----- 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 5824. set(hyper_res). assign(pick_given_ratio,3). clear(back_sub). assign(max_proofs,2). assign(max_weight,16). clear(print_kept). set(order_history). list(usable). 1 [] -P(e(x,y))| -P(x)|P(y). end_of_list. list(sos). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). end_of_list. list(passive). 3 [] -P(e(e(e(a,b),e(c,a)),e(b,c)))|$Ans(EC_1). 4 [] -P(e(e(a,e(b,c)),e(e(a,b),c)))|$Ans(EC_2). end_of_list. list(demodulators). 5 [] e(e(x,x),y)=junk. 6 [] e(y,e(x,x))=junk. 7 [] e(x,junk)=junk. 8 [] e(junk,x)=junk. 9 [] P(junk)=$T. end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). given clause #2: (wt=16) 10 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). given clause #3: (wt=8) 12 [hyper,1,10,2] P(e(e(x,y),e(x,y))). given clause #4: (wt=12) 13 [hyper,1,2,12] P(e(e(x,e(y,z)),e(e(y,z),x))). given clause #5: (wt=16) 11 [hyper,1,10,10] P(e(e(x,y),e(e(x,z),e(e(u,y),e(z,u))))). given clause #6: (wt=12) 14 [hyper,1,13,13] P(e(e(e(x,y),z),e(z,e(x,y)))). given clause #7: (wt=12) 15 [hyper,1,10,13] P(e(e(x,y),e(e(x,z),e(z,y)))). given clause #8: (wt=12) 18 [hyper,1,13,2] P(e(e(e(x,y),e(z,x)),e(z,y))). given clause #9: (wt=16) 16 [hyper,1,2,13] P(e(e(x,e(e(y,z),u)),e(e(u,e(y,z)),x))). given clause #10: (wt=4) 32 [hyper,1,18,14] P(e(x,x)). given clause #11: (wt=8) 31 [hyper,1,18,15] P(e(e(e(x,y),x),y)). given clause #12: (wt=8) 39 [hyper,1,15,32] P(e(e(x,y),e(y,x))). given clause #13: (wt=16) 17 [hyper,1,13,10] P(e(e(e(x,y),z),e(z,e(e(u,y),e(x,u))))). given clause #14: (wt=8) 43 [hyper,1,14,31] P(e(x,e(e(y,x),y))). given clause #15: (wt=8) 55 [hyper,1,18,43] P(e(e(x,e(x,y)),y)). given clause #16: (wt=8) 66 [hyper,1,39,55] P(e(x,e(y,e(y,x)))). given clause #17: (wt=16) 19 [hyper,1,13,11] P(e(e(e(x,y),e(e(z,u),e(y,z))),e(x,u))). given clause #18: (wt=8) 67 [hyper,1,18,55] P(e(x,e(y,e(x,y)))). given clause #19: (wt=8) 79 [hyper,1,10,66] P(e(e(e(x,y),y),x)). given clause #20: (wt=8) 94 [hyper,1,39,67] P(e(e(x,e(y,x)),y)). given clause #21: (wt=12) 20 [hyper,1,10,11] P(e(e(e(x,y),z),e(e(z,x),y))). given clause #22: (wt=8) 110 [hyper,1,39,79] P(e(x,e(e(x,y),y))). given clause #23: (wt=12) 24 [hyper,1,14,15] P(e(e(e(x,y),e(y,z)),e(x,z))). given clause #24: (wt=12) 33 [hyper,1,18,11] P(e(e(e(e(x,y),e(z,x)),z),y)). given clause #25: (wt=16) 21 [hyper,1,11,12] P(e(e(e(x,y),z),e(e(u,e(x,y)),e(z,u)))). given clause #26: (wt=12) 40 [hyper,1,11,32] P(e(e(x,y),e(e(z,x),e(y,z)))). -------- PROOF -------- 197 [binary,196.1,3.1] $Ans(EC_1). ----> UNIT CONFLICT at 0.01 sec ----> 197 [binary,196.1,3.1] $Ans(EC_1). Length of proof is 11. Level of proof is 7. ---------------- PROOF ---------------- 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). 3 [] -P(e(e(e(a,b),e(c,a)),e(b,c)))|$Ans(EC_1). 10 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). 11 [hyper,1,10,10] P(e(e(x,y),e(e(x,z),e(e(u,y),e(z,u))))). 12 [hyper,1,10,2] P(e(e(x,y),e(x,y))). 13 [hyper,1,2,12] P(e(e(x,e(y,z)),e(e(y,z),x))). 14 [hyper,1,13,13] P(e(e(e(x,y),z),e(z,e(x,y)))). 15 [hyper,1,10,13] P(e(e(x,y),e(e(x,z),e(z,y)))). 18 [hyper,1,13,2] P(e(e(e(x,y),e(z,x)),e(z,y))). 32 [hyper,1,18,14] P(e(x,x)). 39 [hyper,1,15,32] P(e(e(x,y),e(y,x))). 40 [hyper,1,11,32] P(e(e(x,y),e(e(z,x),e(y,z)))). 196 [hyper,1,39,40] P(e(e(e(x,y),e(z,x)),e(y,z))). 197 [binary,196.1,3.1] $Ans(EC_1). ------------ end of proof ------------- given clause #27: (wt=12) 42 [hyper,1,15,31] P(e(e(e(e(x,y),x),z),e(z,y))). given clause #28: (wt=12) 46 [hyper,1,2,31] P(e(e(x,y),e(e(e(z,y),z),x))). given clause #29: (wt=16) 22 [hyper,1,2,14] P(e(e(x,e(y,e(z,u))),e(e(e(z,u),y),x))). given clause #30: (wt=12) 47 [hyper,1,15,39] P(e(e(e(x,y),z),e(z,e(y,x)))). given clause #31: (wt=12) 49 [hyper,1,2,39] P(e(e(x,e(y,z)),e(e(z,y),x))). given clause #32: (wt=12) 51 [hyper,1,17,31] P(e(x,e(e(y,z),e(e(z,x),y)))). given clause #33: (wt=16) 23 [hyper,1,15,15] P(e(e(e(x,y),z),e(z,e(e(x,u),e(u,y))))). given clause #34: (wt=12) 54 [hyper,1,43,43] P(e(e(x,e(y,e(e(z,y),z))),x)). given clause #35: (wt=12) 57 [hyper,1,15,43] P(e(e(x,y),e(y,e(e(z,x),z)))). given clause #36: (wt=12) 59 [hyper,1,2,43] P(e(e(x,e(e(y,z),y)),e(z,x))). given clause #37: (wt=16) 25 [hyper,1,2,15] P(e(e(x,e(e(y,z),e(z,u))),e(e(y,u),x))). given clause #38: (wt=12) 60 [hyper,1,43,39] P(e(e(x,e(e(y,z),e(z,y))),x)). given clause #39: (wt=12) 61 [hyper,1,43,31] P(e(e(x,e(e(e(y,z),y),z)),x)). given clause #40: (wt=12) 65 [hyper,1,43,55] P(e(e(x,e(e(y,e(y,z)),z)),x)). given clause #41: (wt=16) 26 [hyper,1,15,14] P(e(e(e(e(x,y),z),u),e(u,e(z,e(x,y))))). given clause #42: (wt=12) 68 [hyper,1,17,55] P(e(x,e(e(y,e(z,x)),e(z,y)))). given clause #43: (wt=12) 70 [hyper,1,15,55] P(e(e(e(x,e(x,y)),z),e(z,y))). given clause #44: (wt=12) 73 [hyper,1,2,55] P(e(e(x,y),e(e(z,e(z,y)),x))). -------- PROOF -------- 550 [binary,549.1,4.1] $Ans(EC_2). ----> UNIT CONFLICT at 0.04 sec ----> 550 [binary,549.1,4.1] $Ans(EC_2). Length of proof is 11. Level of proof is 9. ---------------- PROOF ---------------- 1 [] -P(e(x,y))| -P(x)|P(y). 2 [] P(e(e(x,y),e(e(z,y),e(x,z)))). 4 [] -P(e(e(a,e(b,c)),e(e(a,b),c)))|$Ans(EC_2). 10 [hyper,1,2,2] P(e(e(x,e(e(y,z),e(u,y))),e(e(u,z),x))). 12 [hyper,1,10,2] P(e(e(x,y),e(x,y))). 13 [hyper,1,2,12] P(e(e(x,e(y,z)),e(e(y,z),x))). 14 [hyper,1,13,13] P(e(e(e(x,y),z),e(z,e(x,y)))). 15 [hyper,1,10,13] P(e(e(x,y),e(e(x,z),e(z,y)))). 18 [hyper,1,13,2] P(e(e(e(x,y),e(z,x)),e(z,y))). 31 [hyper,1,18,15] P(e(e(e(x,y),x),y)). 43 [hyper,1,14,31] P(e(x,e(e(y,x),y))). 55 [hyper,1,18,43] P(e(e(x,e(x,y)),y)). 73 [hyper,1,2,55] P(e(e(x,y),e(e(z,e(z,y)),x))). 549 [hyper,1,10,73] P(e(e(x,e(y,z)),e(e(x,y),z))). 550 [binary,549.1,4.1] $Ans(EC_2). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 44 clauses generated 1663 hyper_res generated 1663 demod & eval rewrites 62 clauses wt,lit,sk delete 270 tautologies deleted 22 clauses forward subsumed 832 (subsumed by sos) 372 unit deletions 0 factor simplifications 0 clauses kept 539 new demodulators 0 empty clauses 2 clauses back demodulated 0 clauses back subsumed 0 usable size 45 sos size 496 demodulators size 5 passive size 2 hot size 0 Kbytes malloced 447 ----------- times (seconds) ----------- user CPU time 0.04 (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 0.00 pre_process time 0.04 renumber time 0.00 demod time 0.02 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 0.00 delete cl time 0.00 keep cl time 0.00 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 5824 finished Wed Aug 6 14:25:56 2003