%------------------------------------------------------------------------------ % 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 : n028.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 2.12s 2.35s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX198+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : otter-tptp-script %s % 0.16/0.33 % Computer : n028.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 11:08:15 EDT 2026 % 0.16/0.33 % CPUTime : % 1.98/2.18 ----- Otter 3.3f, August 2004 ----- % 1.98/2.18 The process was started by sandbox2 on n028.cluster.edu, % 1.98/2.18 Tue May 5 11:08:15 2026 % 1.98/2.18 The command was "./otter". The process ID is 26180. % 1.98/2.18 % 1.98/2.18 set(prolog_style_variables). % 1.98/2.18 set(auto). % 1.98/2.18 dependent: set(auto1). % 1.98/2.18 dependent: set(process_input). % 1.98/2.18 dependent: clear(print_kept). % 1.98/2.18 dependent: clear(print_new_demod). % 1.98/2.18 dependent: clear(print_back_demod). % 1.98/2.18 dependent: clear(print_back_sub). % 1.98/2.18 dependent: set(control_memory). % 1.98/2.18 dependent: assign(max_mem, 12000). % 1.98/2.18 dependent: assign(pick_given_ratio, 4). % 1.98/2.18 dependent: assign(stats_level, 1). % 1.98/2.18 dependent: assign(max_seconds, 10800). % 1.98/2.18 clear(print_given). % 1.98/2.18 % 1.98/2.18 formula_list(usable). % 1.98/2.18 all A (A=A). % 1.98/2.18 all X X2 (head(cons(X,X2))=X). % 1.98/2.18 all X X2 (tail(cons(X,X2))=X2). % 1.98/2.18 all X X2 (nil!=cons(X,X2)). % 1.98/2.18 all X (proj1S(s(X))=X). % 1.98/2.18 all X (z!=s(X)). % 1.98/2.18 -ltNat(z,z). % 1.98/2.18 all Z ltNat(z,s(Z)). % 1.98/2.18 all X2 (-ltNat(s(X2),z)). % 1.98/2.18 all X2 M (ltNat(s(X2),s(M))<->ltNat(X2,M)). % 1.98/2.18 usorted(nil). % 1.98/2.18 all Y usorted(cons(Y,nil)). % 1.98/2.18 all Y Y2 Xs (usorted(cons(Y,cons(Y2,Xs)))<->ltNat(Y,Y2)&usorted(cons(Y2,Xs))). % 1.98/2.18 all Y le_qNat(z,Y). % 1.98/2.18 all Z (-le_qNat(s(Z),z)). % 1.98/2.18 all Z M (le_qNat(s(Z),s(M))<->le_qNat(Z,M)). % 1.98/2.18 lengthNat(nil)=z. % 1.98/2.18 all Y Xs (lengthNat(cons(Y,Xs))=s(lengthNat(Xs))). % 1.98/2.18 all Y (append(nil,Y)=Y). % 1.98/2.18 all Y Z Xs (append(cons(Z,Xs),Y)=cons(Z,append(Xs,Y))). % 1.98/2.18 rev(nil)=nil. % 1.98/2.18 all Y Xs (rev(cons(Y,Xs))=append(rev(Xs),cons(Y,nil))). % 1.98/2.18 all X allsmall(X,nil). % 1.98/2.18 all X Z Xs (allsmall(X,cons(Z,Xs))<->ltNat(Z,X)&allsmall(X,Xs)). % 1.98/2.18 -(exists Xs (-(usorted(rev(Xs))-> (allsmall(s(z),Xs)->le_qNat(lengthNat(Xs),s(s(z))))))). % 1.98/2.18 end_of_list. % 1.98/2.18 % 1.98/2.18 -------> usable clausifies to: % 1.98/2.18 % 1.98/2.18 list(usable). % 1.98/2.18 0 [] A=A. % 1.98/2.18 0 [] head(cons(X,X2))=X. % 1.98/2.18 0 [] tail(cons(X,X2))=X2. % 1.98/2.18 0 [] nil!=cons(X,X2). % 1.98/2.18 0 [] proj1S(s(X))=X. % 1.98/2.18 0 [] z!=s(X). % 1.98/2.18 0 [] -ltNat(z,z). % 1.98/2.18 0 [] ltNat(z,s(Z)). % 1.98/2.18 0 [] -ltNat(s(X2),z). % 1.98/2.18 0 [] -ltNat(s(X2),s(M))|ltNat(X2,M). % 1.98/2.18 0 [] ltNat(s(X2),s(M))| -ltNat(X2,M). % 1.98/2.18 0 [] usorted(nil). % 1.98/2.18 0 [] usorted(cons(Y,nil)). % 1.98/2.18 0 [] -usorted(cons(Y,cons(Y2,Xs)))|ltNat(Y,Y2). % 1.98/2.18 0 [] -usorted(cons(Y,cons(Y2,Xs)))|usorted(cons(Y2,Xs)). % 1.98/2.18 0 [] usorted(cons(Y,cons(Y2,Xs)))| -ltNat(Y,Y2)| -usorted(cons(Y2,Xs)). % 1.98/2.18 0 [] le_qNat(z,Y). % 1.98/2.18 0 [] -le_qNat(s(Z),z). % 1.98/2.18 0 [] -le_qNat(s(Z),s(M))|le_qNat(Z,M). % 1.98/2.18 0 [] le_qNat(s(Z),s(M))| -le_qNat(Z,M). % 1.98/2.18 0 [] lengthNat(nil)=z. % 1.98/2.18 0 [] lengthNat(cons(Y,Xs))=s(lengthNat(Xs)). % 1.98/2.18 0 [] append(nil,Y)=Y. % 1.98/2.18 0 [] append(cons(Z,Xs),Y)=cons(Z,append(Xs,Y)). % 1.98/2.18 0 [] rev(nil)=nil. % 1.98/2.18 0 [] rev(cons(Y,Xs))=append(rev(Xs),cons(Y,nil)). % 1.98/2.18 0 [] allsmall(X,nil). % 1.98/2.18 0 [] -allsmall(X,cons(Z,Xs))|ltNat(Z,X). % 1.98/2.18 0 [] -allsmall(X,cons(Z,Xs))|allsmall(X,Xs). % 1.98/2.18 0 [] allsmall(X,cons(Z,Xs))| -ltNat(Z,X)| -allsmall(X,Xs). % 1.98/2.18 0 [] -usorted(rev(Xs))| -allsmall(s(z),Xs)|le_qNat(lengthNat(Xs),s(s(z))). % 1.98/2.18 end_of_list. % 1.98/2.18 % 1.98/2.18 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3. % 1.98/2.18 % 1.98/2.18 This is a Horn set with equality. The strategy will be % 1.98/2.18 Knuth-Bendix and hyper_res, with positive clauses in % 1.98/2.18 sos and nonpositive clauses in usable. % 1.98/2.18 % 1.98/2.18 dependent: set(knuth_bendix). % 1.98/2.18 dependent: set(anl_eq). % 1.98/2.18 dependent: set(para_from). % 1.98/2.18 dependent: set(para_into). % 1.98/2.18 dependent: clear(para_from_right). % 1.98/2.18 dependent: clear(para_into_right). % 1.98/2.18 dependent: set(para_from_vars). % 1.98/2.18 dependent: set(eq_units_both_ways). % 1.98/2.18 dependent: set(dynamic_demod_all). % 1.98/2.18 dependent: set(dynamic_demod). % 1.98/2.18 dependent: set(order_eq). % 1.98/2.18 dependent: set(back_demod). % 1.98/2.18 dependent: set(lrpo). % 1.98/2.18 dependent: set(hyper_res). % 1.98/2.18 dependent: clear(order_hyper). % 1.98/2.18 % 1.98/2.18 ------------> process usable: % 1.98/2.18 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] cons(A,B)!=nil. % 1.98/2.18 ** KEPT (pick-wt=4): 4 [copy,3,flip.1] s(A)!=z. % 1.98/2.18 ** KEPT (pick-wt=3): 5 [] -ltNat(z,z). % 1.98/2.18 ** KEPT (pick-wt=4): 6 [] -ltNat(s(A),z). % 1.98/2.18 ** KEPT (pick-wt=8): 7 [] -ltNat(s(A),s(B))|ltNat(A,B). % 1.98/2.18 ** KEPT (pick-wt=8): 8 [] ltNat(s(A),s(B))| -ltNat(A,B). % 1.98/2.18 ** KEPT (pick-wt=9): 9 [] -usorted(cons(A,cons(B,C)))|ltNat(A,B). % 1.98/2.18 ** KEPT (pick-wt=10): 10 [] -usorted(cons(A,cons(B,C)))|usorted(cons(B,C)). % 1.98/2.18 ** KEPT (pick-wt=13): 11 [] usorted(cons(A,cons(B,C)))| -ltNat(A,B)| -usorted(cons(B,C)). % 1.98/2.18 ** KEPT (pick-wt=4): 12 [] -le_qNat(s(A),z). % 1.98/2.18 ** KEPT (pick-wt=8): 13 [] -le_qNat(s(A),s(B))|le_qNat(A,B). % 1.98/2.18 ** KEPT (pick-wt=8): 14 [] le_qNat(s(A),s(B))| -le_qNat(A,B). % 1.98/2.18 ** KEPT (pick-wt=8): 15 [] -allsmall(A,cons(B,C))|ltNat(B,A). % 2.12/2.34 ** KEPT (pick-wt=8): 16 [] -allsmall(A,cons(B,C))|allsmall(A,C). % 2.12/2.34 ** KEPT (pick-wt=11): 17 [] allsmall(A,cons(B,C))| -ltNat(B,A)| -allsmall(A,C). % 2.12/2.34 ** KEPT (pick-wt=13): 18 [] -usorted(rev(A))| -allsmall(s(z),A)|le_qNat(lengthNat(A),s(s(z))). % 2.12/2.34 % 2.12/2.34 ------------> process sos: % 2.12/2.34 ** KEPT (pick-wt=3): 19 [] A=A. % 2.12/2.34 ** KEPT (pick-wt=6): 20 [] head(cons(A,B))=A. % 2.12/2.34 ---> New Demodulator: 21 [new_demod,20] head(cons(A,B))=A. % 2.12/2.34 ** KEPT (pick-wt=6): 22 [] tail(cons(A,B))=B. % 2.12/2.34 ---> New Demodulator: 23 [new_demod,22] tail(cons(A,B))=B. % 2.12/2.34 ** KEPT (pick-wt=5): 24 [] proj1S(s(A))=A. % 2.12/2.34 ---> New Demodulator: 25 [new_demod,24] proj1S(s(A))=A. % 2.12/2.34 ** KEPT (pick-wt=4): 26 [] ltNat(z,s(A)). % 2.12/2.34 ** KEPT (pick-wt=2): 27 [] usorted(nil). % 2.12/2.34 ** KEPT (pick-wt=4): 28 [] usorted(cons(A,nil)). % 2.12/2.34 ** KEPT (pick-wt=3): 29 [] le_qNat(z,A). % 2.12/2.34 ** KEPT (pick-wt=4): 30 [] lengthNat(nil)=z. % 2.12/2.34 ---> New Demodulator: 31 [new_demod,30] lengthNat(nil)=z. % 2.12/2.34 ** KEPT (pick-wt=8): 32 [] lengthNat(cons(A,B))=s(lengthNat(B)). % 2.12/2.34 ** KEPT (pick-wt=5): 33 [] append(nil,A)=A. % 2.12/2.34 ---> New Demodulator: 34 [new_demod,33] append(nil,A)=A. % 2.12/2.34 ** KEPT (pick-wt=11): 36 [copy,35,flip.1] cons(A,append(B,C))=append(cons(A,B),C). % 2.12/2.34 ---> New Demodulator: 37 [new_demod,36] cons(A,append(B,C))=append(cons(A,B),C). % 2.12/2.34 ** KEPT (pick-wt=4): 38 [] rev(nil)=nil. % 2.12/2.34 ---> New Demodulator: 39 [new_demod,38] rev(nil)=nil. % 2.12/2.34 ** KEPT (pick-wt=11): 40 [] rev(cons(A,B))=append(rev(B),cons(A,nil)). % 2.12/2.34 ---> New Demodulator: 41 [new_demod,40] rev(cons(A,B))=append(rev(B),cons(A,nil)). % 2.12/2.34 ** KEPT (pick-wt=3): 42 [] allsmall(A,nil). % 2.12/2.34 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] A=A. % 2.12/2.34 >>>> Starting back demodulation with 21. % 2.12/2.34 >>>> Starting back demodulation with 23. % 2.12/2.34 >>>> Starting back demodulation with 25. % 2.12/2.34 >>>> Starting back demodulation with 31. % 2.12/2.34 ** KEPT (pick-wt=8): 43 [copy,32,flip.1] s(lengthNat(A))=lengthNat(cons(B,A)). % 2.12/2.34 >>>> Starting back demodulation with 34. % 2.12/2.34 >>>> Starting back demodulation with 37. % 2.12/2.34 >>>> Starting back demodulation with 39. % 2.12/2.34 >>>> Starting back demodulation with 41. % 2.12/2.34 Following clause subsumed by 32 during input processing: 0 [copy,43,flip.1] lengthNat(cons(A,B))=s(lengthNat(B)). % 2.12/2.34 % 2.12/2.34 ======= end of input processing ======= % 2.12/2.34 % 2.12/2.34 =========== start of search =========== % 2.12/2.34 % 2.12/2.34 % 2.12/2.34 Resetting weight limit to 11. % 2.12/2.34 % 2.12/2.34 % 2.12/2.34 Resetting weight limit to 11. % 2.12/2.34 % 2.12/2.34 sos_size=431 % 2.12/2.34 % 2.12/2.34 Search stopped because sos empty. % 2.12/2.34 % 2.12/2.34 % 2.12/2.34 Search stopped because sos empty. % 2.12/2.34 % 2.12/2.34 ============ end of search ============ % 2.12/2.34 % 2.12/2.34 -------------- statistics ------------- % 2.12/2.34 clauses given 534 % 2.12/2.34 clauses generated 30108 % 2.12/2.34 clauses kept 596 % 2.12/2.34 clauses forward subsumed 3030 % 2.12/2.34 clauses back subsumed 45 % 2.12/2.34 Kbytes malloced 5859 % 2.12/2.34 % 2.12/2.34 ----------- times (seconds) ----------- % 2.12/2.34 user CPU time 0.16 (0 hr, 0 min, 0 sec) % 2.12/2.34 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 2.12/2.34 wall-clock time 2 (0 hr, 0 min, 2 sec) % 2.12/2.34 % 2.12/2.34 Process 26180 finished Tue May 5 11:08:17 2026 % 2.12/2.34 Otter interrupted % 2.12/2.34 PROOF NOT FOUND %------------------------------------------------------------------------------