----- Otter 3.0.3d, Feb 1995 ----- The job was started by mccune on gyro, Tue Feb 28 10:45:39 1995 The command was "otter3". op(400,xfx,^). op(400,xfx,v). set(knuth_bendix). 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(print_kept). clear(print_new_demod). clear(print_back_demod). assign(max_weight,17). assign(pick_given_ratio,5). assign(max_mem,16000). set(hyper_res). set(order_history). set(para_from_units_only). set(para_into_units_only). list(sos). 0 [] (x^y) v (x^ (x v y))=x. 0 [] (x^x) v (y^ (x v x))=x. 0 [] (x^y) v (y^ (x v y))=y. 0 [] ((x^y) v (y^z)) v y=y. 0 [] ((x v (y v z))^ (u v y))^y=y. end_of_list. list(usable). 0 [] x=x. 0 [] b^ (a v (b v c))!=b| ((b v a)^ (b v c))^b!=b. end_of_list. ------------> process usable: ** KEPT (wt=3): 1 [] x=x. ** KEPT (wt=20): 2 [] b^ (a v (b v c))!=b| ((b v a)^ (b v c))^b!=b. Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] x=x. ------------> process sos: ** KEPT (wt=11): 3 [] (x^y) v (x^ (x v y))=x. ---> New Demodulator: 4 [new_demod,3] (x^y) v (x^ (x v y))=x. ** KEPT (wt=11): 5 [] (x^x) v (y^ (x v x))=x. ---> New Demodulator: 6 [new_demod,5] (x^x) v (y^ (x v x))=x. ** KEPT (wt=11): 7 [] (x^y) v (y^ (x v y))=y. ---> New Demodulator: 8 [new_demod,7] (x^y) v (y^ (x v y))=y. ** KEPT (wt=11): 9 [] ((x^y) v (y^z)) v y=y. ---> New Demodulator: 10 [new_demod,9] ((x^y) v (y^z)) v y=y. ** KEPT (wt=13): 11 [] ((x v (y v z))^ (u v y))^y=y. ---> New Demodulator: 12 [new_demod,11] ((x v (y v z))^ (u v y))^y=y. >>>> Starting back demodulation with 4. >>>> Starting back demodulation with 6. >>>> Starting back demodulation with 8. >>>> Starting back demodulation with 10. >>>> Starting back demodulation with 12. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=11) 3 [] (x^y) v (x^ (x v y))=x. given clause #2: (wt=11) 5 [] (x^x) v (y^ (x v x))=x. given clause #3: (wt=11) 7 [] (x^y) v (y^ (x v y))=y. given clause #4: (wt=11) 9 [] ((x^y) v (y^z)) v y=y. given clause #5: (wt=5) 13 [para_into,9.1.1.1,7.1.1] x v x=x. given clause #6: (wt=5) 25 [para_from,13.1.1,7.1.1.2.2,demod,14] x^x=x. given clause #7: (wt=13) 11 [] ((x v (y v z))^ (u v y))^y=y. given clause #8: (wt=7) 27 [back_demod,15,demod,26] x v (y^x)=x. given clause #9: (wt=7) 47 [para_from,27.1.1,9.1.1.1] (x^y) v y=y. given clause #10: (wt=9) 31 [para_from,25.1.1,9.1.1.1.1] (x v (x^y)) v x=x. given clause #11: (wt=9) 51 [para_from,27.1.1,3.1.1.2.2,demod,26] (x^ (y^x)) v x=x. given clause #12: (wt=9) 53 [para_from,47.1.1,3.1.1.2.2,demod,14] (x^y)^y=x^y. given clause #13: (wt=17) 19 [para_from,9.1.1,3.1.1.2.2,demod,14] ((x^y) v (y^z))^y= (x^y) v (y^z). given clause #14: (wt=9) 55 [back_demod,41,demod,54] (x v (y v z))^y=y. given clause #15: (wt=7) 73 [para_into,55.1.1.1.2,27.1.1] (x v y)^y=y. given clause #16: (wt=7) 77 [para_into,55.1.1.1,51.1.1] (x v y)^x=x. given clause #17: (wt=7) 79 [back_demod,57,demod,78,flip.1] x v (x^y)=x. given clause #18: (wt=7) 111 [para_from,79.1.1,3.1.1.2.2,demod,94,26] (x^y) v x=x. given clause #19: (wt=11) 33 [para_into,11.1.1.1.1.2,13.1.1] ((x v y)^ (z v y))^y=y. given clause #20: (wt=7) 117 [para_into,33.1.1.1.1,111.1.1,demod,116] x^ (y v x)=x. given clause #21: (wt=9) 81 [para_into,73.1.1.1,27.1.1] x^ (y^x)=y^x. given clause #22: (wt=9) 93 [para_into,77.1.1.1,3.1.1] x^ (x^y)=x^y. given clause #23: (wt=9) 99 [para_into,79.1.1.2,77.1.1] (x v y) v x=x v y. given clause #24: (wt=7) 137 [para_from,99.1.1,117.1.1.2] x^ (x v y)=x. given clause #25: (wt=17) 35 [para_into,11.1.1.1.1.2,7.1.1] ((x v y)^ (z v (u^y)))^ (u^y)=u^y. given clause #26: (wt=9) 101 [para_into,79.1.1.2,73.1.1] (x v y) v y=x v y. given clause #27: (wt=9) 105 [back_demod,97,demod,100,26] x v (x v y)=x v y. given clause #28: (wt=9) 107 [back_demod,89,demod,102,26] x v (y v x)=y v x. given clause #29: (wt=9) 115 [para_from,111.1.1,19.1.1.1,demod,112] (x^y)^x=x^y. given clause #30: (wt=9) 143 [para_from,99.1.1,55.1.1.1] ((x v y) v z)^x=x. given clause #31: (wt=17) 37 [para_into,11.1.1.1.1.2,3.1.1] ((x v y)^ (z v (y^u)))^ (y^u)=y^u. given clause #32: (wt=9) 157 [para_from,107.1.1,55.1.1.1.2] (x v (y v z))^z=z. given clause #33: (wt=9) 159 [para_into,115.1.1.1,55.1.1,demod,56] x^ (y v (x v z))=x. given clause #34: (wt=9) 174 [para_into,143.1.1.1.1,107.1.1] ((x v y) v z)^y=y. given clause #35: (wt=9) 178 [para_from,143.1.1,115.1.1.1,demod,144] x^ ((x v y) v z)=x. given clause #36: (wt=9) 200 [para_from,157.1.1,115.1.1.1,demod,158] x^ (y v (z v x))=x. given clause #37: (wt=11) 39 [para_into,11.1.1.1.1,13.1.1] ((x v y)^ (z v x))^x=x. ----> UNIT CONFLICT at 0.82 sec ----> 229 [binary,228.1,1.1] $F. Length of proof is 23. Level of proof is 13. ---------------- PROOF ---------------- 1 [] x=x. 2 [] b^ (a v (b v c))!=b| ((b v a)^ (b v c))^b!=b. 3 [] (x^y) v (x^ (x v y))=x. 5 [] (x^x) v (y^ (x v x))=x. 7 [] (x^y) v (y^ (x v y))=y. 9 [] ((x^y) v (y^z)) v y=y. 11 [] ((x v (y v z))^ (u v y))^y=y. 14,13 [para_into,9.1.1.1,7.1.1] x v x=x. 15 [back_demod,5,demod,14] (x^x) v (y^x)=x. 19 [para_from,9.1.1,3.1.1.2.2,demod,14] ((x^y) v (y^z))^y= (x^y) v (y^z). 26,25 [para_from,13.1.1,7.1.1.2.2,demod,14] x^x=x. 27 [back_demod,15,demod,26] x v (y^x)=x. 31 [para_from,25.1.1,9.1.1.1.1] (x v (x^y)) v x=x. 39 [para_into,11.1.1.1.1,13.1.1] ((x v y)^ (z v x))^x=x. 41 [para_into,11.1.1.1.2,13.1.1] ((x v (y v z))^y)^y=y. 47 [para_from,27.1.1,9.1.1.1] (x^y) v y=y. 51 [para_from,27.1.1,3.1.1.2.2,demod,26] (x^ (y^x)) v x=x. 54,53 [para_from,47.1.1,3.1.1.2.2,demod,14] (x^y)^y=x^y. 56,55 [back_demod,41,demod,54] (x v (y v z))^y=y. 57 [para_from,31.1.1,3.1.1.2.2,demod,14] (x v (x^y))^x=x v (x^y). 78,77 [para_into,55.1.1.1,51.1.1] (x v y)^x=x. 79 [back_demod,57,demod,78,flip.1] x v (x^y)=x. 94,93 [para_into,77.1.1.1,3.1.1] x^ (x^y)=x^y. 99 [para_into,79.1.1.2,77.1.1] (x v y) v x=x v y. 112,111 [para_from,79.1.1,3.1.1.2.2,demod,94,26] (x^y) v x=x. 115 [para_from,111.1.1,19.1.1.1,demod,112] (x^y)^x=x^y. 160,159 [para_into,115.1.1.1,55.1.1,demod,56] x^ (y v (x v z))=x. 167 [back_demod,2,demod,160] b!=b| ((b v a)^ (b v c))^b!=b. 223,222 [para_into,39.1.1.1.2,99.1.1] ((x v y)^ (x v z))^x=x. 228 [back_demod,167,demod,223] b!=b. 229 [binary,228.1,1.1] $F. ------------ end of proof ------------- Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 37 clauses generated 914 hyper_res generated 0 para_from generated 433 para_into generated 481 demod & eval rewrites 1192 clauses wt,lit,sk delete 68 tautologies deleted 0 clauses forward subsumed 762 (subsumed by sos) 0 unit deletions 0 factor simplifications 0 clauses kept 116 new demodulators 112 empty clauses 1 clauses back demodulated 24 clauses back subsumed 0 usable size 33 sos size 59 demodulators size 90 passive size 0 hot size 0 Kbytes malloced 255 ----------- times (seconds) ----------- user CPU time 0.84 (0 hr, 0 min, 0 sec) system CPU time 0.44 (0 hr, 0 min, 0 sec) wall-clock time 1 (0 hr, 0 min, 1 sec) input time 0.05 clausify time 0.00 process input 0.03 hyper_res time 0.00 para_into time 0.05 para_from time 0.06 pre_process time 0.58 renumber time 0.04 demod time 0.25 order equalities 0.03 unit deleletion 0.00 factor simplify 0.00 weigh cl time 0.02 sort lits time 0.00 forward subsume 0.05 delete cl time 0.01 keep cl time 0.07 print_cl time 0.01 conflict time 0.03 new demod time 0.01 post_process time 0.07 back demod time 0.06 back subsume 0.00 factor time 0.00 unindex time 0.00 The job finished Tue Feb 28 10:45:40 1995