Sindbad~EG File Manager

<?php 
require_once("TarskiTheorems.php");

// in the following,  a number represents the length of a proof,
//  and 'false'  means no proof was found.
 
$TarskiFinalResults = array(
	'Satz2.1' => 1,
	'Satz2.2' => 1,
	'Satz2.3' => 2,
	'Satz2.4' => 1,
	'Satz2.5' => 1,
	'Satz2.8' => array(3,"sos"),
	'Satz2.11' => 14,
	'Satz2.12' => 5,
	'Satz2.13' => 1,
	'Satz2.14' => 2,
	'Satz2.15' => array(13,"hints"), // can be proved from 3.1 without hints 
 
	'Satz3.1' => array(2,"sos"),  // array(4, "diagram"),   
	'Satz3.2' => 4,
	'Satz3.3' => 1,
	'Satz3.4' => 9,
	'Satz3.5a' => 4,
	'Satz3.6a' => 4, 
	'Satz3.5b' => 5, 
	'Satz3.6b' => 4,
	'Satz3.7a' => 8,   // diagram not needed
	'Satz3.7b' => 2,
	'Satz3.13a' => 1,
	'Satz3.13b' => 1,
	'Satz3.13c' => 1,
	'Satz3.14a' => 0,
	'Satz3.14b' => 3,
	'Satz3.17' =>  array(8, "diagram"),
 
	'Satz4.2' => array(44,"hints"),   // 46 by hand
	'Satz4.3' => array(4, "max_seconds = 300"),    // 256 seconds required 
	'Satz4.5' => array(24, "subformula", 60), // array(24,"hints"),   // 24 by hand // awaiting replacement with Wos's proof
	'Satz4.6' => array(11, "explicit equality axioms"),   // 10 by hand 
	'Satz4.11a' => 3,
	'Satz4.11b' => 2,
	'Satz4.11c' => 7,
	'Satz4.11d' => 2, 
	'Satz4.11e' => 2,
	'Satz4.12' => 1,
	'Satz4.12b' => 1, 
	'Satz4.13' => 16,
	'Satz4.14' => array(27, "diagram"),
	'Satz4.16' => array(25, "hints", "max_weight = 9", "max_seconds = 300"), 
	         // or array(81, "max_weight = 9" ,"max_seconds = 100000"),   
	    //  25 steps in 231 seconds  using hints, or 81 steps in 95696.25 seconds by just waiting 
	'Satz4.17' => 2,
	'Satz4.18' => 5,
	'Satz4.19' => 12,

	'Satz5.1' => array(127, "hints"),
	'Satz5.2' => 3, // less than 20 seconds
	'Satz5.3' => 15, // less than 120 seconds   
	'Satz5.5a' => 17,
	'Satz5.5b' => 8,
	'Satz5.6' => 7,
	'Satz5.7' => 1, // less than 20 seconds
	'Satz5.8' => 8,   // required more than 20 seconds 
	'Satz5.9' => array(20, "diagram"),
	'Satz5.10' => 5,
	'Satz5.11' => 1, // less than 20 seconds
	'Satz5.12a1'=> 1, // less than 20 seconds
	'Satz5.12a2'=> 2, // less than 20 seconds
	'Satz5.12b' => array(20, "subformula",227), // array(16, "hints"),  
	'NarbouxLemma1' => 4,

// Experiment 66,  Chapter 6 without diagrams, 20 seconds proves all but 6.11a and 6.16.b
// Experiment 67, with sos, 20 seconds, no result
// Experiment 68,  Chapter 6 with diagrams
// Experiment 74,  Chapter 6 with hints
// TestChapter run 9.16.15
 	'Satz6.2a' => 11,
	'Satz6.2b' => 5, 
	'Satz6.3a' => 7,
	'Satz6.3b' => 1,
	'Satz6.4a' => 13,
	'Satz6.4b' => 11,
	'Satz6.5' => 3,
	'Satz6.6' => 5,
	'Satz6.7' => 9,
	'Satz6.11a' => array(21, "diagram"),
	'Satz6.11b' => 17,
	'Satz6.13a' => 11,
	'Satz6.13b' => 1,
	'Satz6.15a' => 10,
	'Satz6.15b' => 1,
	'Satz6.15c' => 9, 
	'Satz6.15d' => 1,
	'Satz6.16a' => 8,
	'Satz6.16b' => array(29, "subformula", 1881),   // array(46, "hints"),
	'Satz6.17a' => 1,
	'Satz6.17b' => 1,
	'Satz6.18' => 19,
	'Satz6.21' => 9,
	'Satz6.25' => 3, 
	'Satz6.28' => array(21, "hints"),  // needs max_vars = 4

 
	'Satz7.2' =>  4,
	'Satz7.3a' => 2,
	'Satz7.3b' =>  2,
	'Satz7.4a' =>  2,
	'Satz7.4b' =>  19,
	'Satz7.6' => 1,  
	'Satz7.7' => 2,
	'Satz7.8' => 5,
	'Satz7.9' => 1,
	'Satz7.10a' => 3, 
	'Satz7.10b' => 4,
	'Satz7.13' =>  array(99, "subformula", 921), // array(72, "hints"),   // our proof is 77 steps
	'Satz7.15a' =>  1,
	'Satz7.15b' =>  2,   
	'Satz7.16a' => 2,
	'Satz7.16b' => 4,
	'Satz7.17' => 17,
	'Satz7.18' => 2,
	'Satz7.19' => array(7, "subformula"), // array(6, "hints"),  // our proof is 9 steps, has hints and a diagram
	'Satz7.20' => 9,
	'Satz7.21' =>  array(26, "hints"),  // our proof is 31 steps
	'Satz7.22a' => array(108, "subformula", 3189), // array(96,"hints"),  // our proof is 132 steps
	'Satz7.22b' => 12,
	'Satz7.22' =>  2,   
	'Satz7.25' =>  array(114, "hints"),  // our proof is 123 steps		
 
 //   Chapter 8 checked on 9.22.13 with max_weight 9, 120 seconds, which did not prove 8.2, 8.12a, 8.13b, 8.14c, and 8.21.
 //                    tried again with max_weight 14, 120 seconds; then 8.2, 8.12a, and 8.14c proved 
//                     tried again with max_weight 20, 120 seconds; that proved 8.21 but not 8.13b 
//                     Actually, 8.13b needs its diagram in the .prf file, so it's correct that it doesn't prove without it.
	'Satz8.2' => 5,
	'Satz8.3' => 13,
	'Satz8.4' => 3,
	'Satz8.5' => 4, 
	'Satz8.6' => 10,
	'Satz8.7' => array(23, "subformula",29), // array(23, "hints"),
	'Satz8.8' => 3,
	'Satz8.9' => 2,
	'Satz8.10' => array(30, "diagram"),  //  28 steps
	'Satz8.12a' => 10,
	'Satz8.12b' => 3,
	'Satz8.13a' => 29,
	'Satz8.13b' => array(15, "diagram"),      // 16 steps
	'Satz8.14a' => array(11, "diagram"),   
	'Satz8.14b' => array(13, "subformula", 332), // array(7, "hints"),
	'Satz8.14c' => 6,
	'Satz8.15' => 2,
	'Satz8.16a' => 5,
	'Satz8.16b' => 14,
	'Satz8.18a' => 12,
	'Satz8.18' =>  array(209, "hints", "max_seconds = 40"),  // 23 seconds
	'Satz8.20a' => array(30, "hints"), // 36 steps
	'Satz8.20b'=>  array(8, "diagram"), 
	'perp1' => array(16,"diagram"),     
	'Satz8.21a' => array(98, "hints"), // 127 steps
	'Satz8.21' => 6,
	'Satz8.22b' => array(182,"hints","max_weight = 7"), // 9.24 seconds
	'Satz8.22' => array(22,"hints"),    // 23 steps 
	'Satz8.24a' =>  array(177, "hints", "max_seconds = 60"),   // 42 seconds
	'Satz8.24b' =>  array(154, "hints", "max_seconds = 60"),   // 43 seconds
	'Satz8.24' => array(3, "diagram"),
 
// Experiment 79, Chapter 9 with no diagrams, 20 seconds, proves 9.2 only
// Experiment 80, Chapter 9 with diagrams, no results
// Experiment 82, Chapter 9 with hints, 60 seconds
// 9.18.15, TestSubformulaStrategy run with one hour per problem 
// 9.19.15,  TestChapter run with $check_only_simple, max_weight 9,  20 seconds gets 9.2 and 9.16
// 9.30.15,   9.19b requires max_weight = 7, and 9.16 requires a diagram.
 	'Satz9.2' =>  10,    
	'Satz9.3a' =>  array(25, "subformula", 46),  // array(25, "hints"),  // 27 steps
	'Satz9.3' =>   array(50, "hints"),   // 52 steps 
	'SideReflect' => array(26, "subformula", 49), //  array(26, "hints"),  //52 steps  
	'Satz9.4a' => array(40, "hints"),  
	'Satz9.4a2' => array(35, "hints"),  // 35 steps
	'Satz9.4b' => array(42,"hints"),  // 48 steps
	'Satz9.4' =>  array(9, "max_weight = 9", "max_seconds = 450"),   // 350 seconds
	'Satz9.4c' => array(41, "hints"),   // 48 steps
	'Satz9.5' => array(30, "subformula",820), // array(12, "hints"),    // 38 steps
	'Satz9.6' => array(98, "subformula", 186), // array(91, "hints"),    // 111 steps
	'Satz9.8' => array(63, "subformula", 1646), //array(48, "hints"),    // 52 steps
	'Satz9.9' => array(6, "max_weight = 8", "max_seconds = 4000"),     
	'Satz9.13' => array(65, "hints"),   
	'Satz9.16' => array(14, "max_weight = 5"), // 7 seconds 
	'Satz9.19b' => array(8, "max_weight = 7"), //  11 seconds         

	//  TestChapter run on Chapter 8A,  9.23.15 and again 9.29.15
	'ext1' => 2,
	'ExtCol2' => 2,
	'ExtPerp' =>  array(36,"hints"),    // 44 steps
	'ExtPerp2' => array(7,"diagram","max_weight = 7"),    // Takes 75 seconds with diagram and max_weight 7.   We found 3 steps  //  max_weight 8
	'ExtPerp3' => 3,       // 21 seconds.   
	'ExtPerp4' => 3,       //  
	'ExtPerp5' => 8, 
	'ExtPerp6' => 3,       // 62 seconds  

	//  TestChapter run on Chapter 9A, 9.23.15 and again 9.29.15
	'ExtSameSide1' => array(16, "hints"),  
	'ExtSameSide2'=> array(16, "hints"),   
    'Lemma9.13a' => 1,
	'Lemma9.13b' => 15,  // 69 seconds
	'Lemma9.13c' => array(11, "max_seconds = 140"),  // 120 seconds (plus or minus a fraction of a second!) 
	'Lemma9.13d' => 11,   // 68 seconds
	'Lemma9.13e' => 3,
	'Lemma9.13g' => array(22,"hints"),  
	'Lemma9.13f-case1' => array(40,"hints"),    
	'Lemma9.13f-case2' => array(42,"hints"),   
	'Lemma9.13f' => 1,    
	// Experiment 33,  Chapter 9A with diagrams, 20 seconds.  Nothing more proves.
	// Experiment 34,  Chapter 10 without diagrams, 20 seconds.  We got a bunch of 
	// bogus proofs, exposing the incorrect positive form of Satz10.2a. Ran it again:
	// 9.18.15, ran TestChapter on Chapter 10 with diagrams, but no hints, 60 seconds--no results.
	// Then tried hints, with 120 seconds. 
	// 9.19.15, started TestChapter again, messing up the input files, oops. 
	// 9.19.15, ran TestChapter with hints on, only proved 10.4. 
	// 9.22.15  TestChapter ran successfully
	// 9.29.15, TestChapter failed to prove 10.7 and 10.8a as well as 10.2b, but 
	//          that's because those need special settings that weren't in the code.
 
	'Satz10.2a' =>array(45, "hints"),   
	'Satz10.2b' => array(49, "hints"),   
	'Satz10.4' => array(17, "hints"),   
	'Satz10.5' => 4,
	'Satz10.6' => 6,
	'Satz10.7' => array(3, "max_weight = 15", "ratio = 1"),  	               
	'Satz10.8a' => 5,   // or  array(3, "hints"),     
	'Satz10.8a' => array(3, "max_weight = 15", "ratio = 1"),   //  same settings also worked here
	'Satz10.8b' => 3,
	'Satz10.10a' => array(13, "hints"),    // 33 steps
	'Satz10.10' => array(72, "hints"),     // 92 steps
	'Satz10.12b' => array(91, "hints", "max_weight = 8"),   // 100 steps, but using illegal demodulators
	'Satz10.12c' => 18,      // 11 steps, after using the steps of this one as hints
	'Satz10.12a' => array(60, "hints"),    // 71 steps
	'Satz10.12' => array(26, "hints"),    // 26 steps
	'Satz10.14' => array(10, "diagram", "max_weight = 10"),   
	'Satz10.15' => array(74, "hints"),    // 78 steps 
	'Satz10.16a' => array(44, "hints"),    // 58 steps
	'Satz10.16b' => array(56, "hints"),    // 87 steps
 

	// TestChapter run 9.30.15
	'Satz11.3a' => array(43, "hints", "max_seconds = 200"),   
	'Satz11.3d' => array(6, "hints"),    
	'Satz11.4b' => array(37, "hints"),  
	'Satz11.4' => array(39,"hints"),     
	'Satz11.4d' => 6,
	'Satz11.6' => 1,  
	'Satz11.7' => array(8, "hints", 8, "diagram", "max_seconds = 1700"),
	'Satz11.8' => array(34, "hints"),
	'Satz11.9' => 1,
	'Satz11.15a' => array(78, "hints"),  
	'Satz11.15b' =>array(51, "hints"),    // 18 seconds, max_vars = 4 required
	'Satz11.49a' =>array(5, "hints"),     
	'Satz11.49b' => array(15, "hints"),
	 
	// TestChapter run 9.28.15
	'ExtParallel' => array(24,"hints"), 
	'Satz12.6' => array(16,"hints"),  // max_weight 6 is enough      
	'Lemma12.11-case1' => array(8, "hints"),  
	'Lemma12.11-case2' => array(32, "hints", "max_seconds = 1200"),  // 763 with max_vars 3 and pick_given 2, 827 with max_vars 4 and pick_given 4 and max_weight 8
	'Lemma12.11' => array(16, "hints", "max_seconds = 400"),   // proved by the two preceding cases
	'Satz12.11-case1' => array(49, "hints", "max_seconds = 600"),  // 301 seconds required
	'Satz12.11-case2' => array(56, "hints", "max_seconds = 1200"),
	'Satz12.11' => false  // not yet proved.
 
);


?>