----- Otter 3.3, August 2003 ----- The process was started by mccune on gyro.thornwood, Wed Aug 6 14:25:54 2003 The command was "../../bin/otter". The process ID is 5741. set(auto). dependent: set(auto1). dependent: set(process_input). dependent: clear(print_kept). dependent: clear(print_new_demod). dependent: clear(print_back_demod). dependent: clear(print_back_sub). dependent: set(control_memory). dependent: assign(max_mem, 12000). dependent: assign(pick_given_ratio, 4). dependent: assign(stats_level, 1). dependent: assign(max_seconds, 10800). list(usable). 0 [] x=x. 0 [] x+y=y+x. 0 [] (x+y)+z=x+y+z. 0 [] n(n(x+y)+n(x+n(y)))=x. 0 [] x+C=C. 0 [] n(A+n(B))+n(n(A)+n(B))!=B. end_of_list. SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. All clauses are units, and equality is present; the strategy will be Knuth-Bendix with positive clauses in sos. dependent: set(knuth_bendix). dependent: set(anl_eq). dependent: set(para_from). dependent: set(para_into). dependent: clear(para_from_right). dependent: clear(para_into_right). dependent: set(para_from_vars). dependent: set(eq_units_both_ways). dependent: set(dynamic_demod_all). dependent: set(dynamic_demod). dependent: set(order_eq). dependent: set(back_demod). dependent: set(lrpo). ------------> process usable: ** KEPT (pick-wt=14): 1 [] n(A+n(B))+n(n(A)+n(B))!=B. ------------> process sos: ** KEPT (pick-wt=3): 2 [] x=x. ** KEPT (pick-wt=7): 3 [] x+y=y+x. ** KEPT (pick-wt=11): 4 [] (x+y)+z=x+y+z. ---> New Demodulator: 5 [new_demod,4] (x+y)+z=x+y+z. ** KEPT (pick-wt=13): 6 [] n(n(x+y)+n(x+n(y)))=x. ---> New Demodulator: 7 [new_demod,6] n(n(x+y)+n(x+n(y)))=x. ** KEPT (pick-wt=5): 8 [] x+C=C. ---> New Demodulator: 9 [new_demod,8] x+C=C. Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] x=x. Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] x+y=y+x. >>>> Starting back demodulation with 5. >>>> Starting back demodulation with 7. >>>> Starting back demodulation with 9. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=3) 2 [] x=x. given clause #2: (wt=5) 8 [] x+C=C. given clause #3: (wt=7) 3 [] x+y=y+x. given clause #4: (wt=5) 10 [para_into,3.1.1,8.1.1,flip.1] C+x=C. given clause #5: (wt=11) 4 [] (x+y)+z=x+y+z. given clause #6: (wt=13) 6 [] n(n(x+y)+n(x+n(y)))=x. given clause #7: (wt=8) 18 [para_into,6.1.1.1.1.1,10.1.1,demod,11] n(n(C)+n(C))=C. given clause #8: (wt=11) 15 [para_into,4.1.1.1,3.1.1,demod,5] x+y+z=y+x+z. given clause #9: (wt=11) 16 [para_into,4.1.1,3.1.1] x+y+z=y+z+x. given clause #10: (wt=11) 17 [copy,16,flip.1] x+y+z=z+x+y. given clause #11: (wt=14) 12 [para_from,3.1.1,1.1.1] n(n(A)+n(B))+n(A+n(B))!=B. given clause #12: (wt=11) 20 [para_into,6.1.1.1.1.1,8.1.1] n(n(C)+n(x+n(C)))=x. given clause #13: (wt=11) 40 [para_into,15.1.1,3.1.1,demod,5] x+y+z=x+z+y. given clause #14: (wt=11) 46 [para_into,16.1.1.2,3.1.1] x+y+z=z+y+x. given clause #15: (wt=11) 62 [para_into,20.1.1.1.2.1,3.1.1] n(n(C)+n(n(C)+x))=x. given clause #16: (wt=14) 13 [para_from,3.1.1,1.1.1.2.1] n(A+n(B))+n(n(B)+n(A))!=B. given clause #17: (wt=11) 64 [para_into,20.1.1.1,3.1.1] n(n(x+n(C))+n(C))=x. given clause #18: (wt=5) 107 [back_demod,89,demod,106,102] n(n(x))=x. -------- PROOF -------- ----> UNIT CONFLICT at 0.01 sec ----> 122 [binary,121.1,2.1] $F. Length of proof is 17. Level of proof is 8. ---------------- PROOF ---------------- 1 [] n(A+n(B))+n(n(A)+n(B))!=B. 2 [] x=x. 3 [] x+y=y+x. 4 [] (x+y)+z=x+y+z. 6 [] n(n(x+y)+n(x+n(y)))=x. 9,8 [] x+C=C. 11,10 [para_into,3.1.1,8.1.1,flip.1] C+x=C. 13 [para_from,3.1.1,1.1.1.2.1] n(A+n(B))+n(n(B)+n(A))!=B. 18 [para_into,6.1.1.1.1.1,10.1.1,demod,11] n(n(C)+n(C))=C. 20 [para_into,6.1.1.1.1.1,8.1.1] n(n(C)+n(x+n(C)))=x. 36 [para_from,18.1.1,6.1.1.1.2.1.2,demod,9] n(n(x+n(C)+n(C))+n(C))=x. 62 [para_into,20.1.1.1.2.1,3.1.1] n(n(C)+n(n(C)+x))=x. 64 [para_into,20.1.1.1,3.1.1] n(n(x+n(C))+n(C))=x. 88 [para_into,62.1.1.1.2,20.1.1] n(n(C)+x)=n(x+n(C)). 89 [para_into,62.1.1.1,3.1.1] n(n(n(C)+x)+n(C))=x. 91 [copy,88,flip.1] n(x+n(C))=n(n(C)+x). 98 [para_into,13.1.1.1.1,3.1.1] n(n(B)+A)+n(n(B)+n(A))!=B. 100,99 [para_into,64.1.1.1.1.1,4.1.1] n(n(x+y+n(C))+n(C))=x+y. 102,101 [back_demod,36,demod,100] x+n(C)=x. 106,105 [back_demod,91,demod,102,flip.1] n(n(C)+x)=n(x). 108,107 [back_demod,89,demod,106,102] n(n(x))=x. 120,119 [para_into,107.1.1.1,6.1.1,flip.1] n(x+y)+n(x+n(y))=n(x). 121 [back_demod,98,demod,120,108] B!=B. 122 [binary,121.1,2.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 18 clauses generated 213 clauses kept 81 clauses forward subsumed 191 clauses back subsumed 0 Kbytes malloced 287 ----------- times (seconds) ----------- user CPU time 0.01 (0 hr, 0 min, 0 sec) system CPU time 0.00 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) para_into time 0.00 para_from time 0.00 for_sub time 0.01 back_sub time 0.00 conflict time 0.00 demod time 0.00 That finishes the proof of the theorem. Process 5741 finished Wed Aug 6 14:25:54 2003