%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWX202+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 3.51s 3.74s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX202+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : otter-tptp-script %s % 0.16/0.33 % Computer : n006.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue May 5 11:22:00 EDT 2026 % 0.16/0.33 % CPUTime : % 1.41/2.03 ----- Otter 3.3f, August 2004 ----- % 1.41/2.03 The process was started by sandbox2 on n006.cluster.edu, % 1.41/2.03 Tue May 5 11:22:01 2026 % 1.41/2.03 The command was "./otter". The process ID is 15224. % 1.41/2.03 % 1.41/2.03 set(prolog_style_variables). % 1.41/2.03 set(auto). % 1.41/2.03 dependent: set(auto1). % 1.41/2.03 dependent: set(process_input). % 1.41/2.03 dependent: clear(print_kept). % 1.41/2.03 dependent: clear(print_new_demod). % 1.41/2.03 dependent: clear(print_back_demod). % 1.41/2.03 dependent: clear(print_back_sub). % 1.41/2.03 dependent: set(control_memory). % 1.41/2.03 dependent: assign(max_mem, 12000). % 1.41/2.03 dependent: assign(pick_given_ratio, 4). % 1.41/2.03 dependent: assign(stats_level, 1). % 1.41/2.03 dependent: assign(max_seconds, 10800). % 1.41/2.03 clear(print_given). % 1.41/2.03 % 1.41/2.03 formula_list(usable). % 1.41/2.03 all A (A=A). % 1.41/2.03 all X X2 (proj1pair(pair2(X,X2))=X). % 1.41/2.03 all X X2 (proj2pair(pair2(X,X2))=X2). % 1.41/2.03 all X X2 (head(cons(X,X2))=X). % 1.41/2.03 all X X2 (tail(cons(X,X2))=X2). % 1.41/2.03 all X X2 (nil!=cons(X,X2)). % 1.41/2.03 all X (proj1S(s(X))=X). % 1.41/2.03 all X (z!=s(X)). % 1.41/2.03 all Y (splitAtNat(z,Y)=pair2(nil,Y)). % 1.41/2.03 all Z (splitAtNat(s(Z),nil)=pair2(nil,nil)). % 1.41/2.03 all Z X2 X3 Ys1 Zs (splitAtNat(Z,X3)=pair2(Ys1,Zs)->splitAtNat(s(Z),cons(X2,X3))=pair2(cons(X2,Ys1),Zs)). % 1.41/2.03 all Y le_qNat(z,Y). % 1.41/2.03 all Z (-le_qNat(s(Z),z)). % 1.41/2.03 all Z M (le_qNat(s(Z),s(M))<->le_qNat(Z,M)). % 1.41/2.03 all Y (merge(nil,Y)=Y). % 1.41/2.03 all Z Xs (merge(cons(Z,Xs),nil)=cons(Z,Xs)). % 1.41/2.03 all Z Xs Y2 Ys (le_qNat(Z,Y2)->merge(cons(Z,Xs),cons(Y2,Ys))=cons(Z,merge(Xs,cons(Y2,Ys)))). % 1.41/2.03 all Z Xs Y2 Ys (-le_qNat(Z,Y2)->merge(cons(Z,Xs),cons(Y2,Ys))=cons(Y2,merge(cons(Z,Xs),Ys))). % 1.41/2.03 lengthNat(nil)=z. % 1.41/2.03 all Y Xs (lengthNat(cons(Y,Xs))=s(lengthNat(Xs))). % 1.41/2.03 div2(z)=z. % 1.41/2.03 div2(s(z))=z. % 1.41/2.03 all N (div2(s(s(N)))=s(div2(N))). % 1.41/2.03 msort(nil)=nil. % 1.41/2.03 all Y (msort(cons(Y,nil))=cons(Y,nil)). % 1.41/2.03 all Y X2 X3 Ys1 Zs (splitAtNat(div2(lengthNat(cons(Y,cons(X2,X3)))),cons(Y,cons(X2,X3)))=pair2(Ys1,Zs)->msort(cons(Y,cons(X2,X3)))=merge(msort(Ys1),msort(Zs))). % 1.41/2.03 all X (count(X,nil)=z). % 1.41/2.03 all X Z Xs (Z=X->count(X,cons(Z,Xs))=s(count(X,Xs))). % 1.41/2.03 all X Z Xs (Z!=X->count(X,cons(Z,Xs))=count(X,Xs)). % 1.41/2.03 -(exists Xs X (-(-le_qNat(count(X,Xs),s(s(s(s(s(z))))))->count(s(X),Xs)=count(X,msort(Xs))))). % 1.41/2.03 end_of_list. % 1.41/2.03 % 1.41/2.03 -------> usable clausifies to: % 1.41/2.03 % 1.41/2.03 list(usable). % 1.41/2.03 0 [] A=A. % 1.41/2.03 0 [] proj1pair(pair2(X,X2))=X. % 1.41/2.03 0 [] proj2pair(pair2(X,X2))=X2. % 1.41/2.03 0 [] head(cons(X,X2))=X. % 1.41/2.03 0 [] tail(cons(X,X2))=X2. % 1.41/2.03 0 [] nil!=cons(X,X2). % 1.41/2.03 0 [] proj1S(s(X))=X. % 1.41/2.03 0 [] z!=s(X). % 1.41/2.03 0 [] splitAtNat(z,Y)=pair2(nil,Y). % 1.41/2.03 0 [] splitAtNat(s(Z),nil)=pair2(nil,nil). % 1.41/2.03 0 [] splitAtNat(Z,X3)!=pair2(Ys1,Zs)|splitAtNat(s(Z),cons(X2,X3))=pair2(cons(X2,Ys1),Zs). % 1.41/2.03 0 [] le_qNat(z,Y). % 1.41/2.03 0 [] -le_qNat(s(Z),z). % 1.41/2.03 0 [] -le_qNat(s(Z),s(M))|le_qNat(Z,M). % 1.41/2.03 0 [] le_qNat(s(Z),s(M))| -le_qNat(Z,M). % 1.41/2.03 0 [] merge(nil,Y)=Y. % 1.41/2.03 0 [] merge(cons(Z,Xs),nil)=cons(Z,Xs). % 1.41/2.03 0 [] -le_qNat(Z,Y2)|merge(cons(Z,Xs),cons(Y2,Ys))=cons(Z,merge(Xs,cons(Y2,Ys))). % 1.41/2.03 0 [] le_qNat(Z,Y2)|merge(cons(Z,Xs),cons(Y2,Ys))=cons(Y2,merge(cons(Z,Xs),Ys)). % 1.41/2.03 0 [] lengthNat(nil)=z. % 1.41/2.03 0 [] lengthNat(cons(Y,Xs))=s(lengthNat(Xs)). % 1.41/2.03 0 [] div2(z)=z. % 1.41/2.03 0 [] div2(s(z))=z. % 1.41/2.03 0 [] div2(s(s(N)))=s(div2(N)). % 1.41/2.03 0 [] msort(nil)=nil. % 1.41/2.03 0 [] msort(cons(Y,nil))=cons(Y,nil). % 1.41/2.03 0 [] splitAtNat(div2(lengthNat(cons(Y,cons(X2,X3)))),cons(Y,cons(X2,X3)))!=pair2(Ys1,Zs)|msort(cons(Y,cons(X2,X3)))=merge(msort(Ys1),msort(Zs)). % 1.41/2.03 0 [] count(X,nil)=z. % 1.41/2.03 0 [] Z!=X|count(X,cons(Z,Xs))=s(count(X,Xs)). % 1.41/2.03 0 [] Z=X|count(X,cons(Z,Xs))=count(X,Xs). % 1.41/2.03 0 [] le_qNat(count(X,Xs),s(s(s(s(s(z))))))|count(s(X),Xs)=count(X,msort(Xs)). % 1.41/2.03 end_of_list. % 1.41/2.03 % 1.41/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2. % 1.41/2.03 % 1.41/2.03 This ia a non-Horn set with equality. The strategy will be % 1.41/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit % 1.41/2.03 deletion, with positive clauses in sos and nonpositive % 1.41/2.03 clauses in usable. % 1.41/2.03 % 1.41/2.03 dependent: set(knuth_bendix). % 1.41/2.03 dependent: set(anl_eq). % 1.41/2.03 dependent: set(para_from). % 1.41/2.03 dependent: set(para_into). % 1.41/2.03 dependent: clear(para_from_right). % 1.41/2.03 dependent: clear(para_into_right). % 1.41/2.03 dependent: set(para_from_vars). % 1.41/2.03 dependent: set(eq_units_both_ways). % 1.41/2.03 dependent: set(dynamic_demod_all). % 1.41/2.03 dependent: set(dynamic_demod). % 1.41/2.03 dependent: set(order_eq). % 1.41/2.03 dependent: set(back_demod). % 1.41/2.03 dependent: set(lrpo). % 1.41/2.03 dependent: set(hyper_res). % 1.41/2.03 dependent: set(unit_deletion). % 1.41/2.03 dependent: set(factor). % 1.41/2.03 % 1.41/2.03 ------------> process usable: % 1.41/2.03 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] cons(A,B)!=nil. % 3.51/3.73 ** KEPT (pick-wt=4): 4 [copy,3,flip.1] s(A)!=z. % 3.51/3.73 ** KEPT (pick-wt=19): 5 [] splitAtNat(A,B)!=pair2(C,D)|splitAtNat(s(A),cons(E,B))=pair2(cons(E,C),D). % 3.51/3.73 ** KEPT (pick-wt=4): 6 [] -le_qNat(s(A),z). % 3.51/3.73 ** KEPT (pick-wt=8): 7 [] -le_qNat(s(A),s(B))|le_qNat(A,B). % 3.51/3.73 ** KEPT (pick-wt=8): 8 [] le_qNat(s(A),s(B))| -le_qNat(A,B). % 3.51/3.73 ** KEPT (pick-wt=18): 9 [] -le_qNat(A,B)|merge(cons(A,C),cons(B,D))=cons(A,merge(C,cons(B,D))). % 3.51/3.73 ** KEPT (pick-wt=29): 10 [] splitAtNat(div2(lengthNat(cons(A,cons(B,C)))),cons(A,cons(B,C)))!=pair2(D,E)|msort(cons(A,cons(B,C)))=merge(msort(D),msort(E)). % 3.51/3.73 ** KEPT (pick-wt=13): 11 [] A!=B|count(B,cons(A,C))=s(count(B,C)). % 3.51/3.73 % 3.51/3.73 ------------> process sos: % 3.51/3.73 ** KEPT (pick-wt=3): 12 [] A=A. % 3.51/3.73 ** KEPT (pick-wt=6): 13 [] proj1pair(pair2(A,B))=A. % 3.51/3.73 ---> New Demodulator: 14 [new_demod,13] proj1pair(pair2(A,B))=A. % 3.51/3.73 ** KEPT (pick-wt=6): 15 [] proj2pair(pair2(A,B))=B. % 3.51/3.73 ---> New Demodulator: 16 [new_demod,15] proj2pair(pair2(A,B))=B. % 3.51/3.73 ** KEPT (pick-wt=6): 17 [] head(cons(A,B))=A. % 3.51/3.73 ---> New Demodulator: 18 [new_demod,17] head(cons(A,B))=A. % 3.51/3.73 ** KEPT (pick-wt=6): 19 [] tail(cons(A,B))=B. % 3.51/3.73 ---> New Demodulator: 20 [new_demod,19] tail(cons(A,B))=B. % 3.51/3.73 ** KEPT (pick-wt=5): 21 [] proj1S(s(A))=A. % 3.51/3.73 ---> New Demodulator: 22 [new_demod,21] proj1S(s(A))=A. % 3.51/3.73 ** KEPT (pick-wt=7): 23 [] splitAtNat(z,A)=pair2(nil,A). % 3.51/3.73 ---> New Demodulator: 24 [new_demod,23] splitAtNat(z,A)=pair2(nil,A). % 3.51/3.73 ** KEPT (pick-wt=8): 25 [] splitAtNat(s(A),nil)=pair2(nil,nil). % 3.51/3.73 ---> New Demodulator: 26 [new_demod,25] splitAtNat(s(A),nil)=pair2(nil,nil). % 3.51/3.73 ** KEPT (pick-wt=3): 27 [] le_qNat(z,A). % 3.51/3.73 ** KEPT (pick-wt=5): 28 [] merge(nil,A)=A. % 3.51/3.73 ---> New Demodulator: 29 [new_demod,28] merge(nil,A)=A. % 3.51/3.73 ** KEPT (pick-wt=9): 30 [] merge(cons(A,B),nil)=cons(A,B). % 3.51/3.73 ---> New Demodulator: 31 [new_demod,30] merge(cons(A,B),nil)=cons(A,B). % 3.51/3.73 ** KEPT (pick-wt=18): 32 [] le_qNat(A,B)|merge(cons(A,C),cons(B,D))=cons(B,merge(cons(A,C),D)). % 3.51/3.73 ** KEPT (pick-wt=4): 33 [] lengthNat(nil)=z. % 3.51/3.73 ---> New Demodulator: 34 [new_demod,33] lengthNat(nil)=z. % 3.51/3.73 ** KEPT (pick-wt=8): 35 [] lengthNat(cons(A,B))=s(lengthNat(B)). % 3.51/3.73 ** KEPT (pick-wt=4): 36 [] div2(z)=z. % 3.51/3.73 ---> New Demodulator: 37 [new_demod,36] div2(z)=z. % 3.51/3.73 ** KEPT (pick-wt=5): 38 [] div2(s(z))=z. % 3.51/3.73 ---> New Demodulator: 39 [new_demod,38] div2(s(z))=z. % 3.51/3.73 ** KEPT (pick-wt=8): 40 [] div2(s(s(A)))=s(div2(A)). % 3.51/3.73 ---> New Demodulator: 41 [new_demod,40] div2(s(s(A)))=s(div2(A)). % 3.51/3.73 ** KEPT (pick-wt=4): 42 [] msort(nil)=nil. % 3.51/3.73 ---> New Demodulator: 43 [new_demod,42] msort(nil)=nil. % 3.51/3.73 ** KEPT (pick-wt=8): 44 [] msort(cons(A,nil))=cons(A,nil). % 3.51/3.73 ---> New Demodulator: 45 [new_demod,44] msort(cons(A,nil))=cons(A,nil). % 3.51/3.73 ** KEPT (pick-wt=5): 46 [] count(A,nil)=z. % 3.51/3.73 ---> New Demodulator: 47 [new_demod,46] count(A,nil)=z. % 3.51/3.73 ** KEPT (pick-wt=12): 48 [] A=B|count(B,cons(A,C))=count(B,C). % 3.51/3.73 ** KEPT (pick-wt=19): 49 [] le_qNat(count(A,B),s(s(s(s(s(z))))))|count(s(A),B)=count(A,msort(B)). % 3.51/3.73 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A. % 3.51/3.73 >>>> Starting back demodulation with 14. % 3.51/3.73 >>>> Starting back demodulation with 16. % 3.51/3.73 >>>> Starting back demodulation with 18. % 3.51/3.73 >>>> Starting back demodulation with 20. % 3.51/3.73 >>>> Starting back demodulation with 22. % 3.51/3.73 >>>> Starting back demodulation with 24. % 3.51/3.73 >>>> Starting back demodulation with 26. % 3.51/3.73 >>>> Starting back demodulation with 29. % 3.51/3.73 >>>> Starting back demodulation with 31. % 3.51/3.73 >>>> Starting back demodulation with 34. % 3.51/3.73 ** KEPT (pick-wt=8): 50 [copy,35,flip.1] s(lengthNat(A))=lengthNat(cons(B,A)). % 3.51/3.73 >>>> Starting back demodulation with 37. % 3.51/3.73 >>>> Starting back demodulation with 39. % 3.51/3.73 >>>> Starting back demodulation with 41. % 3.51/3.73 >>>> Starting back demodulation with 43. % 3.51/3.73 >>>> Starting back demodulation with 45. % 3.51/3.73 >>>> Starting back demodulation with 47. % 3.51/3.73 Following clause subsumed by 35 during input processing: 0 [copy,50,flip.1] lengthNat(cons(A,B))=s(lengthNat(B)). % 3.51/3.73 % 3.51/3.73 ======= end of input processing ======= % 3.51/3.73 % 3.51/3.73 =========== start of search =========== % 3.51/3.73 % 3.51/3.73 % 3.51/3.73 Resetting weight limit to 11. % 3.51/3.73 % 3.51/3.73 % 3.51/3.73 Resetting weight limit to 11. % 3.51/3.73 % 3.51/3.73 sos_size=431 % 3.51/3.73 % 3.51/3.73 Search stopped because sos empty. % 3.51/3.73 % 3.51/3.73 % 3.51/3.73 Search stopped because sos empty. % 3.51/3.73 % 3.51/3.73 ============ end of search ============ % 3.51/3.73 % 3.51/3.73 -------------- statistics ------------- % 3.51/3.74 clauses given 586 % 3.51/3.74 clauses generated 226447 % 3.51/3.74 clauses kept 630 % 3.51/3.74 clauses forward subsumed 6400 % 3.51/3.74 clauses back subsumed 42 % 3.51/3.74 Kbytes malloced 7812 % 3.51/3.74 % 3.51/3.74 ----------- times (seconds) ----------- % 3.51/3.74 user CPU time 1.71 (0 hr, 0 min, 1 sec) % 3.51/3.74 system CPU time 0.00 (0 hr, 0 min, 0 sec) % 3.51/3.74 wall-clock time 3 (0 hr, 0 min, 3 sec) % 3.51/3.74 % 3.51/3.74 Process 15224 finished Tue May 5 11:22:04 2026 % 3.51/3.74 Otter interrupted % 3.51/3.74 PROOF NOT FOUND %------------------------------------------------------------------------------