bytes (ratio approx. 51.0120)">dProofs153‑unfiltered153+.txt</a></small></td>
<td style="text-align:right">24 783 434 283</td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/dProofs153-unfiltered153+_48cpu.log">158.55</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/utilization/153-153.log">55.60</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/jobsRSS.txt#L21-L28">86.32</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=13257500572%2F2394008601" title="size(dProofs153-unfiltered153+.txt) / size(dProofs151.txt)">5.5377...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/XxcFxSKQ#S7A_wpPAHPKUK56Sxsd6S3V8Kpxiga2VdPMVfvkqjr0" title="18'088'589'265 bytes compressed into 348'720'195 bytes (ratio approx. 51.8714)">dProofs155‑unfiltered153+.txt</a></small></td>
<td style="text-align:right">42 872 023 548</td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/dProofs155-unfiltered153+_48cpu.log">230.07</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/utilization/155-153.log"> 95.18</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/jobsRSS.txt#L30-L37">137.85</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=18088589265%2F13257500572" title="size(dProofs155-unfiltered153+.txt) / size(dProofs153-unfiltered153+.txt)">1.3644...</a></td>
</tr>
<tr>
<td><small><a href="https://mega.nz/file/zsUTEI7b#BOSxu1sy1SH8O_4ooXLauOyMgO0PoBKHff-GRu1dkOc" title="26'019'597'453 bytes compressed into 493'724'872 bytes (ratio approx. 52.7006)">dProofs157‑unfiltered153+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">68 891 621 001</td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/dProofs157-unfiltered153+_64cpu.log">302.65</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/utilization/157-153.log">151.49</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/jobsRSS.txt#L39-L46">199.75</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=26019597453%2F18088589265" title="size(dProofs157-unfiltered153+.txt) / size(dProofs155-unfiltered153+.txt)">1.4384...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/sxQG1x4rWREeGt6" title="34'641'539'688 bytes compressed into 651'219'941 bytes (ratio approx. 53.1948)">dProofs159‑unfiltered153+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">103 533 160 689</td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/dProofs159-unfiltered153+_64cpu.log">453.35</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/utilization/159-153.log">226.16</a></td>
<td style="text-align:right"><a href="log/custom/walsh4-CpCCNqCCNrsCtqCCrtCrq/jobsRSS.txt#L48-L55">293.63</a></td>
<td style="text-align:right"><a href="https://www.wolframalpha.com/input?i=34641539688%2F26019597453" title="size(dProofs159-unfiltered153+.txt) / size(dProofs157-unfiltered153+.txt)">1.3313...</a></td>
</tr>
<tr>
<td><small><a href="https://rwth-aachen.sciebo.de/s/BFnkL1fAj8Vi9Z9" title="55'681'200'733 bytes compressed into 1'040'015'069 bytes (ratio approx. 53.5388)">dProofs161‑unfiltered153+.txt</a></small><sup>✻</sup></td>
<td style="text-align:right">159 214 361 422</td>