c Boolean vector synthesis problem 2bitadd_12 c n=4 m=3 k=12 A=16 c Specification: c 0 0 0 0 --> 0 0 0 c 0 0 0 1 --> 0 0 1 c 0 0 1 0 --> 0 1 0 c 0 0 1 1 --> 0 1 1 c 0 1 0 0 --> 0 0 1 c 0 1 0 1 --> 0 1 0 c 0 1 1 0 --> 0 1 1 c 0 1 1 1 --> 1 0 0 c 1 0 0 0 --> 0 1 0 c 1 0 0 1 --> 0 1 1 c 1 0 1 0 --> 1 0 0 c 1 0 1 1 --> 1 0 1 c 1 1 0 0 --> 0 1 1 c 1 1 0 1 --> 1 0 0 c 1 1 1 0 --> 1 0 1 c 1 1 1 1 --> 1 1 0 c Decision variables: c s[1][1] is 1 c s[1][2] is 2 c s[1][3] is 3 c s[1][4] is 4 c s[2][1] is 5 c s[2][2] is 6 c s[2][3] is 7 c s[2][4] is 8 c s[3][1] is 9 c s[3][2] is 10 c s[3][3] is 11 c s[3][4] is 12 c s[4][1] is 13 c s[4][2] is 14 c s[4][3] is 15 c s[4][4] is 16 c s[5][1] is 17 c s[5][2] is 18 c s[5][3] is 19 c s[5][4] is 20 c s[6][1] is 21 c s[6][2] is 22 c s[6][3] is 23 c s[6][4] is 24 c s[7][1] is 25 c s[7][2] is 26 c s[7][3] is 27 c s[7][4] is 28 c s[8][1] is 29 c s[8][2] is 30 c s[8][3] is 31 c s[8][4] is 32 c s[9][1] is 33 c s[9][2] is 34 c s[9][3] is 35 c s[9][4] is 36 c s[10][1] is 37 c s[10][2] is 38 c s[10][3] is 39 c s[10][4] is 40 c s[11][1] is 41 c s[11][2] is 42 c s[11][3] is 43 c s[11][4] is 44 c s[12][1] is 45 c s[12][2] is 46 c s[12][3] is 47 c s[12][4] is 48 c sp[1][1] is 49 c sp[1][2] is 50 c sp[1][3] is 51 c sp[1][4] is 52 c sp[2][1] is 53 c sp[2][2] is 54 c sp[2][3] is 55 c sp[2][4] is 56 c sp[3][1] is 57 c sp[3][2] is 58 c sp[3][3] is 59 c sp[3][4] is 60 c sp[4][1] is 61 c sp[4][2] is 62 c sp[4][3] is 63 c sp[4][4] is 64 c sp[5][1] is 65 c sp[5][2] is 66 c sp[5][3] is 67 c sp[5][4] is 68 c sp[6][1] is 69 c sp[6][2] is 70 c sp[6][3] is 71 c sp[6][4] is 72 c sp[7][1] is 73 c sp[7][2] is 74 c sp[7][3] is 75 c sp[7][4] is 76 c sp[8][1] is 77 c sp[8][2] is 78 c sp[8][3] is 79 c sp[8][4] is 80 c sp[9][1] is 81 c sp[9][2] is 82 c sp[9][3] is 83 c sp[9][4] is 84 c sp[10][1] is 85 c sp[10][2] is 86 c sp[10][3] is 87 c sp[10][4] is 88 c sp[11][1] is 89 c sp[11][2] is 90 c sp[11][3] is 91 c sp[11][4] is 92 c sp[12][1] is 93 c sp[12][2] is 94 c sp[12][3] is 95 c sp[12][4] is 96 c w[1][1] is 97 c w[1][2] is 98 c w[1][3] is 99 c w[2][1] is 100 c w[2][2] is 101 c w[2][3] is 102 c w[3][1] is 103 c w[3][2] is 104 c w[3][3] is 105 c w[4][1] is 106 c w[4][2] is 107 c w[4][3] is 108 c w[5][1] is 109 c w[5][2] is 110 c w[5][3] is 111 c w[6][1] is 112 c w[6][2] is 113 c w[6][3] is 114 c w[7][1] is 115 c w[7][2] is 116 c w[7][3] is 117 c w[8][1] is 118 c w[8][2] is 119 c w[8][3] is 120 c w[9][1] is 121 c w[9][2] is 122 c w[9][3] is 123 c w[10][1] is 124 c w[10][2] is 125 c w[10][3] is 126 c w[11][1] is 127 c w[11][2] is 128 c w[11][3] is 129 c w[12][1] is 130 c w[12][2] is 131 c w[12][3] is 132 c Auxiliary variables: c z[1][1][1] is 133 c z[1][1][2] is 134 c z[1][1][3] is 135 c z[1][2][1] is 136 c z[1][2][2] is 137 c z[1][2][3] is 138 c z[1][3][1] is 139 c z[1][3][2] is 140 c z[1][3][3] is 141 c z[1][4][1] is 142 c z[1][4][2] is 143 c z[1][4][3] is 144 c z[1][5][1] is 145 c z[1][5][2] is 146 c z[1][5][3] is 147 c z[1][6][1] is 148 c z[1][6][2] is 149 c z[1][6][3] is 150 c z[1][7][1] is 151 c z[1][7][2] is 152 c z[1][7][3] is 153 c z[1][8][1] is 154 c z[1][8][2] is 155 c z[1][8][3] is 156 c z[1][9][1] is 157 c z[1][9][2] is 158 c z[1][9][3] is 159 c z[1][10][1] is 160 c z[1][10][2] is 161 c z[1][10][3] is 162 c z[1][11][1] is 163 c z[1][11][2] is 164 c z[1][11][3] is 165 c z[1][12][1] is 166 c z[1][12][2] is 167 c z[1][12][3] is 168 c z[2][1][1] is 169 c z[2][1][2] is 170 c z[2][1][3] is 171 c z[2][2][1] is 172 c z[2][2][2] is 173 c z[2][2][3] is 174 c z[2][3][1] is 175 c z[2][3][2] is 176 c z[2][3][3] is 177 c z[2][4][1] is 178 c z[2][4][2] is 179 c z[2][4][3] is 180 c z[2][5][1] is 181 c z[2][5][2] is 182 c z[2][5][3] is 183 c z[2][6][1] is 184 c z[2][6][2] is 185 c z[2][6][3] is 186 c z[2][7][1] is 187 c z[2][7][2] is 188 c z[2][7][3] is 189 c z[2][8][1] is 190 c z[2][8][2] is 191 c z[2][8][3] is 192 c z[2][9][1] is 193 c z[2][9][2] is 194 c z[2][9][3] is 195 c z[2][10][1] is 196 c z[2][10][2] is 197 c z[2][10][3] is 198 c z[2][11][1] is 199 c z[2][11][2] is 200 c z[2][11][3] is 201 c z[2][12][1] is 202 c z[2][12][2] is 203 c z[2][12][3] is 204 c z[3][1][1] is 205 c z[3][1][2] is 206 c z[3][1][3] is 207 c z[3][2][1] is 208 c z[3][2][2] is 209 c z[3][2][3] is 210 c z[3][3][1] is 211 c z[3][3][2] is 212 c z[3][3][3] is 213 c z[3][4][1] is 214 c z[3][4][2] is 215 c z[3][4][3] is 216 c z[3][5][1] is 217 c z[3][5][2] is 218 c z[3][5][3] is 219 c z[3][6][1] is 220 c z[3][6][2] is 221 c z[3][6][3] is 222 c z[3][7][1] is 223 c z[3][7][2] is 224 c z[3][7][3] is 225 c z[3][8][1] is 226 c z[3][8][2] is 227 c z[3][8][3] is 228 c z[3][9][1] is 229 c z[3][9][2] is 230 c z[3][9][3] is 231 c z[3][10][1] is 232 c z[3][10][2] is 233 c z[3][10][3] is 234 c z[3][11][1] is 235 c z[3][11][2] is 236 c z[3][11][3] is 237 c z[3][12][1] is 238 c z[3][12][2] is 239 c z[3][12][3] is 240 c z[4][1][1] is 241 c z[4][1][2] is 242 c z[4][1][3] is 243 c z[4][2][1] is 244 c z[4][2][2] is 245 c z[4][2][3] is 246 c z[4][3][1] is 247 c z[4][3][2] is 248 c z[4][3][3] is 249 c z[4][4][1] is 250 c z[4][4][2] is 251 c z[4][4][3] is 252 c z[4][5][1] is 253 c z[4][5][2] is 254 c z[4][5][3] is 255 c z[4][6][1] is 256 c z[4][6][2] is 257 c z[4][6][3] is 258 c z[4][7][1] is 259 c z[4][7][2] is 260 c z[4][7][3] is 261 c z[4][8][1] is 262 c z[4][8][2] is 263 c z[4][8][3] is 264 c z[4][9][1] is 265 c z[4][9][2] is 266 c z[4][9][3] is 267 c z[4][10][1] is 268 c z[4][10][2] is 269 c z[4][10][3] is 270 c z[4][11][1] is 271 c z[4][11][2] is 272 c z[4][11][3] is 273 c z[4][12][1] is 274 c z[4][12][2] is 275 c z[4][12][3] is 276 c z[5][1][1] is 277 c z[5][1][2] is 278 c z[5][1][3] is 279 c z[5][2][1] is 280 c z[5][2][2] is 281 c z[5][2][3] is 282 c z[5][3][1] is 283 c z[5][3][2] is 284 c z[5][3][3] is 285 c z[5][4][1] is 286 c z[5][4][2] is 287 c z[5][4][3] is 288 c z[5][5][1] is 289 c z[5][5][2] is 290 c z[5][5][3] is 291 c z[5][6][1] is 292 c z[5][6][2] is 293 c z[5][6][3] is 294 c z[5][7][1] is 295 c z[5][7][2] is 296 c z[5][7][3] is 297 c z[5][8][1] is 298 c z[5][8][2] is 299 c z[5][8][3] is 300 c z[5][9][1] is 301 c z[5][9][2] is 302 c z[5][9][3] is 303 c z[5][10][1] is 304 c z[5][10][2] is 305 c z[5][10][3] is 306 c z[5][11][1] is 307 c z[5][11][2] is 308 c z[5][11][3] is 309 c z[5][12][1] is 310 c z[5][12][2] is 311 c z[5][12][3] is 312 c z[6][1][1] is 313 c z[6][1][2] is 314 c z[6][1][3] is 315 c z[6][2][1] is 316 c z[6][2][2] is 317 c z[6][2][3] is 318 c z[6][3][1] is 319 c z[6][3][2] is 320 c z[6][3][3] is 321 c z[6][4][1] is 322 c z[6][4][2] is 323 c z[6][4][3] is 324 c z[6][5][1] is 325 c z[6][5][2] is 326 c z[6][5][3] is 327 c z[6][6][1] is 328 c z[6][6][2] is 329 c z[6][6][3] is 330 c z[6][7][1] is 331 c z[6][7][2] is 332 c z[6][7][3] is 333 c z[6][8][1] is 334 c z[6][8][2] is 335 c z[6][8][3] is 336 c z[6][9][1] is 337 c z[6][9][2] is 338 c z[6][9][3] is 339 c z[6][10][1] is 340 c z[6][10][2] is 341 c z[6][10][3] is 342 c z[6][11][1] is 343 c z[6][11][2] is 344 c z[6][11][3] is 345 c z[6][12][1] is 346 c z[6][12][2] is 347 c z[6][12][3] is 348 c z[7][1][1] is 349 c z[7][1][2] is 350 c z[7][1][3] is 351 c z[7][2][1] is 352 c z[7][2][2] is 353 c z[7][2][3] is 354 c z[7][3][1] is 355 c z[7][3][2] is 356 c z[7][3][3] is 357 c z[7][4][1] is 358 c z[7][4][2] is 359 c z[7][4][3] is 360 c z[7][5][1] is 361 c z[7][5][2] is 362 c z[7][5][3] is 363 c z[7][6][1] is 364 c z[7][6][2] is 365 c z[7][6][3] is 366 c z[7][7][1] is 367 c z[7][7][2] is 368 c z[7][7][3] is 369 c z[7][8][1] is 370 c z[7][8][2] is 371 c z[7][8][3] is 372 c z[7][9][1] is 373 c z[7][9][2] is 374 c z[7][9][3] is 375 c z[7][10][1] is 376 c z[7][10][2] is 377 c z[7][10][3] is 378 c z[7][11][1] is 379 c z[7][11][2] is 380 c z[7][11][3] is 381 c z[7][12][1] is 382 c z[7][12][2] is 383 c z[7][12][3] is 384 c z[8][1][1] is 385 c z[8][1][2] is 386 c z[8][1][3] is 387 c z[8][2][1] is 388 c z[8][2][2] is 389 c z[8][2][3] is 390 c z[8][3][1] is 391 c z[8][3][2] is 392 c z[8][3][3] is 393 c z[8][4][1] is 394 c z[8][4][2] is 395 c z[8][4][3] is 396 c z[8][5][1] is 397 c z[8][5][2] is 398 c z[8][5][3] is 399 c z[8][6][1] is 400 c z[8][6][2] is 401 c z[8][6][3] is 402 c z[8][7][1] is 403 c z[8][7][2] is 404 c z[8][7][3] is 405 c z[8][8][1] is 406 c z[8][8][2] is 407 c z[8][8][3] is 408 c z[8][9][1] is 409 c z[8][9][2] is 410 c z[8][9][3] is 411 c z[8][10][1] is 412 c z[8][10][2] is 413 c z[8][10][3] is 414 c z[8][11][1] is 415 c z[8][11][2] is 416 c z[8][11][3] is 417 c z[8][12][1] is 418 c z[8][12][2] is 419 c z[8][12][3] is 420 c z[9][1][1] is 421 c z[9][1][2] is 422 c z[9][1][3] is 423 c z[9][2][1] is 424 c z[9][2][2] is 425 c z[9][2][3] is 426 c z[9][3][1] is 427 c z[9][3][2] is 428 c z[9][3][3] is 429 c z[9][4][1] is 430 c z[9][4][2] is 431 c z[9][4][3] is 432 c z[9][5][1] is 433 c z[9][5][2] is 434 c z[9][5][3] is 435 c z[9][6][1] is 436 c z[9][6][2] is 437 c z[9][6][3] is 438 c z[9][7][1] is 439 c z[9][7][2] is 440 c z[9][7][3] is 441 c z[9][8][1] is 442 c z[9][8][2] is 443 c z[9][8][3] is 444 c z[9][9][1] is 445 c z[9][9][2] is 446 c z[9][9][3] is 447 c z[9][10][1] is 448 c z[9][10][2] is 449 c z[9][10][3] is 450 c z[9][11][1] is 451 c z[9][11][2] is 452 c z[9][11][3] is 453 c z[9][12][1] is 454 c z[9][12][2] is 455 c z[9][12][3] is 456 c z[10][1][1] is 457 c z[10][1][2] is 458 c z[10][1][3] is 459 c z[10][2][1] is 460 c z[10][2][2] is 461 c z[10][2][3] is 462 c z[10][3][1] is 463 c z[10][3][2] is 464 c z[10][3][3] is 465 c z[10][4][1] is 466 c z[10][4][2] is 467 c z[10][4][3] is 468 c z[10][5][1] is 469 c z[10][5][2] is 470 c z[10][5][3] is 471 c z[10][6][1] is 472 c z[10][6][2] is 473 c z[10][6][3] is 474 c z[10][7][1] is 475 c z[10][7][2] is 476 c z[10][7][3] is 477 c z[10][8][1] is 478 c z[10][8][2] is 479 c z[10][8][3] is 480 c z[10][9][1] is 481 c z[10][9][2] is 482 c z[10][9][3] is 483 c z[10][10][1] is 484 c z[10][10][2] is 485 c z[10][10][3] is 486 c z[10][11][1] is 487 c z[10][11][2] is 488 c z[10][11][3] is 489 c z[10][12][1] is 490 c z[10][12][2] is 491 c z[10][12][3] is 492 c z[11][1][1] is 493 c z[11][1][2] is 494 c z[11][1][3] is 495 c z[11][2][1] is 496 c z[11][2][2] is 497 c z[11][2][3] is 498 c z[11][3][1] is 499 c z[11][3][2] is 500 c z[11][3][3] is 501 c z[11][4][1] is 502 c z[11][4][2] is 503 c z[11][4][3] is 504 c z[11][5][1] is 505 c z[11][5][2] is 506 c z[11][5][3] is 507 c z[11][6][1] is 508 c z[11][6][2] is 509 c z[11][6][3] is 510 c z[11][7][1] is 511 c z[11][7][2] is 512 c z[11][7][3] is 513 c z[11][8][1] is 514 c z[11][8][2] is 515 c z[11][8][3] is 516 c z[11][9][1] is 517 c z[11][9][2] is 518 c z[11][9][3] is 519 c z[11][10][1] is 520 c z[11][10][2] is 521 c z[11][10][3] is 522 c z[11][11][1] is 523 c z[11][11][2] is 524 c z[11][11][3] is 525 c z[11][12][1] is 526 c z[11][12][2] is 527 c z[11][12][3] is 528 c z[12][1][1] is 529 c z[12][1][2] is 530 c z[12][1][3] is 531 c z[12][2][1] is 532 c z[12][2][2] is 533 c z[12][2][3] is 534 c z[12][3][1] is 535 c z[12][3][2] is 536 c z[12][3][3] is 537 c z[12][4][1] is 538 c z[12][4][2] is 539 c z[12][4][3] is 540 c z[12][5][1] is 541 c z[12][5][2] is 542 c z[12][5][3] is 543 c z[12][6][1] is 544 c z[12][6][2] is 545 c z[12][6][3] is 546 c z[12][7][1] is 547 c z[12][7][2] is 548 c z[12][7][3] is 549 c z[12][8][1] is 550 c z[12][8][2] is 551 c z[12][8][3] is 552 c z[12][9][1] is 553 c z[12][9][2] is 554 c z[12][9][3] is 555 c z[12][10][1] is 556 c z[12][10][2] is 557 c z[12][10][3] is 558 c z[12][11][1] is 559 c z[12][11][2] is 560 c z[12][11][3] is 561 c z[12][12][1] is 562 c z[12][12][2] is 563 c z[12][12][3] is 564 c z[13][1][1] is 565 c z[13][1][2] is 566 c z[13][1][3] is 567 c z[13][2][1] is 568 c z[13][2][2] is 569 c z[13][2][3] is 570 c z[13][3][1] is 571 c z[13][3][2] is 572 c z[13][3][3] is 573 c z[13][4][1] is 574 c z[13][4][2] is 575 c z[13][4][3] is 576 c z[13][5][1] is 577 c z[13][5][2] is 578 c z[13][5][3] is 579 c z[13][6][1] is 580 c z[13][6][2] is 581 c z[13][6][3] is 582 c z[13][7][1] is 583 c z[13][7][2] is 584 c z[13][7][3] is 585 c z[13][8][1] is 586 c z[13][8][2] is 587 c z[13][8][3] is 588 c z[13][9][1] is 589 c z[13][9][2] is 590 c z[13][9][3] is 591 c z[13][10][1] is 592 c z[13][10][2] is 593 c z[13][10][3] is 594 c z[13][11][1] is 595 c z[13][11][2] is 596 c z[13][11][3] is 597 c z[13][12][1] is 598 c z[13][12][2] is 599 c z[13][12][3] is 600 c z[14][1][1] is 601 c z[14][1][2] is 602 c z[14][1][3] is 603 c z[14][2][1] is 604 c z[14][2][2] is 605 c z[14][2][3] is 606 c z[14][3][1] is 607 c z[14][3][2] is 608 c z[14][3][3] is 609 c z[14][4][1] is 610 c z[14][4][2] is 611 c z[14][4][3] is 612 c z[14][5][1] is 613 c z[14][5][2] is 614 c z[14][5][3] is 615 c z[14][6][1] is 616 c z[14][6][2] is 617 c z[14][6][3] is 618 c z[14][7][1] is 619 c z[14][7][2] is 620 c z[14][7][3] is 621 c z[14][8][1] is 622 c z[14][8][2] is 623 c z[14][8][3] is 624 c z[14][9][1] is 625 c z[14][9][2] is 626 c z[14][9][3] is 627 c z[14][10][1] is 628 c z[14][10][2] is 629 c z[14][10][3] is 630 c z[14][11][1] is 631 c z[14][11][2] is 632 c z[14][11][3] is 633 c z[14][12][1] is 634 c z[14][12][2] is 635 c z[14][12][3] is 636 c z[15][1][1] is 637 c z[15][1][2] is 638 c z[15][1][3] is 639 c z[15][2][1] is 640 c z[15][2][2] is 641 c z[15][2][3] is 642 c z[15][3][1] is 643 c z[15][3][2] is 644 c z[15][3][3] is 645 c z[15][4][1] is 646 c z[15][4][2] is 647 c z[15][4][3] is 648 c z[15][5][1] is 649 c z[15][5][2] is 650 c z[15][5][3] is 651 c z[15][6][1] is 652 c z[15][6][2] is 653 c z[15][6][3] is 654 c z[15][7][1] is 655 c z[15][7][2] is 656 c z[15][7][3] is 657 c z[15][8][1] is 658 c z[15][8][2] is 659 c z[15][8][3] is 660 c z[15][9][1] is 661 c z[15][9][2] is 662 c z[15][9][3] is 663 c z[15][10][1] is 664 c z[15][10][2] is 665 c z[15][10][3] is 666 c z[15][11][1] is 667 c z[15][11][2] is 668 c z[15][11][3] is 669 c z[15][12][1] is 670 c z[15][12][2] is 671 c z[15][12][3] is 672 c z[16][1][1] is 673 c z[16][1][2] is 674 c z[16][1][3] is 675 c z[16][2][1] is 676 c z[16][2][2] is 677 c z[16][2][3] is 678 c z[16][3][1] is 679 c z[16][3][2] is 680 c z[16][3][3] is 681 c z[16][4][1] is 682 c z[16][4][2] is 683 c z[16][4][3] is 684 c z[16][5][1] is 685 c z[16][5][2] is 686 c z[16][5][3] is 687 c z[16][6][1] is 688 c z[16][6][2] is 689 c z[16][6][3] is 690 c z[16][7][1] is 691 c z[16][7][2] is 692 c z[16][7][3] is 693 c z[16][8][1] is 694 c z[16][8][2] is 695 c z[16][8][3] is 696 c z[16][9][1] is 697 c z[16][9][2] is 698 c z[16][9][3] is 699 c z[16][10][1] is 700 c z[16][10][2] is 701 c z[16][10][3] is 702 c z[16][11][1] is 703 c z[16][11][2] is 704 c z[16][11][3] is 705 c z[16][12][1] is 706 c z[16][12][2] is 707 c z[16][12][3] is 708 p cnf 708 1702 1 49 0 5 53 0 9 57 0 13 61 0 17 65 0 21 69 0 25 73 0 29 77 0 33 81 0 37 85 0 41 89 0 45 93 0 2 50 0 6 54 0 10 58 0 14 62 0 18 66 0 22 70 0 26 74 0 30 78 0 34 82 0 38 86 0 42 90 0 46 94 0 3 51 0 7 55 0 11 59 0 15 63 0 19 67 0 23 71 0 27 75 0 31 79 0 35 83 0 39 87 0 43 91 0 47 95 0 4 52 0 8 56 0 12 60 0 16 64 0 20 68 0 24 72 0 28 76 0 32 80 0 36 84 0 40 88 0 44 92 0 48 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