%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n010.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 07:05:26 PM UTC 2026 % Result : Unknown 1.92s 2.20s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.13 % Command : otter-tptp-script %s % 0.15/0.33 % Computer : n010.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue May 5 12:14:21 EDT 2026 % 0.15/0.33 % CPUTime : % 1.92/2.14 ----- Otter 3.3f, August 2004 ----- % 1.92/2.14 The process was started by sandbox on n010.cluster.edu, % 1.92/2.14 Tue May 5 12:14:21 2026 % 1.92/2.14 The command was "./otter". The process ID is 27904. % 1.92/2.14 % 1.92/2.14 set(prolog_style_variables). % 1.92/2.14 set(auto). % 1.92/2.14 dependent: set(auto1). % 1.92/2.14 dependent: set(process_input). % 1.92/2.14 dependent: clear(print_kept). % 1.92/2.14 dependent: clear(print_new_demod). % 1.92/2.14 dependent: clear(print_back_demod). % 1.92/2.14 dependent: clear(print_back_sub). % 1.92/2.14 dependent: set(control_memory). % 1.92/2.14 dependent: assign(max_mem, 12000). % 1.92/2.14 dependent: assign(pick_given_ratio, 4). % 1.92/2.14 dependent: assign(stats_level, 1). % 1.92/2.14 dependent: assign(max_seconds, 10800). % 1.92/2.14 clear(print_given). % 1.92/2.14 % 1.92/2.14 formula_list(usable). % 1.92/2.14 all A (A=A). % 1.92/2.14 all X X2 (head(cons(X,X2))=X). % 1.92/2.14 all X X2 (tail(cons(X,X2))=X2). % 1.92/2.14 all X X2 (nil!=cons(X,X2)). % 1.92/2.14 all X (proj1Suc(suc(X))=X). % 1.92/2.14 all X (zero!=suc(X)). % 1.92/2.14 i!=o. % 1.92/2.14 half(zero)=zero. % 1.92/2.14 half(suc(zero))=zero. % 1.92/2.14 all N (half(suc(suc(N)))=suc(half(N))). % 1.92/2.14 evenNat(zero). % 1.92/2.14 all N (evenNat(suc(N))<-> -evenNat(N)). % 1.92/2.14 shw(zero)=nil. % 1.92/2.14 all Y (evenNat(suc(Y))->shw(suc(Y))=cons(o,shw(half(suc(Y))))). % 1.92/2.14 all Y (-evenNat(suc(Y))->shw(suc(Y))=cons(i,shw(half(suc(Y))))). % 1.92/2.14 all Y (append(nil,Y)=Y). % 1.92/2.14 all Y Z Xs (append(cons(Z,Xs),Y)=cons(Z,append(Xs,Y))). % 1.92/2.14 all Y (addNat(zero,Y)=Y). % 1.92/2.14 all Y Z (addNat(suc(Z),Y)=suc(addNat(Z,Y))). % 1.92/2.14 all X (double(X)=addNat(X,X)). % 1.92/2.14 rd(nil)=zero. % 1.92/2.14 all Xs (rd(cons(i,Xs))=suc(double(rd(Xs)))). % 1.92/2.14 all Xs (rd(cons(o,Xs))=double(rd(Xs))). % 1.92/2.14 all X Y (x(X,Y)=rd(append(shw(X),shw(Y)))). % 1.92/2.14 -(exists X Y (x(X,Y)!=x(Y,X))). % 1.92/2.14 end_of_list. % 1.92/2.14 % 1.92/2.14 -------> usable clausifies to: % 1.92/2.14 % 1.92/2.14 list(usable). % 1.92/2.14 0 [] A=A. % 1.92/2.14 0 [] head(cons(X,X2))=X. % 1.92/2.14 0 [] tail(cons(X,X2))=X2. % 1.92/2.14 0 [] nil!=cons(X,X2). % 1.92/2.14 0 [] proj1Suc(suc(X))=X. % 1.92/2.14 0 [] zero!=suc(X). % 1.92/2.14 0 [] i!=o. % 1.92/2.14 0 [] half(zero)=zero. % 1.92/2.14 0 [] half(suc(zero))=zero. % 1.92/2.14 0 [] half(suc(suc(N)))=suc(half(N)). % 1.92/2.14 0 [] evenNat(zero). % 1.92/2.14 0 [] -evenNat(suc(N))| -evenNat(N). % 1.92/2.14 0 [] evenNat(suc(N))|evenNat(N). % 1.92/2.14 0 [] shw(zero)=nil. % 1.92/2.14 0 [] -evenNat(suc(Y))|shw(suc(Y))=cons(o,shw(half(suc(Y)))). % 1.92/2.14 0 [] evenNat(suc(Y))|shw(suc(Y))=cons(i,shw(half(suc(Y)))). % 1.92/2.14 0 [] append(nil,Y)=Y. % 1.92/2.14 0 [] append(cons(Z,Xs),Y)=cons(Z,append(Xs,Y)). % 1.92/2.14 0 [] addNat(zero,Y)=Y. % 1.92/2.14 0 [] addNat(suc(Z),Y)=suc(addNat(Z,Y)). % 1.92/2.14 0 [] double(X)=addNat(X,X). % 1.92/2.14 0 [] rd(nil)=zero. % 1.92/2.14 0 [] rd(cons(i,Xs))=suc(double(rd(Xs))). % 1.92/2.14 0 [] rd(cons(o,Xs))=double(rd(Xs)). % 1.92/2.14 0 [] x(X,Y)=rd(append(shw(X),shw(Y))). % 1.92/2.14 0 [] x(X,Y)=x(Y,X). % 1.92/2.14 end_of_list. % 1.92/2.14 % 1.92/2.14 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2. % 1.92/2.14 % 1.92/2.14 This ia a non-Horn set with equality. The strategy will be % 1.92/2.14 Knuth-Bendix, ordered hyper_res, factoring, and unit % 1.92/2.14 deletion, with positive clauses in sos and nonpositive % 1.92/2.14 clauses in usable. % 1.92/2.14 % 1.92/2.14 dependent: set(knuth_bendix). % 1.92/2.14 dependent: set(anl_eq). % 1.92/2.14 dependent: set(para_from). % 1.92/2.14 dependent: set(para_into). % 1.92/2.14 dependent: clear(para_from_right). % 1.92/2.14 dependent: clear(para_into_right). % 1.92/2.14 dependent: set(para_from_vars). % 1.92/2.14 dependent: set(eq_units_both_ways). % 1.92/2.14 dependent: set(dynamic_demod_all). % 1.92/2.14 dependent: set(dynamic_demod). % 1.92/2.14 dependent: set(order_eq). % 1.92/2.14 dependent: set(back_demod). % 1.92/2.14 dependent: set(lrpo). % 1.92/2.14 dependent: set(hyper_res). % 1.92/2.14 dependent: set(unit_deletion). % 1.92/2.14 dependent: set(factor). % 1.92/2.14 % 1.92/2.14 ------------> process usable: % 1.92/2.14 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] cons(A,B)!=nil. % 1.92/2.14 ** KEPT (pick-wt=4): 4 [copy,3,flip.1] suc(A)!=zero. % 1.92/2.14 ** KEPT (pick-wt=3): 6 [copy,5,flip.1] o!=i. % 1.92/2.14 ** KEPT (pick-wt=5): 7 [] -evenNat(suc(A))| -evenNat(A). % 1.92/2.14 ** KEPT (pick-wt=13): 9 [copy,8,flip.2] -evenNat(suc(A))|cons(o,shw(half(suc(A))))=shw(suc(A)). % 1.92/2.14 % 1.92/2.14 ------------> process sos: % 1.92/2.14 ** KEPT (pick-wt=3): 10 [] A=A. % 1.92/2.14 ** KEPT (pick-wt=6): 11 [] head(cons(A,B))=A. % 1.92/2.14 ---> New Demodulator: 12 [new_demod,11] head(cons(A,B))=A. % 1.92/2.14 ** KEPT (pick-wt=6): 13 [] tail(cons(A,B))=B. % 1.92/2.14 ---> New Demodulator: 14 [new_demod,13] tail(cons(A,B))=B. % 1.92/2.14 ** KEPT (pick-wt=5): 15 [] proj1Suc(suc(A))=A. % 1.92/2.14 ---> New Demodulator: 16 [new_demod,15] proj1Suc(suc(A))=A. % 1.92/2.14 ** KEPT (pick-wt=4): 17 [] half(zero)=zero. % 1.92/2.14 ---> New Demodulator: 18 [new_demod,17] half(zero)=zero. % 1.92/2.14 ** KEPT (pick-wt=5): 19 [] half(suc(zero))=zero. % 1.92/2.14 ---> New Demodulator: 20 [new_demod,19] half(suc(zero))=zero. % 1.92/2.14 ** KEPT (pick-wt=8): 21 [] half(suc(suc(A)))=suc(half(A)). % 1.92/2.14 ---> New Demodulator: 22 [new_demod,21] half(suc(suc(A)))=suc(half(A)). % 1.92/2.19 ** KEPT (pick-wt=2): 23 [] evenNat(zero). % 1.92/2.19 ** KEPT (pick-wt=5): 24 [] evenNat(suc(A))|evenNat(A). % 1.92/2.19 ** KEPT (pick-wt=4): 25 [] shw(zero)=nil. % 1.92/2.19 ---> New Demodulator: 26 [new_demod,25] shw(zero)=nil. % 1.92/2.19 ** KEPT (pick-wt=13): 28 [copy,27,flip.2] evenNat(suc(A))|cons(i,shw(half(suc(A))))=shw(suc(A)). % 1.92/2.19 ** KEPT (pick-wt=5): 29 [] append(nil,A)=A. % 1.92/2.19 ---> New Demodulator: 30 [new_demod,29] append(nil,A)=A. % 1.92/2.19 ** KEPT (pick-wt=11): 32 [copy,31,flip.1] cons(A,append(B,C))=append(cons(A,B),C). % 1.92/2.19 ---> New Demodulator: 33 [new_demod,32] cons(A,append(B,C))=append(cons(A,B),C). % 1.92/2.19 ** KEPT (pick-wt=5): 34 [] addNat(zero,A)=A. % 1.92/2.19 ---> New Demodulator: 35 [new_demod,34] addNat(zero,A)=A. % 1.92/2.19 ** KEPT (pick-wt=9): 37 [copy,36,flip.1] suc(addNat(A,B))=addNat(suc(A),B). % 1.92/2.19 ---> New Demodulator: 38 [new_demod,37] suc(addNat(A,B))=addNat(suc(A),B). % 1.92/2.19 ** KEPT (pick-wt=6): 39 [] double(A)=addNat(A,A). % 1.92/2.19 ---> New Demodulator: 40 [new_demod,39] double(A)=addNat(A,A). % 1.92/2.19 ** KEPT (pick-wt=4): 41 [] rd(nil)=zero. % 1.92/2.19 ---> New Demodulator: 42 [new_demod,41] rd(nil)=zero. % 1.92/2.19 ** KEPT (pick-wt=11): 44 [copy,43,demod,40,38,flip.1] addNat(suc(rd(A)),rd(A))=rd(cons(i,A)). % 1.92/2.19 ---> New Demodulator: 45 [new_demod,44] addNat(suc(rd(A)),rd(A))=rd(cons(i,A)). % 1.92/2.19 ** KEPT (pick-wt=10): 47 [copy,46,demod,40] rd(cons(o,A))=addNat(rd(A),rd(A)). % 1.92/2.19 ---> New Demodulator: 48 [new_demod,47] rd(cons(o,A))=addNat(rd(A),rd(A)). % 1.92/2.19 ** KEPT (pick-wt=10): 50 [copy,49,flip.1] rd(append(shw(A),shw(B)))=x(A,B). % 1.92/2.19 ---> New Demodulator: 51 [new_demod,50] rd(append(shw(A),shw(B)))=x(A,B). % 1.92/2.19 ** KEPT (pick-wt=7): 52 [] x(A,B)=x(B,A). % 1.92/2.19 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A. % 1.92/2.19 >>>> Starting back demodulation with 12. % 1.92/2.19 >>>> Starting back demodulation with 14. % 1.92/2.19 >>>> Starting back demodulation with 16. % 1.92/2.19 >>>> Starting back demodulation with 18. % 1.92/2.19 >>>> Starting back demodulation with 20. % 1.92/2.19 >>>> Starting back demodulation with 22. % 1.92/2.19 >>>> Starting back demodulation with 26. % 1.92/2.19 >>>> Starting back demodulation with 30. % 1.92/2.19 >>>> Starting back demodulation with 33. % 1.92/2.19 >>>> Starting back demodulation with 35. % 1.92/2.19 >>>> Starting back demodulation with 38. % 1.92/2.19 >>>> Starting back demodulation with 40. % 1.92/2.19 >>>> Starting back demodulation with 42. % 1.92/2.19 >>>> Starting back demodulation with 45. % 1.92/2.19 >>>> Starting back demodulation with 48. % 1.92/2.19 >>>> Starting back demodulation with 51. % 1.92/2.19 Following clause subsumed by 52 during input processing: 0 [copy,52,flip.1] x(A,B)=x(B,A). % 1.92/2.19 % 1.92/2.19 ======= end of input processing ======= % 1.92/2.19 % 1.92/2.19 =========== start of search =========== % 1.92/2.19 % 1.92/2.19 % 1.92/2.19 Resetting weight limit to 11. % 1.92/2.19 % 1.92/2.19 % 1.92/2.19 Resetting weight limit to 11. % 1.92/2.19 % 1.92/2.19 sos_size=79 % 1.92/2.19 % 1.92/2.19 Search stopped because sos empty. % 1.92/2.19 % 1.92/2.19 % 1.92/2.19 Search stopped because sos empty. % 1.92/2.19 % 1.92/2.19 ============ end of search ============ % 1.92/2.19 % 1.92/2.19 -------------- statistics ------------- % 1.92/2.19 clauses given 146 % 1.92/2.19 clauses generated 3262 % 1.92/2.19 clauses kept 367 % 1.92/2.19 clauses forward subsumed 678 % 1.92/2.19 clauses back subsumed 8 % 1.92/2.19 Kbytes malloced 5859 % 1.92/2.19 % 1.92/2.19 ----------- times (seconds) ----------- % 1.92/2.19 user CPU time 0.06 (0 hr, 0 min, 0 sec) % 1.92/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec) % 1.92/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec) % 1.92/2.19 % 1.92/2.19 Process 27904 finished Tue May 5 12:14:23 2026 % 1.92/2.19 Otter interrupted % 1.92/2.19 PROOF NOT FOUND %------------------------------------------------------------------------------