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
