----- Otter 3.3, August 2003 ----- The process was started by mccune on gyro.thornwood, Wed Aug 6 14:25:58 2003 The command was "../../bin/otter". The process ID is 5955. 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(process_input). dependent: set(lrpo). clear(eq_units_both_ways). WARNING: set(process_input) flag already set. set(process_input). WARNING: set(index_for_back_demod) flag already set. set(index_for_back_demod). WARNING: set(lrpo) flag already set. set(lrpo). lex([e,f(x,x),g(x)]). assign(pick_given_ratio,3). assign(max_proofs,4). assign(max_mem,12000). assign(max_weight,80). assign(demod_limit,-1). assign(change_limit_after,12). assign(new_max_weight,25). clear(print_kept). clear(print_new_demod). clear(print_back_demod). weight_list(pick_and_purge). weight(EQ(f(e,e),e),2). weight(EQ(f(e,f(x,f(x,f(x,e)))),e),2). weight(EQ(f(f(x,e),f(f(x,e),f(x,e))),e),2). weight(EQ(f(f(x,e),f(f(x,e),f(x,f(f(f(e,f(x,e)),y),f(y,y))))),f(x,e)),2). weight(EQ(f(f(x,y),e),f(x,f(y,f(z,f(z,f(z,e)))))),2). weight(EQ(f(f(x,y),f(e,z)),f(x,f(y,z))),2). weight(EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e),2). weight(EQ(f(x,e),x),2). weight(EQ(f(x,f(f(x,f(f(x,y),f(e,f(f(e,z),f(e,z))))),z)),y),2). weight(EQ(f(x,f(f(x,f(f(x,y),f(e,f(z,z)))),f(f(e,f(f(e,z),u)),f(e,f(u,u))))),y),2). weight(EQ(f(x,f(f(x,f(f(x,y),z)),f(f(e,z),f(e,z)))),y),2). weight(EQ(f(x,f(f(y,z),u)),f(f(x,y),f(f(e,z),u))),2). weight(EQ(f(x,f(x,f(f(x,f(y,f(z,e))),f(f(f(e,e),u),f(u,u))))),f(y,z)),2). weight(EQ(f(x,f(x,f(f(y,z),f(z,z)))),f(x,f(x,f(y,e)))),2). weight(EQ(f(x,f(x,f(x,e))),e),2). weight(EQ(f(x,f(x,f(x,f(y,e)))),y),2). weight(EQ(f(x,f(x,f(x,f(y,f(z,e))))),f(y,z)),2). weight(EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)),2). end_of_list. list(usable). 0 [] EQ(x,x). end_of_list. list(sos). 0 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). end_of_list. list(passive). 1 [] -EQ(f(e,a),a)|$ANS(lid). 2 [] -EQ(f(a,e),a)|$ANS(rid). 3 [] -EQ(f(a,f(a,a)),e)|$ANS(exp3). 4 [] -EQ(f(f(a,b),c),f(a,f(b,c)))|$ANS(assoc). end_of_list. ------------> process usable: ** KEPT (pick-wt=3): 5 [] EQ(x,x). ------------> process sos: ** KEPT (pick-wt=17): 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). ---> New Demodulator: 7 [new_demod,6] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). >>>> Starting back demodulation with 7. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=17) 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). given clause #2: (wt=2) 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). given clause #3: (wt=2) 22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). given clause #4: (wt=2) 34 [para_into,22.1.1.1,22.1.1,demod,23] EQ(f(x,f(f(y,z),u)),f(f(x,y),f(f(e,z),u))). given clause #5: (wt=15) 24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). given clause #6: (wt=15) 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). given clause #7: (wt=2) 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). given clause #8: (wt=2) 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). -------- PROOF -------- 155 [binary,153.1,2.1] $ANS(rid). ----> UNIT CONFLICT at 0.00 sec ----> 155 [binary,153.1,2.1] $ANS(rid). Length of proof is 8. Level of proof is 6. ---------------- PROOF ---------------- 2 [] -EQ(f(a,e),a)|$ANS(rid). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 155 [binary,153.1,2.1] $ANS(rid). ------------ end of proof ------------- -------- PROOF -------- 178 [binary,176.1,3.1] $ANS(exp3). ----> UNIT CONFLICT at 0.00 sec ----> 178 [binary,176.1,3.1] $ANS(exp3). Length of proof is 10. Level of proof is 7. ---------------- PROOF ---------------- 3 [] -EQ(f(a,f(a,a)),e)|$ANS(exp3). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 25,24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 141 [para_into,99.1.1.2.2,24.1.1] EQ(f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),y)),e). 154,153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 176 [back_demod,141,demod,154,154,25,154,154,25] EQ(f(x,f(x,x)),e). 178 [binary,176.1,3.1] $ANS(exp3). ------------ end of proof ------------- -------- PROOF -------- 201 [binary,199.1,1.1] $ANS(lid). ----> UNIT CONFLICT at 0.00 sec ----> 201 [binary,199.1,1.1] $ANS(lid). Length of proof is 12. Level of proof is 8. ---------------- PROOF ---------------- 1 [] -EQ(f(e,a),a)|$ANS(lid). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 25,24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 109 [para_from,79.1.1,24.1.1.1.2.2] EQ(f(f(f(x,e),f(f(x,e),x)),f(x,e)),f(x,e)). 141 [para_into,99.1.1.2.2,24.1.1] EQ(f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),y)),e). 154,153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 177,176 [back_demod,141,demod,154,154,25,154,154,25] EQ(f(x,f(x,x)),e). 199 [back_demod,109,demod,154,154,177,154,154] EQ(f(e,x),x). 201 [binary,199.1,1.1] $ANS(lid). ------------ end of proof ------------- -------- PROOF -------- 220 [binary,218.1,4.1] $ANS(assoc). ----> UNIT CONFLICT at 0.01 sec ----> 220 [binary,218.1,4.1] $ANS(assoc). Length of proof is 17. Level of proof is 9. ---------------- PROOF ---------------- 4 [] -EQ(f(f(a,b),c),f(a,f(b,c)))|$ANS(assoc). 6 [] EQ(f(x,f(f(x,f(f(x,y),z)),f(e,f(z,z)))),y). 11 [para_into,6.1.1.2.1,6.1.1] EQ(f(x,f(y,f(e,f(f(e,f(z,z)),f(e,f(z,z)))))),f(f(x,y),z)). 23,22 [para_into,11.1.1.2.2,6.1.1,flip.1] EQ(f(f(x,y),f(e,z)),f(x,f(y,z))). 25,24 [para_into,11.1.1,6.1.1,demod,23,flip.1] EQ(f(f(x,f(x,f(x,f(y,f(z,z))))),z),y). 28 [back_demod,11,demod,23] EQ(f(x,f(y,f(e,f(e,f(f(z,z),f(z,z)))))),f(f(x,y),z)). 32 [back_demod,6,demod,23] EQ(f(x,f(x,f(f(f(x,y),z),f(z,z)))),y). 79 [para_into,32.1.1.2.2,22.1.1,demod,23] EQ(f(x,f(x,f(x,f(y,e)))),y). 99 [para_into,79.1.1.2.2,22.1.1] EQ(f(f(x,y),f(f(x,y),f(x,f(y,e)))),e). 108,107 [para_from,79.1.1,24.1.1.1.2] EQ(f(f(x,e),e),x). 109 [para_from,79.1.1,24.1.1.1.2.2] EQ(f(f(f(x,e),f(f(x,e),x)),f(x,e)),f(x,e)). 119,118 [para_from,79.1.1,32.1.1.2.2.1.1] EQ(f(x,f(x,f(f(y,z),f(z,z)))),f(x,f(x,f(y,e)))). 130 [back_demod,28,demod,119] EQ(f(x,f(y,f(e,f(e,f(z,e))))),f(f(x,y),z)). 141 [para_into,99.1.1.2.2,24.1.1] EQ(f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),f(f(f(x,f(x,f(x,f(y,f(f(z,e),f(z,e)))))),z),y)),e). 154,153 [para_from,99.1.1,24.1.1.1.2,demod,108] EQ(f(x,e),x). 177,176 [back_demod,141,demod,154,154,25,154,154,25] EQ(f(x,f(x,x)),e). 185 [back_demod,130,demod,154,flip.1] EQ(f(f(x,y),z),f(x,f(y,f(e,f(e,z))))). 200,199 [back_demod,109,demod,154,154,177,154,154] EQ(f(e,x),x). 218 [back_demod,185,demod,200,200] EQ(f(f(x,y),z),f(x,f(y,z))). 220 [binary,218.1,4.1] $ANS(assoc). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 8 clauses generated 124 para_from generated 49 para_into generated 75 demod & eval rewrites 1119 clauses wt,lit,sk delete 2 tautologies deleted 0 clauses forward subsumed 110 (subsumed by sos) 9 unit deletions 0 factor simplifications 0 clauses kept 115 new demodulators 97 empty clauses 4 clauses back demodulated 101 clauses back subsumed 0 usable size 1 sos size 13 demodulators size 13 passive size 4 hot size 0 Kbytes malloced 479 ----------- times (seconds) ----------- user CPU time 0.01 (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 process input 0.00 pick given time 0.00 para_into time 0.00 para_from time 0.00 pre_process time 0.01 renumber time 0.00 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 0.00 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 5955 finished Wed Aug 6 14:25:58 2003