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testdrive.php
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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>TGP testdrive</title>
<link href="https://fonts.googleapis.com/css?family=M+PLUS+1p:400,500&display=swap" rel="stylesheet">
<link rel="stylesheet" href="style.css" type="text/css">
<?php
$scripts = array("array", "formula", "parser", "prover", "equality", "modelfinder", "sentree", "painter");
if (isset($_GET['debug'])) {
foreach ($scripts as $script) {
print "<script type='text/javascript' src='$script.debug.js?".time()."'></script>\n";
}
?>
<script>
function log(str) {
if (!self.debugWin) debugPopup();
debugWin.document.write("<pre>"+str+"</pre>");
}
function debugPopup() {
self.debugWin = self.open("about:blank","debugWin");
if (!self.debugWin) alert("unblock popups!");
}
log("hello, this is the debugging window");
</script>
<?php
}
else {
$allscripts = implode("-", $scripts);
print "<script type='text/javascript' src='$allscripts.js'></script>\n";
}
?>
</head>
<body id="testdrive" style="margin:10px 50px;">
<h2>Tree Proof Generator Test Drive</h2>
<h3>Valid Cases</h3>
<table style="max-width:1200px;">
<tr><th>Label</th><th>Input</th><th>Time</th><th>Steps</th><th>Nodes</th></tr>
<?php
$valid_tests = [
['simp', '(p∨(q∧r))→((p∨q)∧(p∨r))'],
['merg', '¬((p∧¬(p→p))∨¬(p→p))'],
['fun', '∀ x F(x) → Ff(a)'],
['func', '¬(Pa∧¬Pf(f(a))∧∀x(Px→Pf(x)))'],
['bost2nnf', '¬(∀x(f(x)∧g(a)∨¬f(x)∧¬g(a)) ∧ ∀y∀z(f(b)∧¬g(y)∨g(z)∧¬f(b)) ∨ ∀w(f(d)∧¬g(w)∨¬f(d)∧g(w)) ∧ ∀s((¬f(s)∨g(e)) ∧ (¬g(k)∨f(s))))'],
['t5', '∃x(P∧Fx)↔P∧∃xFx'],
['t6', '∀x∃y(Fx↔Gy)→∃y∃z∀x((Fx→Gy)∧(Gz→Fx))'],
['t7', '∃y∃z∀x((Fx→Gy)∧(Gz→Fx))→∀x∃y(Fx↔Gy)'],
['t8', '∀x(Fx→Ff(x))∧Ff(a)→Ff(f(f(a)))'],
['t9', '∀x(Fx→Ff(x))∧Ff(g(f(a),b))→Ff(f(f(g(f(a),b))))'],
['ddelta', '¬∀x(Fx∧∃y¬Fy)'],
['b162.2', '∀y∃x(Fx∧Gy)→∃x∀y(Fx∧Gy)'],
['b164.1', '∃x(Fx→∀xFx)'],
['b164.k', '∀x∃y(Fx↔Gy)↔∃y∀x(Fx→Gy)∧∃y∀x(Gy→Fx)'],
['b164.l', '∀x∃y(Fx↔Gy)↔∃y∃z∀x((Fx→Gy)∧(Gz→Fx))'],
['conpos', '∀y(Iy→∀x(Px↔Cxy))∧∃yIy→∀x(Px↔∀y(Iy→Cxy))'],
['carnap', '(∃xFx→Fw)∧(¬∃xFx∧∃xGx→Gw)↔(∃x(Fx∨(¬∃yFy∧Gx))→(Fw∨(¬∃yFy∧Gw)))'],
['fd1eaff', 'Ac, ∀x(Ax→Tx), ∀x(Mx→¬Tx), Mb, ∀xIxx, ∀x∀y(Ixy→Iyx), ∀x∀y(Ixy→(Ax→Ay)), ∀x∀y(Ixy→(Mx→My)), ∀x∀y(Ixy→(Tx→Ty)) |= ¬Ibc'],
['id1', 'c=b ∧ Fc → Fb'],
['id2', 'a=b ∧ b=c ∧ Paa → Pcc'],
['id3', '∀x∀y(f(x)=f(y)→x=y), f(a)=k, f(b)=k |= a=b'],
['id4', '∀x∀y(f(x)=f(y)→x=y), ∀x∃y(Ryx∧f(y)=k) |= ∃y∀xRyx'],
['beckert97a', '∀x(g(x)=f(x) ∨ ¬(x=a)) ∧ ∀x(g(f(x))=x) ∧ b=c ∧ Pg(g(a))b → Pac'],
['beckert98ex4', '∀x(g(x)=f(x) ∨ ¬(x=a)) ∧ ∀x(f(x)=x) ∧ Pg(a)f(b) → Pab'],
['dv98ex1.1', '∃x∃y∃u∃v((a = b → g(x, u, v) = g(y, f(c), f(d))) ∧ (c = d → g(u, x, y) = g(v, f(a), f(b))))'],
['franssen08fibo', '∀xp(x, z) = x ∧ ∀x∀yp(x,y) = p(y,x) ∧ f(z) = z ∧ f(s(z)) = s(z) ∧ ∀yf(s(s(y))) = p(f(y), f(s(y))) → f(s(s(z))) = s(z)'],
['multiinst', '(∀x(P(x)→P(f(x)))) ∧ P(d)→P(f(f(f(d))))'],
['tseitin', '((∃x∀y(Px↔Py)↔(∃zQz↔∀wQw))↔(∃x2∀x3(Qx2↔Qx3)↔(∃x4Px4↔∀x5Px5)))'],
['pel1', '((p→q)↔(¬q→¬p))'],
['pel2', '(¬¬p↔p)'],
['pel3', '(¬(p→q)→(q→p))'],
['pel4', '((¬p→q)↔(¬q→p))'],
['pel5', '(((p∨q)→(p∨r))→(p∨(q→r)))'],
['pel6', '(p∨¬p)'],
['pel7', '(p∨¬(¬(¬p)))'],
['pel8', '(((p→q)→p)→p)'],
['pel9', '((((p∨q)∧(¬p∨q))∧(p∨¬q)) → ¬(¬p∨¬q))'],
['pel10', '¬(¬(p↔q)∧(q→r) ∧(r→(p∧q))∧(p→(q∨r)))'],
['pel11', '(p↔p)'],
['pel12', '(((p↔q)↔r) ↔ (p↔(q↔r)))'],
['pel13', '((p∨(q∧r))↔((p∨q)∧(p∨r)))'],
['pel14', '((p↔q)↔((q∨¬p)∧(¬q∨p)))'],
['pel15', '((p→q)↔(¬p∨q))'],
['pel16', '((p→q)∨(q→p))'],
['pel17', '(((p∧(q→r))→s) ↔ (((¬p∨q)∨s)∧((¬p∨¬r)∨s)))'],
['pel18', '∃y∀x(Fy→Fx)'],
['pel19', '∃x∀y∀z((Py→Qz)→(Px→Qx))'],
['pel20', '(∀x∀y∃z∀w((Px∧Qy)→(Rz∧Sw)) → ∃x1∃y1((Px1∧Qy1)→∃z1(Rz1)))'],
['pel21', '¬(¬∃x(P↔Fx) ∧∃x1(P→Fx1)∧∃x2(Fx2→P))'],
['pel22', '∀x(P↔Fx)→(P↔∀yFy)'],
['pel23', '∀x(P∨Fx)↔(P∨∀yFy)'],
['pel24', '¬(¬∃x(Px∧Rx) ∧ ¬∃y(Sy∧Qy) ∧ ∀v(Pv→(Qv∨Rv)) ∧ (¬∃yPy→∃zQz) ∧ ∀w((Qw∨Rw)→Sw))'],
['pel25', '¬(¬∃x(Qx∧Px) ∧ ∃yPy ∧ ∀y(Fy→(¬Gy∧Ry)) ∧ ∀y(Py→(Gy∧Fy)) ∧ (∀y(Py→Qy)∨∃z(Pz∧Rz)))'],
['pel26', '¬(¬(∀x(Px→Rx)↔∀y(Qy→Sy)) ∧ (∃zPz↔∃zQz) ∧ ∀x∀y((Px∧Qy)→(Rx↔Sy)))'],
['pel26nnf', '¬(((q(a)∧ ¬s(a))∧ ∀x(¬p(x)∨r(x))∨ (p(b)∧ ¬r(b))∧ ∀y(¬q(y)∨s(y)))∧ (p(c)∧ q(d)∨∀z¬p(z)∧ ∀w¬q(w))∧ ∀v∀w((¬p(v)∨¬q(w))∨r(v)∧ s(w)∨¬r(v)∧ ¬s(w)))'],
['pel27', '¬(¬∀x (J(x) → ¬I(x)) ∧ ∃y (F(y) ∧ ¬G(y)) ∧ ∀z (F(z) → H(z)) ∧ ∀w ((J(w) ∧ I(w)) → F(w)) ∧ (∃x2 (H(x2) ∧ ¬G(x2)) → ∀x3 (I(x3) → ¬H(x3))))'],
['pel28', '¬(¬∀x ((P(x) ∧ F(x)) → G(x)) ∧ ∀y (P(y) → ∀z (Q(z))) ∧ (∀w (Q(w) ∨ R(w)) → ∃x2 (Q(x2) ∧ S(x2))) ∧ (∃x3 (S(x3)) → ∀x4 (F(x4) → G(x4))))'],
['pel29', '¬(¬((∀x (F(x) → H(x)) ∧ ∀y (G(y) → J(y))) ↔ ∀z ∀w ((F(z) ∧ G(w)) → (H(z) ∧ J(w)))) ∧ (∃x2 (F(x2)) ∧ ∃x3 (G(x3))))'],
['pel30', '¬(¬∀x (I(x)) ∧ ∀y ((F(y) ∨ G(y)) → ¬H(y)) ∧ ∀z ((G(z) → ¬I(z)) → (F(z) ∧ H(z))))'],
['pel31', '¬(¬∃x (I(x) ∧ J(x)) ∧ ¬∃y (F(y) ∧ (G(y) ∨ H(y))) ∧ ∃z (I(z) ∧ F(z)) ∧ ∀w (¬H(w) → J(w)))'],
['pel32', '¬(¬∀x ((F(x) ∧ K(x)) → J(x)) ∧ ∀y ((F(y) ∧ (G(y) ∨ H(y))) → I(y)) ∧ ∀z ((I(z) ∧ H(z)) → J(z)) ∧ ∀w (K(w) → H(w)))'],
['pel33', '∀x ((P(a) ∧ (P(x) → P(b))) → P(c)) ↔ ∀y ((¬P(a) ∨ (P(y) ∨ P(c))) ∧ (¬P(a) ∨ (¬P(b) ∨ P(c))))'],
['pel34', '(∃x ∀y (P(x) ↔ P(y)) ↔ (∃z (Q(z)) ↔ ∀w (Q(w)))) ↔ (∃x2 ∀x3 (Q(x2) ↔ Q(x3)) ↔ (∃x4 (P(x4)) ↔ ∀x5 (P(x5))))'],
['pel35', '∃x ∃y (P(x,y) → ∀z ∀w (P(z,w)))'],
['pel36', '¬(¬∀x ∃y (H(x,y)) ∧ ∀z ∃w (F(z,w)) ∧ ∀x2 ∃x3 (G(x2,x3)) ∧ ∀x4 ∀x5 ((F(x4,x5) ∨ G(x4,x5)) → ∀x6 ((F(x5,x6) ∨ G(x5,x6)) → H(x4,x6))))'],
['pel37', '¬(¬∀x ∃y (R(x,y)) ∧ ∀z ∃w ∀x2 ∃x3 (P(x2,z) → ((P(x3,w) ∧ P(x3,z)) ∧ (P(x3,w) → ∃x4 (Q(x4,w))))) ∧ ∀x5 ∀x6 (¬P(x5,x6) →∃x7 (Q(x7,x6))) ∧ (∃x8 ∃x9 (Q(x8,x9)) → ∀y1 (R(y1,y1))))'],
['pel38', '∀x ((P(a) ∧ (P(x) → ∃y (P(y) ∧ R(x,y)))) → ∃z ∃w ((P(z) ∧ R(x,w)) ∧ R(w,z))) ↔ ∀x2 ((((¬P(a)) ∨ P(x2)) ∨ ∃x3 ∃x4 ((P(x3) ∧ R(x2,x4)) ∧ R(x4,x3))) ∧ (((¬P(a)) ∨ (¬∃x5 (P(x5) ∧ R(x2,x5)))) ∨ ∃x6 ∃x7 ((P(x6) ∧ R(x2,x7)) ∧ R(x7,x6))))'],
['pel39', '¬∃x ∀y (F(y,x) ↔ ¬F(y,y))'],
['pel40', '∃x ∀y (F(y,x) ↔ F(y,y)) → ¬∀z ∃w ∀x2 (F(x2,w) ↔ ¬F(x2,z))'],
['pel43', '∀x∀y(Qxy ↔ ∀z(Fzx ↔ Fzy)) |= ∀x∀y(Qxy ↔ Qyx)'],
['pel48', '(a=b ∨ c=d) ∧ (a=c ∨ b=d) → (a=d ∨ b=c)'],
['pel49', '∃x∃y∀z(z=x ∨ z=y) ∧ Pa ∧ Pb ∧ ¬(a=b) → ∀xPx'],
['pel51', '∃z∃w∀x∀y(Fxy ↔ (x=z ∧ y=w)) |= ∃z∀x(∃w∀y(Fxy ↔ y=w) ↔ x=z)'],
['pel52', '∃z∃w∀x∀y(Fxy ↔ (x=z ∧ y=w)) |= ∃w∀y(∃z∀x(Fxy ↔ x=z) ↔ y=w)'],
['pel55', '∃x(Lx ∧ Kxa), La ∧ Lb ∧ Lc, ∀x∀y(Kxy → Hxy), ∀x∀y(Kxy → ¬ Rxy), ∀x (Hax → ¬ Hcx), ∀x(¬x=b → Hax), ∀x(¬ Rxa → Hbx), ∀x(Hax → Hbx), ∀x(Lx → (x=a ∨ x=b ∨ x=c)), ∀x∃y(¬Hxy), ¬(a=b) |= Kaa'],
['pel56', '∀x(∃y(Fy ∧ x=f(y)) →Fx) ↔ ∀x(Fx → Ff(x))'],
['pel57', 'Ff(a,b)f(b,c), Ff(b,c)f(a,c), ∀x∀y∀z(Fxy ∧ Fyz → Fxz) |= Ff(a,b)f(a,c)'],
['pel58', '∀x∀yf(x)=g(y) |= ∀x∀yf(f(x))=f(g(y))'],
['pel59', '∀x(P(x) ↔ ¬P(f(x))) → ∃x(P(x) ∧ ¬P(f(x)))'],
['pel61', '∀x∀y∀zf(x,f(y,z))=f(f(x,y),z) |= ∀x∀y∀z∀wf(x,f(y,f(z,w)))=f(f(f(x,y),z),w)'],
['rel1', '(∀x∃yCxy∧∀x∀y(Cxy→Cyx)∧∀x∀y∀z((Cxy∧Cyz)→Cxz)) → ∀xCxx'],
['issue23a', '∀x∀y∃z∀v(Evz ↔ (Ivx ∨ Ivy)) → ∀y∃z∀v(Evz ↔ Ivy)'],
['issue23b', '∀x∀y∃z∀v(Evz ↔ (v=x ∨ v=y)) → ∀y∃z∀v(Evz ↔ v=y)'],
['issue23c', '∀x∀y∃z∀v(Evz ↔ (v=x ∨ v=y)) → ∀y∃z∀v(Evz ↔ (v=y ∨ v=y))'],
['mod1', '(□p ∧ ◇q)→◇(p∧q)'],
['mod2', '◇(p ∨ q)↔(◇p ∨ ◇q)'],
['s5', 'p→◇p||universality'],
['narrow_D', '(p→□r)→((p∧q)→□r)||seriality'],
['BFCBF', '∀x□Fx ↔ □∀xFx'],
['BFCBF2', '∀x□□∀y□□Fxy ↔ □∀y□∀x□□Fxy'],
['ex5.3', '□(N → (s → p)) ∧ N |= □(N → (s → (□(N → (s → p)) ∧ N))) ∧ N||universality'],
['ex10.2d', '□◇∃xFx → □∃x◇(Fx ∨ Gx)'],
['nni', '∀x∀y(¬x=y ↔ □¬x=y)||reflexivity'],
['emil_S5', '◇□A→(◇□B→◇□(A∧B))||reflexivity|symmetry|transitivity'],
['withee', '□∀x□∀y(□Fx∨□Gy)→(□∀x□Fx∨□∀x□Gx)||reflexivity|transitivity'],
['witheeKon', '(□∀x□Fx∨□∀x□Gx) → □∀x□∀y(□Fx∨□Gy)||reflexivity|transitivity'],
['04vsG0_S4', '((A ∧ ¬□A)→□¬□A) ∧ ((¬A ∧ ◇A) →□◇A) → (◇□A→□◇A)||reflexivity|transitivity'],
['pel54', '∀y∃z∀x(Fxz ↔ x=y) |= ¬∃w∀x(Fxw ↔ ∀u(Fxu → ∃y(Fyu ∧ ¬∃z(Fzu ∧ Fzy))))'],
['beckert97bid','∀x(i(u,x)=x) ∧ ∀x∀y∀z(i(i(x,y),i(i(y,z),i(x,z)))=u) ∧ ∀x∀y(i(i(x,y),y) = i(i(y,x),x)) → ∀x∀y∀z∃w(i(x,w)=u ∧ w=i(y,i(z,y)))']
];
foreach ($valid_tests as $test) {
print("<tr><td><a href='./#$test[1]'>$test[0]</a> (<a href='./?debug=1#$test[1]'>d</a>)</td><td class='formula valid'>$test[1]</td><td></td><td></td><td></td></tr>\n");
}
?>
</table>
<h3>Invalid Cases</h3>
<table>
<tr><th>Label</th><th>Input</th><th>Time</th><th>Steps</th><th>Nodes</th></tr>
<?php
$invalid_tests = [
['i1', 'p'],
['i2', '((p→q)↔(q→p))'],
['i3', '∀xFx'],
['i4', '∃xFx'],
['i5', '∀x∃yRxy'],
['i6', '∃y∀xFxy'],
['ifun', '∀x∃y (Fx → Ff(y)) → (¬Fa ∨ Ff(a))'],
['Her', '¬∀x((Fx ∧ ¬Fa)∨ Ga)'],
['bost1', '∀x∀y∀z(Fxy∧Fyz→Fxz) ∧ ∀x∀y(Fxy→Fyx) ∧ ∃x∃yFxy → ∀xFxx'],
['2ind', '¬∃x∃y(Fx∧¬Fy)'],
['3ind', '¬∀y∃x(Ryx ∧ ¬Rxy)'],
['4indsimp', '¬(Fa ∧ Ga ∧ Fb ∧ ¬Gb ∧ ¬Fc ∧ Gc ∧ ¬Fd ∧ ¬Gd)'],
['4ind', '∀z∀y∃x(Rzx ∧ ¬Rxy)'],
['bx', '∀y∃xFxy→∃x∀yFxy'],
['bn', '∃y∃z∀x((Fx→Gy)∧(Gz→Fx))→∀x∃y(Fy↔Gy)'],
['conpos1', '∀y(Iy→∀x(Px↔Cxy))→∀x(Px↔∀y(Iy→Cxy))'],
['conpos2', '∀x(Px↔∀y(Iy→Cxy))→∀y(Iy→∀x(Px↔Cxy))'],
['pel48s', '(a=b ∨ c=d) ∧ (a=c ∨ b=d) → a=d'],
['T_in_K', 'p→◇p'],
['emil_in_K4', '◇□A → (◇□B → ◇□(A ∧ B))||transitivity'],
['T_in_K', 'p→◇p'],
['parsercopy', 'p → ◇□p↔□◇□p'],
['04vsG0_K4', '((A ∧ ¬□A)→□¬□A) ∧ ((¬A ∧ ◇A) →□◇A) → (◇□A→□◇A)||transitivity'],
['redinexD', '◇(p→□◇p)||seriality'],
['boxreds4', '◇□p↔□◇□p||reflexivity|transitivity'],
['github16', '((∃x(◇(Ox∧Px)∧□(Ox→Mx)))∧(∀x(◇(Ox∧Mx)→□(Ox→Sx))∧◇∃x(Ox∧Mx)))→(∃x((Ox∧Sx)∧◇(Ox∧Px)))'],
['withee_K4', '□∀x□∀y(□Fx∨□Gy)→(□∀x□Fx∨□∀x□Gx)||transitivity'],
['7ind', '¬∀z∀y∃x¬((Rxy → Ryx) ∨ Rzx)'],
['infinity', '¬(∀x∃yFxy ∧ ∀x∀y∀z(Fxy∧Fyz→Fxz) ∧ ∀x¬Fxx)'],
];
// $invalid_tests = [];
foreach ($invalid_tests as $test) {
print("<tr><td><a href='./#$test[1]'>$test[0]</a> (<a href='./?debug=1#$test[1]'>d</a>)</td><td class='formula invalid'>$test[1]</td><td></td><td></td><td></td></tr>\n");
}
?>
</table>
<script type="text/javascript">
var tests = [];
document.querySelectorAll('.formula').forEach(function(td) {
var formula = td.innerHTML;
td.onclick = function(e) {
prove(td.innerHTML, td.parentNode, td.className.indexOf('invalid')==-1);
}
tests.push(td.onclick);
});
var prover;
var stopTimer;
var provingAll;
function prove(fla, tableRow, isValid) {
var parser = new Parser();
var accessibilityConstraints = null;
if (fla.indexOf('||') > 0) {
accessibilityConstraints = fla.split('||')[1].split('|');
fla = fla.split('||')[0];
}
console.log('testing '+fla);
var parsedInput = parser.parseInput(fla);
var premises = parsedInput[0];
var conclusion = parsedInput[1];
var initFormulas = premises.concat([conclusion.negate()]);
var startTime = performance.now();
prover = new Prover(initFormulas, parser, accessibilityConstraints);
prover.onfinished = function(status) {
var endTime = performance.now();
console.log('done with '+fla);
var calcTime = Math.round(endTime - startTime);
var timeTd = tableRow.childNodes[2];
var stepsTd = tableRow.childNodes[3];
var nodesTd = tableRow.childNodes[4];
if (status != isValid) {
timeTd.innerHTML = "<b>wrongly found "+(status ? "valid" : "invalid")+"!</b>";
}
else {
timeTd.innerHTML = calcTime;
stepsTd.innerHTML = prover.step;
}
if (status) {
nodesTd.innerHTML = new SenTree(prover.tree, parser).nodes.length;
}
if (provingAll) {
// console.log('clearing timer '+stopTimer);
clearTimeout(stopTimer);
setTimeout('proveNext()', 100);
}
};
prover.start();
}
var index;
var timeLimit;
function proveAll(tLimit) {
index = 0;
provingAll = true;
timeLimit = tLimit;
proveNext();
}
function proveNext() {
if (index >= tests.length) {
provingAll = false;
return;
}
console.log('launching test '+self.index);
stopTimer = setTimeout(function() {
console.log('aborting test');
prover.stop();
proveNext();
}, timeLimit);
tests[index]();
index++;
}
</script>
<br><br><br><br>
<div style="position:fixed; bottom:0; left:0; padding:10px; width:100%; background-color:#ccc">
<form action="#" method="get" style="display:inline">
<input type="button" onclick="proveAll(this.form.l.value)" value="run all tests">
Limit <input type="text" size="7" name="l" value="5000"> ms/test
</form>
</div>
</body>
</html>