# Formulas in predicate logic/3 places
## List

list :
| example sentence | formula | pairs | | coord | var | bin | rank |
| Someone wants that someone loves someone. | ∃x ∃y ∃z Pxyz e123 | 777 | 777 | 444 | 3 | 111 | 6 |
| For everyone there is someone who wants them to be loved by someone. | ∀z ∃x ∃y Pxyz a3 e12 | 733 | 337 | 442 | 3 | 110 | 5 |
| For everyone there is someone who wants them to love someone. | ∀y ∃x ∃z Pxyz a2 e13 | 376 | 673 | 424 | 3 | 101 | 5 |
| Everyone wants someone to love someone. | ∀x ∃y ∃z Pxyz a1 e23 | 667 | 766 | 244 | 3 | 011 | 5 |
| There is a y for which for every z exists an x that wants y to love z. There is someone so that for every other person exists someone who wants them to love that other person. | ∃y ∀z ∃x Pxyz e2 a3 e1 | 731 | 137 | 431 | 3 | 110 | 4 |
| There is someone who wants that everyone is loved by someone. | ∃x ∀z ∃y Pxyz e1 a3 e2 | 713 | 317 | 341 | 3 | 110 | 4 |
| There is a z for which for every y exists an x that wants y to love z. There is someone so that for every other person exists someone who wants them to be loved by that other person. | ∃z ∀y ∃x Pxyz e3 a2 e1 | 374 | 473 | 413 | 3 | 101 | 4 |
| Someone wants everyone to love someone. | ∃x ∀y ∃z Pxyz e1 a2 e3 | 176 | 671 | 314 | 3 | 101 | 4 |
| There is someone whom everyone wishes to be loved by someone. | ∃z ∀x ∃y Pxyz e3 a1 e2 | 647 | 746 | 143 | 3 | 011 | 4 |
| There is someone whom everyone wishes to love someone. | ∃y ∀x ∃z Pxyz e2 a1 e3 | 467 | 764 | 134 | 3 | 011 | 4 |
| Someone wishes someone to love everyone. | ∃x ∃y ∀z Pxyz e12 a3 | 711 | 117 | 330 | 3 | 110 | 3 |
| Someone wishes someone to be loved by everyone. | ∃x ∃z ∀y Pxyz e13 a2 | 174 | 471 | 303 | 3 | 101 | 3 |
| There are y and z, and every x wants that y loves z. There are two people, and everyone wants one of them to love the other one. | ∃y ∃z ∀x Pxyz e23 a1 | 447 | 744 | 033 | 3 | 011 | 3 |
| For every pair of people (y, z) there is some person x who wants y to love z. For every two people a and b there is someone who wants a to love b and someone who wants b to love a. | ∀y ∀z ∃x Pxyz a23 e1 | 330 | 033 | 411 | 3 | 100 | 3 |
| Everyone wants everyone to be loved by someone. | ∀x ∀z ∃y Pxyz a13 e2 | 603 | 306 | 141 | 3 | 010 | 3 |
| Everyone wants everyone to love someone. | ∀x ∀y ∃z Pxyz a12 e3 | 066 | 660 | 114 | 3 | 001 | 3 |
| For everyone there is someone who wants them to love everyone. | ∀y ∃x ∀z Pxyz a2 e1 a3 | 310 | 013 | 310 | 3 | 100 | 2 |
| For everyone there is someone who wants them to be loved by everyone. | ∀z ∃x ∀y Pxyz a3 e1 a2 | 130 | 031 | 301 | 3 | 100 | 2 |
| Everyone wishes someone to love everyone. | ∀x ∃y ∀z Pxyz a1 e2 a3 | 601 | 106 | 130 | 3 | 010 | 2 |
| For everyone there is someone whom everyone wants to love them. | ∀z ∃y ∀x Pxyz a3 e2 a1 | 403 | 304 | 031 | 3 | 010 | 2 |
| Everyone wishes someone to be loved by everyone. | ∀x ∃z ∀y Pxyz a1 e3 a2 | 064 | 460 | 103 | 3 | 001 | 2 |
| For everyone there is someone whom everyone wants them to love. | ∀y ∃z ∀x Pxyz a2 e3 a1 | 046 | 640 | 013 | 3 | 001 | 2 |
| Someone wants that everyone loves everyone. | ∃x ∀y ∀z Pxyz e1 a23 | 110 | 011 | 200 | 3 | 100 | 1 |
| There is someone whom everyone wishes to love everyone. | ∃y ∀x ∀z Pxyz e2 a13 | 401 | 104 | 020 | 3 | 010 | 1 |
| There is someone whom everyone wishes to be loved by everyone. | ∃z ∀x ∀y Pxyz e3 a12 | 044 | 440 | 002 | 3 | 001 | 1 |
| Everyone wants everyone to love everyone. | ∀x ∀y ∀z Pxyz a123 | 000 | 000 | 000 | 3 | 000 | 0 |
| Someone wants to love someone. | ∃x ∃y Pxxy e(12)3 | 577 | 775 | 334 | 2 | 111 | 5 |
| For everyone there is someone who wants to love them. | ∀y ∃x Pxxy a3 e(12) | 533 | 335 | 332 | 2 | 110 | 4 |
| Everyone wants to love someone. | ∀x ∃y Pxxy a(12) e3 | 266 | 662 | 224 | 2 | 001 | 4 |
| Someone wants to love everyone. | ∃x ∀y Pxxy e(12) a3 | 511 | 115 | 220 | 2 | 110 | 2 |
| There is someone whom everyone wants to love. | ∃y ∀x Pxxy e3 a(12) | 244 | 442 | 112 | 2 | 001 | 2 |
| Everyone wants to love everyone. | ∀x ∀y Pxxy a(12)3 | 200 | 002 | 110 | 2 | 000 | 1 |
| Someone wants to be loved by someone. | ∃x ∃y Pxyx e(13)2 | 757 | 757 | 343 | 2 | 111 | 5 |
| For everyone there is someone who wants to be loved by them. | ∀y ∃x Pxyx a2 e(13) | 356 | 653 | 323 | 2 | 101 | 4 |
| Everyone wants to be loved by someone. | ∀x ∃y Pxyx a(13) e2 | 623 | 326 | 242 | 2 | 010 | 4 |
| Someone wants to be loved by everyone. | ∃x ∀y Pxyx e(13) a2 | 154 | 451 | 202 | 2 | 101 | 2 |
| There is someone by whom everyone wants to be loved. | ∃y ∀x Pxyx e2 a(13) | 421 | 124 | 121 | 2 | 010 | 2 |
| Everyone wants to be loved by everyone. | ∀x ∀y Pxyx a(13)2 | 020 | 020 | 101 | 2 | 000 | 1 |
| Someone wishes someone to love themselves. | ∃x ∃y Pxyy e1(23) | 775 | 577 | 433 | 2 | 111 | 5 |
| Everyone wishes someone to love themselves. | ∀x ∃y Pxyy a1 e(23) | 665 | 566 | 233 | 2 | 011 | 4 |
| For everyone there is someone who wishes them to love themselves. | ∀y ∃x Pxyy a(23) e1 | 332 | 233 | 422 | 2 | 100 | 4 |
| There is someone whom everyone wishes to love themselves. | ∃y ∀x Pxyy e(23) a1 | 445 | 544 | 022 | 2 | 011 | 2 |
| Someone wishes everyone to love themselves. | ∃x ∀y Pxyy e1 a(23) | 112 | 211 | 211 | 2 | 100 | 2 |
| Everyone wishes everyone to love themselves. | ∀x ∀y Pxyy a1(23) | 002 | 200 | 011 | 2 | 000 | 1 |
| Someone wants to love themselves. | ∃x Pxxx e(123) | 555 | 555 | 244.5 | 1 | 111 | 4 |
| Everyone wants to love themselves. | ∀x Pxxx a(123) | 222 | 222 | 143.5 | 1 | 000 | 2 |

## Implications

substructures :