%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWX198-1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Tue May 5 07:05:24 PM UTC 2026 % Result : Unknown 1.80s 2.06s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SWX198-1 : TPTP v9.3.0. Released v9.3.0. % 0.11/0.12 % Command : otter-tptp-script %s % 0.14/0.33 % Computer : n006.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Tue May 5 11:10:00 EDT 2026 % 0.14/0.33 % CPUTime : % 1.37/2.01 ----- Otter 3.3f, August 2004 ----- % 1.37/2.01 The process was started by sandbox2 on n006.cluster.edu, % 1.37/2.01 Tue May 5 11:10:01 2026 % 1.37/2.01 The command was "./otter". The process ID is 5468. % 1.37/2.01 % 1.37/2.01 set(prolog_style_variables). % 1.37/2.01 set(auto). % 1.37/2.01 dependent: set(auto1). % 1.37/2.01 dependent: set(process_input). % 1.37/2.01 dependent: clear(print_kept). % 1.37/2.01 dependent: clear(print_new_demod). % 1.37/2.01 dependent: clear(print_back_demod). % 1.37/2.01 dependent: clear(print_back_sub). % 1.37/2.01 dependent: set(control_memory). % 1.37/2.01 dependent: assign(max_mem, 12000). % 1.37/2.01 dependent: assign(pick_given_ratio, 4). % 1.37/2.01 dependent: assign(stats_level, 1). % 1.37/2.01 dependent: assign(max_seconds, 10800). % 1.37/2.01 clear(print_given). % 1.37/2.01 % 1.37/2.01 list(usable). % 1.37/2.01 0 [] A=A. % 1.37/2.01 0 [] ltNat(z,z)=bfalse. % 1.37/2.01 0 [] ltNat(z,s(Z))=btrue. % 1.37/2.01 0 [] ltNat(s(X2),z)=bfalse. % 1.37/2.01 0 [] ltNat(s(X2),s(M))=ltNat(X2,M). % 1.37/2.01 0 [] le_qNat(z,Y)=btrue. % 1.37/2.01 0 [] le_qNat(s(Z),z)=bfalse. % 1.37/2.01 0 [] le_qNat(s(Z),s(M))=le_qNat(Z,M). % 1.37/2.01 0 [] lengthNat(nil)=z. % 1.37/2.01 0 [] lengthNat(cons(Y,Xs))=s(lengthNat(Xs)). % 1.37/2.01 0 [] impl(btrue,Q)=Q. % 1.37/2.01 0 [] impl(bfalse,Q)=btrue. % 1.37/2.01 0 [] append(nil,Y)=Y. % 1.37/2.01 0 [] append(cons(Z,Xs),Y)=cons(Z,append(Xs,Y)). % 1.37/2.01 0 [] rev(nil)=nil. % 1.37/2.01 0 [] rev(cons(Y,Xs))=append(rev(Xs),cons(Y,nil)). % 1.37/2.01 0 [] andb(btrue,Q)=Q. % 1.37/2.01 0 [] andb(bfalse,Q)=bfalse. % 1.37/2.01 0 [] usorted(nil)=btrue. % 1.37/2.01 0 [] usorted(cons(Y,nil))=btrue. % 1.37/2.01 0 [] usorted(cons(Y,cons(Y2,Xs)))=andb(ltNat(Y,Y2),usorted(cons(Y2,Xs))). % 1.37/2.01 0 [] allsmall(X,nil)=btrue. % 1.37/2.01 0 [] allsmall(X,cons(Z,Xs))=andb(ltNat(Z,X),allsmall(X,Xs)). % 1.37/2.01 0 [] pallsmall(X)=impl(e_q2(usorted(rev(X)),btrue),impl(e_q2(allsmall(s(z),X),btrue),e_q2(le_qNat(lengthNat(X),s(s(z))),btrue))). % 1.37/2.01 0 [] e_q2(bfalse,btrue)=bfalse. % 1.37/2.01 0 [] e_q2(btrue,bfalse)=bfalse. % 1.37/2.01 0 [] e_q(s(X),s(Y))=e_q(X,Y). % 1.37/2.01 0 [] e_q(z,s(X))=bfalse. % 1.37/2.01 0 [] e_q(s(X),z)=bfalse. % 1.37/2.01 0 [] e_q(X,X)=btrue. % 1.37/2.01 0 [] e_q2(X,X)=btrue. % 1.37/2.01 0 [] e_q2(pallsmall(X),bfalse)!=btrue. % 1.37/2.01 end_of_list. % 1.37/2.01 % 1.37/2.01 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1. % 1.37/2.01 % 1.37/2.01 All clauses are units, and equality is present; the % 1.37/2.01 strategy will be Knuth-Bendix with positive clauses in sos. % 1.37/2.01 % 1.37/2.01 dependent: set(knuth_bendix). % 1.37/2.01 dependent: set(anl_eq). % 1.37/2.01 dependent: set(para_from). % 1.37/2.01 dependent: set(para_into). % 1.37/2.01 dependent: clear(para_from_right). % 1.37/2.01 dependent: clear(para_into_right). % 1.37/2.01 dependent: set(para_from_vars). % 1.37/2.01 dependent: set(eq_units_both_ways). % 1.37/2.01 dependent: set(dynamic_demod_all). % 1.37/2.01 dependent: set(dynamic_demod). % 1.37/2.01 dependent: set(order_eq). % 1.37/2.01 dependent: set(back_demod). % 1.37/2.01 dependent: set(lrpo). % 1.37/2.01 % 1.37/2.01 ------------> process usable: % 1.37/2.01 ** KEPT (pick-wt=6): 1 [] e_q2(pallsmall(A),bfalse)!=btrue. % 1.37/2.01 % 1.37/2.01 ------------> process sos: % 1.37/2.01 ** KEPT (pick-wt=3): 2 [] A=A. % 1.37/2.01 ** KEPT (pick-wt=5): 3 [] ltNat(z,z)=bfalse. % 1.37/2.01 ---> New Demodulator: 4 [new_demod,3] ltNat(z,z)=bfalse. % 1.37/2.01 ** KEPT (pick-wt=6): 5 [] ltNat(z,s(A))=btrue. % 1.37/2.01 ---> New Demodulator: 6 [new_demod,5] ltNat(z,s(A))=btrue. % 1.37/2.01 ** KEPT (pick-wt=6): 7 [] ltNat(s(A),z)=bfalse. % 1.37/2.01 ---> New Demodulator: 8 [new_demod,7] ltNat(s(A),z)=bfalse. % 1.37/2.01 ** KEPT (pick-wt=9): 9 [] ltNat(s(A),s(B))=ltNat(A,B). % 1.37/2.01 ---> New Demodulator: 10 [new_demod,9] ltNat(s(A),s(B))=ltNat(A,B). % 1.37/2.01 ** KEPT (pick-wt=5): 11 [] le_qNat(z,A)=btrue. % 1.37/2.01 ---> New Demodulator: 12 [new_demod,11] le_qNat(z,A)=btrue. % 1.37/2.01 ** KEPT (pick-wt=6): 13 [] le_qNat(s(A),z)=bfalse. % 1.37/2.01 ---> New Demodulator: 14 [new_demod,13] le_qNat(s(A),z)=bfalse. % 1.37/2.01 ** KEPT (pick-wt=9): 15 [] le_qNat(s(A),s(B))=le_qNat(A,B). % 1.37/2.01 ---> New Demodulator: 16 [new_demod,15] le_qNat(s(A),s(B))=le_qNat(A,B). % 1.37/2.01 ** KEPT (pick-wt=4): 17 [] lengthNat(nil)=z. % 1.37/2.01 ---> New Demodulator: 18 [new_demod,17] lengthNat(nil)=z. % 1.37/2.01 ** KEPT (pick-wt=8): 19 [] lengthNat(cons(A,B))=s(lengthNat(B)). % 1.37/2.01 ** KEPT (pick-wt=5): 20 [] impl(btrue,A)=A. % 1.37/2.01 ---> New Demodulator: 21 [new_demod,20] impl(btrue,A)=A. % 1.37/2.01 ** KEPT (pick-wt=5): 22 [] impl(bfalse,A)=btrue. % 1.37/2.01 ---> New Demodulator: 23 [new_demod,22] impl(bfalse,A)=btrue. % 1.37/2.01 ** KEPT (pick-wt=5): 24 [] append(nil,A)=A. % 1.37/2.01 ---> New Demodulator: 25 [new_demod,24] append(nil,A)=A. % 1.37/2.01 ** KEPT (pick-wt=11): 27 [copy,26,flip.1] cons(A,append(B,C))=append(cons(A,B),C). % 1.37/2.01 ---> New Demodulator: 28 [new_demod,27] cons(A,append(B,C))=append(cons(A,B),C). % 1.37/2.01 ** KEPT (pick-wt=4): 29 [] rev(nil)=nil. % 1.37/2.01 ---> New Demodulator: 30 [new_demod,29] rev(nil)=nil. % 1.37/2.01 ** KEPT (pick-wt=11): 31 [] rev(cons(A,B))=append(rev(B),cons(A,nil)). % 1.80/2.06 ---> New Demodulator: 32 [new_demod,31] rev(cons(A,B))=append(rev(B),cons(A,nil)). % 1.80/2.06 ** KEPT (pick-wt=5): 33 [] andb(btrue,A)=A. % 1.80/2.06 ---> New Demodulator: 34 [new_demod,33] andb(btrue,A)=A. % 1.80/2.06 ** KEPT (pick-wt=5): 35 [] andb(bfalse,A)=bfalse. % 1.80/2.06 ---> New Demodulator: 36 [new_demod,35] andb(bfalse,A)=bfalse. % 1.80/2.06 ** KEPT (pick-wt=4): 37 [] usorted(nil)=btrue. % 1.80/2.06 ---> New Demodulator: 38 [new_demod,37] usorted(nil)=btrue. % 1.80/2.06 ** KEPT (pick-wt=6): 39 [] usorted(cons(A,nil))=btrue. % 1.80/2.06 ---> New Demodulator: 40 [new_demod,39] usorted(cons(A,nil))=btrue. % 1.80/2.06 ** KEPT (pick-wt=15): 41 [] usorted(cons(A,cons(B,C)))=andb(ltNat(A,B),usorted(cons(B,C))). % 1.80/2.06 ---> New Demodulator: 42 [new_demod,41] usorted(cons(A,cons(B,C)))=andb(ltNat(A,B),usorted(cons(B,C))). % 1.80/2.06 ** KEPT (pick-wt=5): 43 [] allsmall(A,nil)=btrue. % 1.80/2.06 ---> New Demodulator: 44 [new_demod,43] allsmall(A,nil)=btrue. % 1.80/2.06 ** KEPT (pick-wt=13): 45 [] allsmall(A,cons(B,C))=andb(ltNat(B,A),allsmall(A,C)). % 1.80/2.06 ** KEPT (pick-wt=24): 47 [copy,46,flip.1] impl(e_q2(usorted(rev(A)),btrue),impl(e_q2(allsmall(s(z),A),btrue),e_q2(le_qNat(lengthNat(A),s(s(z))),btrue)))=pallsmall(A). % 1.80/2.06 ---> New Demodulator: 48 [new_demod,47] impl(e_q2(usorted(rev(A)),btrue),impl(e_q2(allsmall(s(z),A),btrue),e_q2(le_qNat(lengthNat(A),s(s(z))),btrue)))=pallsmall(A). % 1.80/2.06 ** KEPT (pick-wt=5): 49 [] e_q2(bfalse,btrue)=bfalse. % 1.80/2.06 ---> New Demodulator: 50 [new_demod,49] e_q2(bfalse,btrue)=bfalse. % 1.80/2.06 ** KEPT (pick-wt=5): 51 [] e_q2(btrue,bfalse)=bfalse. % 1.80/2.06 ---> New Demodulator: 52 [new_demod,51] e_q2(btrue,bfalse)=bfalse. % 1.80/2.06 ** KEPT (pick-wt=9): 53 [] e_q(s(A),s(B))=e_q(A,B). % 1.80/2.06 ---> New Demodulator: 54 [new_demod,53] e_q(s(A),s(B))=e_q(A,B). % 1.80/2.06 ** KEPT (pick-wt=6): 55 [] e_q(z,s(A))=bfalse. % 1.80/2.06 ---> New Demodulator: 56 [new_demod,55] e_q(z,s(A))=bfalse. % 1.80/2.06 ** KEPT (pick-wt=6): 57 [] e_q(s(A),z)=bfalse. % 1.80/2.06 ---> New Demodulator: 58 [new_demod,57] e_q(s(A),z)=bfalse. % 1.80/2.06 ** KEPT (pick-wt=5): 59 [] e_q(A,A)=btrue. % 1.80/2.06 ---> New Demodulator: 60 [new_demod,59] e_q(A,A)=btrue. % 1.80/2.06 ** KEPT (pick-wt=5): 61 [] e_q2(A,A)=btrue. % 1.80/2.06 ---> New Demodulator: 62 [new_demod,61] e_q2(A,A)=btrue. % 1.80/2.06 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A. % 1.80/2.06 >>>> Starting back demodulation with 4. % 1.80/2.06 >>>> Starting back demodulation with 6. % 1.80/2.06 >>>> Starting back demodulation with 8. % 1.80/2.06 >>>> Starting back demodulation with 10. % 1.80/2.06 >>>> Starting back demodulation with 12. % 1.80/2.06 >>>> Starting back demodulation with 14. % 1.80/2.06 >>>> Starting back demodulation with 16. % 1.80/2.06 >>>> Starting back demodulation with 18. % 1.80/2.06 ** KEPT (pick-wt=8): 63 [copy,19,flip.1] s(lengthNat(A))=lengthNat(cons(B,A)). % 1.80/2.06 >>>> Starting back demodulation with 21. % 1.80/2.06 >>>> Starting back demodulation with 23. % 1.80/2.06 >>>> Starting back demodulation with 25. % 1.80/2.06 >>>> Starting back demodulation with 28. % 1.80/2.06 >>>> Starting back demodulation with 30. % 1.80/2.06 >>>> Starting back demodulation with 32. % 1.80/2.06 >>>> Starting back demodulation with 34. % 1.80/2.06 >>>> Starting back demodulation with 36. % 1.80/2.06 >>>> Starting back demodulation with 38. % 1.80/2.06 >>>> Starting back demodulation with 40. % 1.80/2.06 >>>> Starting back demodulation with 42. % 1.80/2.06 >>>> Starting back demodulation with 44. % 1.80/2.06 ** KEPT (pick-wt=13): 64 [copy,45,flip.1] andb(ltNat(A,B),allsmall(B,C))=allsmall(B,cons(A,C)). % 1.80/2.06 >>>> Starting back demodulation with 48. % 1.80/2.06 >>>> Starting back demodulation with 50. % 1.80/2.06 >>>> Starting back demodulation with 52. % 1.80/2.06 >>>> Starting back demodulation with 54. % 1.80/2.06 >>>> Starting back demodulation with 56. % 1.80/2.06 >>>> Starting back demodulation with 58. % 1.80/2.06 >>>> Starting back demodulation with 60. % 1.80/2.06 >>>> Starting back demodulation with 62. % 1.80/2.06 Following clause subsumed by 19 during input processing: 0 [copy,63,flip.1] lengthNat(cons(A,B))=s(lengthNat(B)). % 1.80/2.06 Following clause subsumed by 45 during input processing: 0 [copy,64,flip.1] allsmall(A,cons(B,C))=andb(ltNat(B,A),allsmall(A,C)). % 1.80/2.06 % 1.80/2.06 ======= end of input processing ======= % 1.80/2.06 % 1.80/2.06 =========== start of search =========== % 1.80/2.06 % 1.80/2.06 % 1.80/2.06 Resetting weight limit to 11. % 1.80/2.06 % 1.80/2.06 % 1.80/2.06 Resetting weight limit to 11. % 1.80/2.06 % 1.80/2.06 sos_size=151 % 1.80/2.06 % 1.80/2.06 Search stopped because sos empty. % 1.80/2.06 % 1.80/2.06 % 1.80/2.06 Search stopped because sos empty. % 1.80/2.06 % 1.80/2.06 ============ end of search ============ % 1.80/2.06 % 1.80/2.06 -------------- statistics ------------- % 1.80/2.06 clauses given 256 % 1.80/2.06 clauses generated 7536 % 1.80/2.06 clauses kept 283 % 1.80/2.06 clauses forward subsumed 2118 % 1.80/2.06 clauses back subsumed 4 % 1.80/2.06 Kbytes malloced 6835 % 1.80/2.06 % 1.80/2.06 ----------- times (seconds) ----------- % 1.80/2.06 user CPU time 0.05 (0 hr, 0 min, 0 sec) % 1.80/2.06 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 1.80/2.06 wall-clock time 1 (0 hr, 0 min, 1 sec) % 1.80/2.06 % 1.80/2.06 Process 5468 finished Tue May 5 11:10:02 2026 % 1.80/2.06 Otter interrupted % 1.80/2.06 PROOF NOT FOUND %------------------------------------------------------------------------------