----- Otter 3.3, August 2003 ----- The process was started by mccune on gyro.thornwood, Wed Aug 6 14:25:56 2003 The command was "../../bin/otter". The process ID is 5834. set(hyper_res). assign(pick_given_ratio,3). clear(back_sub). assign(max_proofs,3). clear(print_kept). set(order_history). assign(fpa_literals,0). assign(max_mem,1500). list(usable). 1 [] -P(i(x,y))| -P(x)|P(y). end_of_list. list(sos). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). end_of_list. list(passive). 6 [] -P(i(n(n(a)),a))|$ANS(MV_24). 7 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(MV_25). 8 [] -P(i(a,n(n(a))))|$ANS(MV_29). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=6) 2 [] P(i(x,i(y,x))). given clause #2: (wt=8) 9 [hyper,1,2,2] P(i(x,i(y,i(z,y)))). given clause #3: (wt=10) 5 [] P(i(i(n(x),n(y)),i(y,x))). given clause #4: (wt=10) 10 [hyper,1,2,9] P(i(x,i(y,i(z,i(u,z))))). given clause #5: (wt=12) 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). given clause #6: (wt=10) 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). given clause #7: (wt=7) 21 [hyper,1,18,5] P(i(n(x),i(x,y))). given clause #8: (wt=8) 23 [hyper,1,18,2] P(i(x,i(y,i(z,x)))). given clause #9: (wt=12) 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). given clause #10: (wt=8) 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). given clause #11: (wt=9) 25 [hyper,1,2,21] P(i(x,i(n(y),i(y,z)))). given clause #12: (wt=10) 22 [hyper,1,18,3] P(i(x,i(i(x,y),i(z,y)))). given clause #13: (wt=12) 11 [hyper,1,2,5] P(i(x,i(i(n(y),n(z)),i(z,y)))). given clause #14: (wt=10) 27 [hyper,1,18,23] P(i(x,i(y,i(z,i(u,x))))). given clause #15: (wt=10) 29 [hyper,1,2,23] P(i(x,i(y,i(z,i(u,y))))). given clause #16: (wt=10) 40 [hyper,1,4,9] P(i(i(i(x,i(y,x)),z),z)). given clause #17: (wt=12) 12 [hyper,1,2,10] P(i(x,i(y,i(z,i(u,i(v,u)))))). given clause #18: (wt=4) 96 [hyper,1,18,40] P(i(x,x)). given clause #19: (wt=6) 106 [hyper,1,2,96] P(i(x,i(y,y))). given clause #20: (wt=8) 102 [hyper,1,36,96] P(i(i(i(x,x),y),y)). given clause #21: (wt=16) 13 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). given clause #22: (wt=8) 104 [hyper,1,23,96] P(i(x,i(y,i(z,z)))). given clause #23: (wt=10) 43 [hyper,1,18,36] P(i(x,i(i(i(y,x),z),z))). given clause #24: (wt=10) 45 [hyper,1,2,36] P(i(x,i(y,i(i(y,z),z)))). given clause #25: (wt=14) 14 [hyper,1,2,3] P(i(x,i(i(y,z),i(i(z,u),i(y,u))))). given clause #26: (wt=10) 103 [hyper,1,27,96] P(i(x,i(y,i(z,i(u,u))))). given clause #27: (wt=10) 105 [hyper,1,22,96] P(i(i(i(x,x),y),i(z,y))). given clause #28: (wt=10) 107 [hyper,1,36,106] P(i(i(i(x,i(y,y)),z),z)). given clause #29: (wt=14) 15 [hyper,1,3,10] P(i(i(i(x,i(y,i(z,y))),u),i(v,u))). given clause #30: (wt=10) 115 [hyper,1,2,102] P(i(x,i(i(i(y,y),z),z))). given clause #31: (wt=10) 124 [hyper,1,13,40] P(i(i(x,y),i(x,i(z,y)))). given clause #32: (wt=9) 205 [hyper,1,124,21] P(i(n(x),i(y,i(x,z)))). given clause #33: (wt=12) 16 [hyper,1,3,9] P(i(i(i(x,i(y,x)),z),i(u,z))). given clause #34: (wt=10) 203 [hyper,1,124,36] P(i(x,i(y,i(i(x,z),z)))). given clause #35: (wt=11) 24 [hyper,1,3,21] P(i(i(i(x,y),z),i(n(x),z))). given clause #36: (wt=7) 280 [hyper,1,24,102] P(i(n(i(x,x)),y)). given clause #37: (wt=14) 17 [hyper,1,3,5] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). given clause #38: (wt=8) 289 [hyper,1,24,5] P(i(n(n(x)),i(y,x))). given clause #39: (wt=9) 278 [hyper,1,24,107] P(i(n(i(x,i(y,y))),z)). given clause #40: (wt=9) 279 [hyper,1,24,105] P(i(n(i(x,x)),i(y,z))). given clause #41: (wt=14) 19 [hyper,1,3,18] P(i(i(i(x,y),z),i(i(i(u,x),y),z))). given clause #42: (wt=9) 282 [hyper,1,24,40] P(i(n(i(x,i(y,x))),z)). given clause #43: (wt=9) 286 [hyper,1,24,18] P(i(n(i(x,y)),i(y,z))). given clause #44: (wt=9) 298 [hyper,1,2,280] P(i(x,i(n(i(y,y)),z))). given clause #45: (wt=12) 20 [hyper,1,2,18] P(i(x,i(i(i(y,z),u),i(z,u)))). given clause #46: (wt=10) 271 [hyper,1,24,24] P(i(n(i(x,y)),i(n(x),z))). given clause #47: (wt=10) 316 [hyper,1,17,102] P(i(i(n(x),n(i(y,y))),x)). -------- PROOF -------- 413 [binary,412.1,6.1] $ANS(MV_24). ----> UNIT CONFLICT at 0.02 sec ----> 413 [binary,412.1,6.1] $ANS(MV_24). Length of proof is 11. Level of proof is 6. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). 6 [] -P(i(n(n(a)),a))|$ANS(MV_24). 9 [hyper,1,2,2] P(i(x,i(y,i(z,y)))). 17 [hyper,1,3,5] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 21 [hyper,1,18,5] P(i(n(x),i(x,y))). 24 [hyper,1,3,21] P(i(i(i(x,y),z),i(n(x),z))). 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). 40 [hyper,1,4,9] P(i(i(i(x,i(y,x)),z),z)). 96 [hyper,1,18,40] P(i(x,x)). 102 [hyper,1,36,96] P(i(i(i(x,x),y),y)). 316 [hyper,1,17,102] P(i(i(n(x),n(i(y,y))),x)). 412 [hyper,1,24,316] P(i(n(n(x)),x)). 413 [binary,412.1,6.1] $ANS(MV_24). ------------ end of proof ------------- given clause #48: (wt=6) 412 [hyper,1,24,316] P(i(n(n(x)),x)). -------- PROOF -------- 429 [binary,428.1,8.1] $ANS(MV_29). ----> UNIT CONFLICT at 0.02 sec ----> 429 [binary,428.1,8.1] $ANS(MV_29). Length of proof is 12. Level of proof is 7. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 5 [] P(i(i(n(x),n(y)),i(y,x))). 8 [] -P(i(a,n(n(a))))|$ANS(MV_29). 9 [hyper,1,2,2] P(i(x,i(y,i(z,y)))). 17 [hyper,1,3,5] P(i(i(i(x,y),z),i(i(n(y),n(x)),z))). 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 21 [hyper,1,18,5] P(i(n(x),i(x,y))). 24 [hyper,1,3,21] P(i(i(i(x,y),z),i(n(x),z))). 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). 40 [hyper,1,4,9] P(i(i(i(x,i(y,x)),z),z)). 96 [hyper,1,18,40] P(i(x,x)). 102 [hyper,1,36,96] P(i(i(i(x,x),y),y)). 316 [hyper,1,17,102] P(i(i(n(x),n(i(y,y))),x)). 412 [hyper,1,24,316] P(i(n(n(x)),x)). 428 [hyper,1,5,412] P(i(x,n(n(x)))). 429 [binary,428.1,8.1] $ANS(MV_29). ------------ end of proof ------------- given clause #49: (wt=12) 26 [hyper,1,23,23] P(i(x,i(y,i(z,i(u,i(v,z)))))). given clause #50: (wt=6) 421 [hyper,1,316,412] P(n(n(i(x,x)))). given clause #51: (wt=6) 428 [hyper,1,5,412] P(i(x,n(n(x)))). given clause #52: (wt=8) 431 [hyper,1,2,412] P(i(x,i(n(n(y)),y))). given clause #53: (wt=12) 28 [hyper,1,3,23] P(i(i(i(x,i(y,z)),u),i(z,u))). given clause #54: (wt=8) 442 [hyper,1,2,421] P(i(x,n(n(i(y,y))))). given clause #55: (wt=8) 443 [hyper,1,428,428] P(n(n(i(x,n(n(x)))))). given clause #56: (wt=8) 445 [hyper,1,124,428] P(i(x,i(y,n(n(x))))). given clause #57: (wt=11) 30 [hyper,1,23,21] P(i(x,i(y,i(n(z),i(z,u))))). given clause #58: (wt=8) 446 [hyper,1,107,428] P(n(n(i(x,i(y,y))))). given clause #59: (wt=8) 448 [hyper,1,40,428] P(n(n(i(x,i(y,x))))). given clause #60: (wt=8) 455 [hyper,1,18,428] P(i(x,n(n(i(y,x))))). given clause #61: (wt=14) 31 [hyper,1,23,18] P(i(x,i(y,i(i(i(z,u),v),i(u,v))))). given clause #62: (wt=8) 461 [hyper,1,2,428] P(i(x,i(y,n(n(y))))). given clause #63: (wt=8) 462 [hyper,1,428,421] P(n(n(n(n(i(x,x)))))). given clause #64: (wt=8) 463 [hyper,1,428,412] P(n(n(i(n(n(x)),x)))). given clause #65: (wt=14) 32 [hyper,1,23,10] P(i(x,i(y,i(z,i(u,i(v,i(w,v))))))). given clause #66: (wt=8) 649 [hyper,1,5,455] P(i(n(i(x,n(y))),y)). given clause #67: (wt=9) 451 [hyper,1,24,428] P(i(n(x),n(n(i(x,y))))). given clause #68: (wt=7) 753 [hyper,1,5,451] P(i(n(i(x,y)),x)). given clause #69: (wt=14) 33 [hyper,1,23,5] P(i(x,i(y,i(i(n(z),n(u)),i(u,z))))). given clause #70: (wt=7) 769 [hyper,1,5,753] P(i(x,i(n(x),y))). given clause #71: (wt=9) 469 [hyper,1,428,280] P(n(n(i(n(i(x,x)),y)))). given clause #72: (wt=9) 492 [hyper,1,428,21] P(n(n(i(n(x),i(x,y))))). given clause #73: (wt=16) 34 [hyper,1,23,3] P(i(x,i(y,i(i(z,u),i(i(u,v),i(z,v)))))). given clause #74: (wt=9) 543 [hyper,1,21,443] P(i(n(i(x,n(n(x)))),y)). given clause #75: (wt=9) 714 [hyper,1,21,462] P(i(n(n(n(i(x,x)))),y)). given clause #76: (wt=9) 725 [hyper,1,21,463] P(i(n(i(n(n(x)),x)),y)). given clause #77: (wt=16) 35 [hyper,1,23,4] P(i(x,i(y,i(i(i(z,u),u),i(i(u,z),z))))). given clause #78: (wt=9) 761 [hyper,1,428,753] P(n(n(i(n(i(x,y)),x)))). given clause #79: (wt=9) 763 [hyper,1,124,753] P(i(n(i(x,y)),i(z,x))). given clause #80: (wt=9) 771 [hyper,1,2,753] P(i(x,i(n(i(y,z)),y))). given clause #81: (wt=16) 37 [hyper,1,3,4] P(i(i(i(i(x,y),y),z),i(i(i(y,x),x),z))). given clause #82: (wt=9) 781 [hyper,1,428,769] P(n(n(i(x,i(n(x),y))))). given clause #83: (wt=9) 783 [hyper,1,124,769] P(i(x,i(y,i(n(x),z)))). given clause #84: (wt=9) 792 [hyper,1,18,769] P(i(x,i(n(i(y,x)),z))). given clause #85: (wt=14) 38 [hyper,1,2,4] P(i(x,i(i(i(y,z),z),i(i(z,y),y)))). given clause #86: (wt=9) 797 [hyper,1,2,769] P(i(x,i(y,i(n(y),z)))). given clause #87: (wt=10) 332 [hyper,1,124,289] P(i(n(n(x)),i(y,i(z,x)))). given clause #88: (wt=10) 339 [hyper,1,2,289] P(i(x,i(n(n(y)),i(z,y)))). given clause #89: (wt=12) 39 [hyper,1,4,10] P(i(i(i(x,i(y,i(z,y))),u),u)). given clause #90: (wt=10) 424 [hyper,1,36,412] P(i(i(i(n(n(x)),x),y),y)). given clause #91: (wt=10) 426 [hyper,1,23,412] P(i(x,i(y,i(n(n(z)),z)))). given clause #92: (wt=10) 430 [hyper,1,3,412] P(i(i(x,y),i(n(n(x)),y))). given clause #93: (wt=12) 41 [hyper,1,36,36] P(i(i(i(x,i(i(x,y),y)),z),z)). given clause #94: (wt=8) 1257 [hyper,1,424,430] P(i(n(n(n(n(x)))),x)). given clause #95: (wt=8) 1336 [hyper,1,5,1257] P(i(x,n(n(n(n(x)))))). given clause #96: (wt=9) 1272 [hyper,1,430,753] P(i(n(n(n(i(x,y)))),x)). given clause #97: (wt=12) 42 [hyper,1,23,36] P(i(x,i(y,i(z,i(i(z,u),u))))). given clause #98: (wt=9) 1296 [hyper,1,430,21] P(i(n(n(n(x))),i(x,y))). given clause #99: (wt=9) 1460 [hyper,1,5,1272] P(i(x,n(n(i(n(x),y))))). given clause #100: (wt=9) 1513 [hyper,1,5,1460] P(i(n(i(n(n(x)),y)),x)). given clause #101: (wt=12) 44 [hyper,1,3,36] P(i(i(i(i(x,y),y),z),i(x,z))). -------- PROOF -------- 1658 [binary,1657.1,7.1] $ANS(MV_25). ----> UNIT CONFLICT at 0.10 sec ----> 1658 [binary,1657.1,7.1] $ANS(MV_25). Length of proof is 5. Level of proof is 4. ---------------- PROOF ---------------- 1 [] -P(i(x,y))| -P(x)|P(y). 2 [] P(i(x,i(y,x))). 3 [] P(i(i(x,y),i(i(y,z),i(x,z)))). 4 [] P(i(i(i(x,y),y),i(i(y,x),x))). 7 [] -P(i(i(a,b),i(i(c,a),i(c,b))))|$ANS(MV_25). 13 [hyper,1,3,3] P(i(i(i(i(x,y),i(z,y)),u),i(i(z,x),u))). 18 [hyper,1,3,2] P(i(i(i(x,y),z),i(y,z))). 36 [hyper,1,18,4] P(i(x,i(i(x,y),y))). 44 [hyper,1,3,36] P(i(i(i(i(x,y),y),z),i(x,z))). 1657 [hyper,1,44,13] P(i(i(x,y),i(i(z,x),i(z,y)))). 1658 [binary,1657.1,7.1] $ANS(MV_25). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 101 clauses generated 6237 hyper_res generated 6237 demod & eval rewrites 0 clauses wt,lit,sk delete 0 tautologies deleted 0 clauses forward subsumed 4590 (subsumed by sos) 599 unit deletions 0 factor simplifications 0 clauses kept 1647 new demodulators 0 empty clauses 3 clauses back demodulated 0 clauses back subsumed 0 usable size 102 sos size 1550 demodulators size 0 passive size 3 hot size 0 Kbytes malloced 766 ----------- times (seconds) ----------- user CPU time 0.10 (0 hr, 0 min, 0 sec) system CPU time 0.02 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) input time 0.00 clausify time 0.00 pick given time 0.00 hyper_res time 0.01 pre_process time 0.09 renumber time 0.02 demod time 0.00 order equalities 0.00 unit deleletion 0.00 factor simplify 0.00 weigh cl time 0.00 hints keep time 0.00 sort lits time 0.00 forward subsume 0.02 delete cl time 0.00 keep cl time 0.01 hints time 0.00 print_cl time 0.00 conflict time 0.00 new demod time 0.00 post_process time 0.00 back demod time 0.00 back subsume 0.00 factor time 0.00 unindex time 0.00 That finishes the proof of the theorem. Process 5834 finished Wed Aug 6 14:25:56 2003