# Formulas in predicate logic/3 places

 Formulas in predicate logic

## List

list
example sentence sketch 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

substructures
diagonal
sides top

weak orderings