example sentence
|
sketch
|
formula
|
pairs
|
|
coord
|
var
|
bin
|
rank
|
Someone wants that someone loves someone.
|
|
∃x ∃y ∃z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Predicate_logic%3B_3_variables%3B_ordered_partition_e123.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e123.svg.png) e123
|
777
|
777
|
444
|
3
|
111
|
6
|
For everyone there is someone who wants them to be loved by someone.
|
|
∀z ∃x ∃y Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Predicate_logic%3B_3_variables%3B_ordered_partition_a3e12.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a3e12.svg.png) a3 e12
|
733
|
337
|
442
|
3
|
110
|
5
|
For everyone there is someone who wants them to love someone.
|
|
∀y ∃x ∃z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Predicate_logic%3B_3_variables%3B_ordered_partition_a2e13.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a2e13.svg.png) a2 e13
|
376
|
673
|
424
|
3
|
101
|
5
|
Everyone wants someone to love someone.
|
|
∀x ∃y ∃z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Predicate_logic%3B_3_variables%3B_ordered_partition_a1e23.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a1e23.svg.png) 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
![](//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Predicate_logic%3B_3_variables%3B_ordered_partition_e2a3e1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e2a3e1.svg.png) e2 a3 e1
|
731
|
137
|
431
|
3
|
110
|
4
|
There is someone who wants that everyone is loved by someone.
|
|
∃x ∀z ∃y Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Predicate_logic%3B_3_variables%3B_ordered_partition_e1a3e2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e1a3e2.svg.png) 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
![](//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Predicate_logic%3B_3_variables%3B_ordered_partition_e3a2e1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e3a2e1.svg.png) e3 a2 e1
|
374
|
473
|
413
|
3
|
101
|
4
|
Someone wants everyone to love someone.
|
|
∃x ∀y ∃z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Predicate_logic%3B_3_variables%3B_ordered_partition_e1a2e3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e1a2e3.svg.png) e1 a2 e3
|
176
|
671
|
314
|
3
|
101
|
4
|
There is someone whom everyone wishes to be loved by someone.
|
|
∃z ∀x ∃y Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Predicate_logic%3B_3_variables%3B_ordered_partition_e3a1e2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e3a1e2.svg.png) e3 a1 e2
|
647
|
746
|
143
|
3
|
011
|
4
|
There is someone whom everyone wishes to love someone.
|
|
∃y ∀x ∃z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Predicate_logic%3B_3_variables%3B_ordered_partition_e2a1e3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e2a1e3.svg.png) e2 a1 e3
|
467
|
764
|
134
|
3
|
011
|
4
|
Someone wishes someone to love everyone.
|
|
∃x ∃y ∀z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/0/09/Predicate_logic%3B_3_variables%3B_ordered_partition_e12a3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e12a3.svg.png) e12 a3
|
711
|
117
|
330
|
3
|
110
|
3
|
Someone wishes someone to be loved by everyone.
|
|
∃x ∃z ∀y Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Predicate_logic%3B_3_variables%3B_ordered_partition_e13a2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e13a2.svg.png) 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
![](//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Predicate_logic%3B_3_variables%3B_ordered_partition_e23a1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e23a1.svg.png) 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
![](//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Predicate_logic%3B_3_variables%3B_ordered_partition_a23e1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a23e1.svg.png) a23 e1
|
330
|
033
|
411
|
3
|
100
|
3
|
Everyone wants everyone to be loved by someone.
|
|
∀x ∀z ∃y Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Predicate_logic%3B_3_variables%3B_ordered_partition_a13e2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a13e2.svg.png) a13 e2
|
603
|
306
|
141
|
3
|
010
|
3
|
Everyone wants everyone to love someone.
|
|
∀x ∀y ∃z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Predicate_logic%3B_3_variables%3B_ordered_partition_a12e3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a12e3.svg.png) a12 e3
|
066
|
660
|
114
|
3
|
001
|
3
|
For everyone there is someone who wants them to love everyone.
|
|
∀y ∃x ∀z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Predicate_logic%3B_3_variables%3B_ordered_partition_a2e1a3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a2e1a3.svg.png) 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
![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Predicate_logic%3B_3_variables%3B_ordered_partition_a3e1a2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a3e1a2.svg.png) a3 e1 a2
|
130
|
031
|
301
|
3
|
100
|
2
|
Everyone wishes someone to love everyone.
|
|
∀x ∃y ∀z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Predicate_logic%3B_3_variables%3B_ordered_partition_a1e2a3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a1e2a3.svg.png) a1 e2 a3
|
601
|
106
|
130
|
3
|
010
|
2
|
For everyone there is someone whom everyone wants to love them.
|
|
∀z ∃y ∀x Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Predicate_logic%3B_3_variables%3B_ordered_partition_a3e2a1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a3e2a1.svg.png) a3 e2 a1
|
403
|
304
|
031
|
3
|
010
|
2
|
Everyone wishes someone to be loved by everyone.
|
|
∀x ∃z ∀y Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Predicate_logic%3B_3_variables%3B_ordered_partition_a1e3a2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a1e3a2.svg.png) a1 e3 a2
|
064
|
460
|
103
|
3
|
001
|
2
|
For everyone there is someone whom everyone wants them to love.
|
|
∀y ∃z ∀x Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Predicate_logic%3B_3_variables%3B_ordered_partition_a2e3a1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a2e3a1.svg.png) a2 e3 a1
|
046
|
640
|
013
|
3
|
001
|
2
|
Someone wants that everyone loves everyone.
|
|
∃x ∀y ∀z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Predicate_logic%3B_3_variables%3B_ordered_partition_e1a23.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e1a23.svg.png) e1 a23
|
110
|
011
|
200
|
3
|
100
|
1
|
There is someone whom everyone wishes to love everyone.
|
|
∃y ∀x ∀z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Predicate_logic%3B_3_variables%3B_ordered_partition_e2a13.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e2a13.svg.png) e2 a13
|
401
|
104
|
020
|
3
|
010
|
1
|
There is someone whom everyone wishes to be loved by everyone.
|
|
∃z ∀x ∀y Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Predicate_logic%3B_3_variables%3B_ordered_partition_e3a12.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e3a12.svg.png) e3 a12
|
044
|
440
|
002
|
3
|
001
|
1
|
Everyone wants everyone to love everyone.
|
|
∀x ∀y ∀z Pxyz
![](//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Predicate_logic%3B_3_variables%3B_ordered_partition_a123.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a123.svg.png) a123
|
000
|
000
|
000
|
3
|
000
|
0
|
Someone wants to love someone.
|
|
∃x ∃y Pxxy
![](//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Predicate_logic%3B_3_variables%3B_ordered_partition_e%2812%293.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e%2812%293.svg.png) e(12)3
|
577
|
775
|
334
|
2
|
111
|
5
|
For everyone there is someone who wants to love them.
|
|
∀y ∃x Pxxy
![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Predicate_logic%3B_3_variables%3B_ordered_partition_a3e%2812%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a3e%2812%29.svg.png) a3 e(12)
|
533
|
335
|
332
|
2
|
110
|
4
|
Everyone wants to love someone.
|
|
∀x ∃y Pxxy
![](//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Predicate_logic%3B_3_variables%3B_ordered_partition_a%2812%29e3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a%2812%29e3.svg.png) a(12) e3
|
266
|
662
|
224
|
2
|
001
|
4
|
Someone wants to love everyone.
|
|
∃x ∀y Pxxy
![](//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Predicate_logic%3B_3_variables%3B_ordered_partition_e%2812%29a3.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e%2812%29a3.svg.png) e(12) a3
|
511
|
115
|
220
|
2
|
110
|
2
|
There is someone whom everyone wants to love.
|
|
∃y ∀x Pxxy
![](//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Predicate_logic%3B_3_variables%3B_ordered_partition_e3a%2812%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e3a%2812%29.svg.png) e3 a(12)
|
244
|
442
|
112
|
2
|
001
|
2
|
Everyone wants to love everyone.
|
|
∀x ∀y Pxxy
![](//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Predicate_logic%3B_3_variables%3B_ordered_partition_a%2812%293.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a%2812%293.svg.png) a(12)3
|
200
|
002
|
110
|
2
|
000
|
1
|
Someone wants to be loved by someone.
|
|
∃x ∃y Pxyx
![](//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Predicate_logic%3B_3_variables%3B_ordered_partition_e%2813%292.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e%2813%292.svg.png) e(13)2
|
757
|
757
|
343
|
2
|
111
|
5
|
For everyone there is someone who wants to be loved by them.
|
|
∀y ∃x Pxyx
![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Predicate_logic%3B_3_variables%3B_ordered_partition_a2e%2813%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a2e%2813%29.svg.png) a2 e(13)
|
356
|
653
|
323
|
2
|
101
|
4
|
Everyone wants to be loved by someone.
|
|
∀x ∃y Pxyx
![](//upload.wikimedia.org/wikipedia/commons/thumb/2/25/Predicate_logic%3B_3_variables%3B_ordered_partition_a%2813%29e2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a%2813%29e2.svg.png) a(13) e2
|
623
|
326
|
242
|
2
|
010
|
4
|
Someone wants to be loved by everyone.
|
|
∃x ∀y Pxyx
![](//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Predicate_logic%3B_3_variables%3B_ordered_partition_e%2813%29a2.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e%2813%29a2.svg.png) e(13) a2
|
154
|
451
|
202
|
2
|
101
|
2
|
There is someone by whom everyone wants to be loved.
|
|
∃y ∀x Pxyx
![](//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Predicate_logic%3B_3_variables%3B_ordered_partition_e2a%2813%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e2a%2813%29.svg.png) e2 a(13)
|
421
|
124
|
121
|
2
|
010
|
2
|
Everyone wants to be loved by everyone.
|
|
∀x ∀y Pxyx
![](//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Predicate_logic%3B_3_variables%3B_ordered_partition_a%2813%292.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a%2813%292.svg.png) a(13)2
|
020
|
020
|
101
|
2
|
000
|
1
|
Someone wishes someone to love themselves.
|
|
∃x ∃y Pxyy
![](//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Predicate_logic%3B_3_variables%3B_ordered_partition_e1%2823%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e1%2823%29.svg.png) e1(23)
|
775
|
577
|
433
|
2
|
111
|
5
|
Everyone wishes someone to love themselves.
|
|
∀x ∃y Pxyy
![](//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Predicate_logic%3B_3_variables%3B_ordered_partition_a1e%2823%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a1e%2823%29.svg.png) a1 e(23)
|
665
|
566
|
233
|
2
|
011
|
4
|
For everyone there is someone who wishes them to love themselves.
|
|
∀y ∃x Pxyy
![](//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Predicate_logic%3B_3_variables%3B_ordered_partition_a%2823%29e1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a%2823%29e1.svg.png) a(23) e1
|
332
|
233
|
422
|
2
|
100
|
4
|
There is someone whom everyone wishes to love themselves.
|
|
∃y ∀x Pxyy
![](//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Predicate_logic%3B_3_variables%3B_ordered_partition_e%2823%29a1.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e%2823%29a1.svg.png) e(23) a1
|
445
|
544
|
022
|
2
|
011
|
2
|
Someone wishes everyone to love themselves.
|
|
∃x ∀y Pxyy
![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Predicate_logic%3B_3_variables%3B_ordered_partition_e1a%2823%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e1a%2823%29.svg.png) e1 a(23)
|
112
|
211
|
211
|
2
|
100
|
2
|
Everyone wishes everyone to love themselves.
|
|
∀x ∀y Pxyy
![](//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Predicate_logic%3B_3_variables%3B_ordered_partition_a1%2823%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a1%2823%29.svg.png) a1(23)
|
002
|
200
|
011
|
2
|
000
|
1
|
Someone wants to love themselves.
|
|
∃x Pxxx
![](//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Predicate_logic%3B_3_variables%3B_ordered_partition_e%28123%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_e%28123%29.svg.png) e(123)
|
555
|
555
|
244.5
|
1
|
111
|
4
|
Everyone wants to love themselves.
|
|
∀x Pxxx
![](//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Predicate_logic%3B_3_variables%3B_ordered_partition_a%28123%29.svg/30px-Predicate_logic%3B_3_variables%3B_ordered_partition_a%28123%29.svg.png) a(123)
|
222
|
222
|
143.5
|
1
|
000
|
2
|