%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWX185+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n020.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 07:05:22 PM UTC 2026 % Result : Unknown 9.55s 9.74s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX185+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.13 % Command : otter-tptp-script %s % 0.18/0.34 % Computer : n020.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue May 5 09:33:19 EDT 2026 % 0.18/0.35 % CPUTime : % 1.93/2.12 ----- Otter 3.3f, August 2004 ----- % 1.93/2.12 The process was started by sandbox on n020.cluster.edu, % 1.93/2.12 Tue May 5 09:33:19 2026 % 1.93/2.12 The command was "./otter". The process ID is 4034. % 1.93/2.12 % 1.93/2.12 set(prolog_style_variables). % 1.93/2.12 set(auto). % 1.93/2.12 dependent: set(auto1). % 1.93/2.12 dependent: set(process_input). % 1.93/2.12 dependent: clear(print_kept). % 1.93/2.12 dependent: clear(print_new_demod). % 1.93/2.12 dependent: clear(print_back_demod). % 1.93/2.12 dependent: clear(print_back_sub). % 1.93/2.12 dependent: set(control_memory). % 1.93/2.12 dependent: assign(max_mem, 12000). % 1.93/2.12 dependent: assign(pick_given_ratio, 4). % 1.93/2.12 dependent: assign(stats_level, 1). % 1.93/2.12 dependent: assign(max_seconds, 10800). % 1.93/2.12 clear(print_given). % 1.93/2.12 % 1.93/2.12 formula_list(usable). % 1.93/2.12 all A (A=A). % 1.93/2.12 all X X2 (head(cons(X,X2))=X). % 1.93/2.12 all X X2 (tail(cons(X,X2))=X2). % 1.93/2.12 all X X2 (nil!=cons(X,X2)). % 1.93/2.12 c!=d. % 1.93/2.12 c!=x. % 1.93/2.12 c!=y. % 1.93/2.12 c!=plus. % 1.93/2.12 c!=mul. % 1.93/2.12 d!=x. % 1.93/2.12 d!=y. % 1.93/2.12 d!=plus. % 1.93/2.12 d!=mul. % 1.93/2.12 x!=y. % 1.93/2.12 x!=plus. % 1.93/2.12 x!=mul. % 1.93/2.12 y!=plus. % 1.93/2.12 y!=mul. % 1.93/2.12 plus!=mul. % 1.93/2.12 all X X2 (proj1(z(X,X2))=X). % 1.93/2.12 all X X2 (proj2(z(X,X2))=X2). % 1.93/2.12 all X X2 (proj12(x2(X,X2))=X). % 1.93/2.12 all X X2 (proj22(x2(X,X2))=X2). % 1.93/2.12 all X X2 X3 X4 (z(X,X2)!=x2(X3,X4)). % 1.93/2.12 all X X2 (z(X,X2)!=eX). % 1.93/2.12 all X X2 (z(X,X2)!=eY). % 1.93/2.12 all X X2 (x2(X,X2)!=eX). % 1.93/2.12 all X X2 (x2(X,X2)!=eY). % 1.93/2.12 eX!=eY. % 1.93/2.12 all X (X!=z(proj1(X),proj2(X))-> (X!=x2(proj12(X),proj22(X))->assoc(X)=X)). % 1.93/2.12 all Y C (Y!=z(proj1(Y),proj2(Y))->assoc(z(Y,C))=z(assoc(Y),assoc(C))). % 1.93/2.12 all C A B (assoc(z(z(A,B),C))=assoc(z(A,z(B,C)))). % 1.93/2.12 all A2 B2 (assoc(x2(A2,B2))=x2(assoc(A2),assoc(B2))). % 1.93/2.12 all Y (append(nil,Y)=Y). % 1.93/2.12 all Y Z Xs (append(cons(Z,Xs),Y)=cons(Z,append(Xs,Y))). % 1.93/2.12 all X (X!=x2(proj12(X),proj22(X))->linTerm(X)=lin(X)). % 1.93/2.12 all A B (linTerm(x2(A,B))=append(cons(c,nil),append(lin(z(A,B)),cons(d,nil)))). % 1.93/2.12 all A B (lin(z(A,B))=append(linTerm(A),append(cons(plus,nil),linTerm(B)))). % 1.93/2.12 all A3 B2 (lin(x2(A3,B2))=append(lin(A3),append(cons(mul,nil),lin(B2)))). % 1.93/2.12 lin(eX)=cons(x,nil). % 1.93/2.12 lin(eY)=cons(y,nil). % 1.93/2.12 -(exists U V (-(lin(U)=lin(V)->assoc(U)=assoc(V)))). % 1.93/2.12 end_of_list. % 1.93/2.12 % 1.93/2.12 -------> usable clausifies to: % 1.93/2.12 % 1.93/2.12 list(usable). % 1.93/2.12 0 [] A=A. % 1.93/2.12 0 [] head(cons(X,X2))=X. % 1.93/2.12 0 [] tail(cons(X,X2))=X2. % 1.93/2.12 0 [] nil!=cons(X,X2). % 1.93/2.12 0 [] c!=d. % 1.93/2.12 0 [] c!=x. % 1.93/2.12 0 [] c!=y. % 1.93/2.12 0 [] c!=plus. % 1.93/2.12 0 [] c!=mul. % 1.93/2.12 0 [] d!=x. % 1.93/2.12 0 [] d!=y. % 1.93/2.12 0 [] d!=plus. % 1.93/2.12 0 [] d!=mul. % 1.93/2.12 0 [] x!=y. % 1.93/2.12 0 [] x!=plus. % 1.93/2.12 0 [] x!=mul. % 1.93/2.12 0 [] y!=plus. % 1.93/2.12 0 [] y!=mul. % 1.93/2.12 0 [] plus!=mul. % 1.93/2.12 0 [] proj1(z(X,X2))=X. % 1.93/2.12 0 [] proj2(z(X,X2))=X2. % 1.93/2.12 0 [] proj12(x2(X,X2))=X. % 1.93/2.12 0 [] proj22(x2(X,X2))=X2. % 1.93/2.12 0 [] z(X,X2)!=x2(X3,X4). % 1.93/2.12 0 [] z(X,X2)!=eX. % 1.93/2.12 0 [] z(X,X2)!=eY. % 1.93/2.12 0 [] x2(X,X2)!=eX. % 1.93/2.12 0 [] x2(X,X2)!=eY. % 1.93/2.12 0 [] eX!=eY. % 1.93/2.12 0 [] X=z(proj1(X),proj2(X))|X=x2(proj12(X),proj22(X))|assoc(X)=X. % 1.93/2.12 0 [] Y=z(proj1(Y),proj2(Y))|assoc(z(Y,C))=z(assoc(Y),assoc(C)). % 1.93/2.12 0 [] assoc(z(z(A,B),C))=assoc(z(A,z(B,C))). % 1.93/2.12 0 [] assoc(x2(A2,B2))=x2(assoc(A2),assoc(B2)). % 1.93/2.12 0 [] append(nil,Y)=Y. % 1.93/2.12 0 [] append(cons(Z,Xs),Y)=cons(Z,append(Xs,Y)). % 1.93/2.12 0 [] X=x2(proj12(X),proj22(X))|linTerm(X)=lin(X). % 1.93/2.12 0 [] linTerm(x2(A,B))=append(cons(c,nil),append(lin(z(A,B)),cons(d,nil))). % 1.93/2.12 0 [] lin(z(A,B))=append(linTerm(A),append(cons(plus,nil),linTerm(B))). % 1.93/2.12 0 [] lin(x2(A3,B2))=append(lin(A3),append(cons(mul,nil),lin(B2))). % 1.93/2.12 0 [] lin(eX)=cons(x,nil). % 1.93/2.12 0 [] lin(eY)=cons(y,nil). % 1.93/2.12 0 [] lin(U)!=lin(V)|assoc(U)=assoc(V). % 1.93/2.12 end_of_list. % 1.93/2.12 % 1.93/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3. % 1.93/2.12 % 1.93/2.12 This ia a non-Horn set with equality. The strategy will be % 1.93/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit % 1.93/2.12 deletion, with positive clauses in sos and nonpositive % 1.93/2.12 clauses in usable. % 1.93/2.12 % 1.93/2.12 dependent: set(knuth_bendix). % 1.93/2.12 dependent: set(anl_eq). % 1.93/2.12 dependent: set(para_from). % 1.93/2.12 dependent: set(para_into). % 1.93/2.12 dependent: clear(para_from_right). % 1.93/2.12 dependent: clear(para_into_right). % 1.93/2.12 dependent: set(para_from_vars). % 1.93/2.12 dependent: set(eq_units_both_ways). % 1.93/2.12 dependent: set(dynamic_demod_all). % 1.93/2.12 dependent: set(dynamic_demod). % 1.93/2.12 dependent: set(order_eq). % 1.93/2.12 dependent: set(back_demod). % 1.93/2.12 dependent: set(lrpo). % 1.93/2.12 dependent: set(hyper_res). % 1.93/2.12 dependent: set(unit_deletion). % 1.93/2.12 dependent: set(factor). % 1.93/2.12 % 1.93/2.12 ------------> process usable: % 1.93/2.12 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] cons(A,B)!=nil. % 1.93/2.12 ** KEPT (pick-wt=3): 4 [copy,3,flip.1] d!=c. % 1.93/2.12 ** KEPT (pick-wt=3): 6 [copy,5,flip.1] x!=c. % 1.93/2.12 ** KEPT (pick-wt=3): 8 [copy,7,flip.1] y!=c. % 1.93/2.12 ** KEPT (pick-wt=3): 10 [copy,9,flip.1] plus!=c. % 1.93/2.12 ** KEPT (pick-wt=3): 12 [copy,11,flip.1] mul!=c. % 1.93/2.12 ** KEPT (pick-wt=3): 14 [copy,13,flip.1] x!=d. % 1.93/2.12 ** KEPT (pick-wt=3): 16 [copy,15,flip.1] y!=d. % 1.93/2.12 ** KEPT (pick-wt=3): 18 [copy,17,flip.1] plus!=d. % 1.93/2.12 ** KEPT (pick-wt=3): 20 [copy,19,flip.1] mul!=d. % 1.93/2.12 ** KEPT (pick-wt=3): 22 [copy,21,flip.1] y!=x. % 1.93/2.12 ** KEPT (pick-wt=3): 23 [] x!=plus. % 1.93/2.12 ** KEPT (pick-wt=3): 24 [] x!=mul. % 1.93/2.12 ** KEPT (pick-wt=3): 25 [] y!=plus. % 1.93/2.12 ** KEPT (pick-wt=3): 26 [] y!=mul. % 1.93/2.12 ** KEPT (pick-wt=3): 27 [] plus!=mul. % 1.93/2.12 ** KEPT (pick-wt=7): 28 [] z(A,B)!=x2(C,D). % 1.93/2.12 ** KEPT (pick-wt=5): 29 [] z(A,B)!=eX. % 1.93/2.12 ** KEPT (pick-wt=5): 30 [] z(A,B)!=eY. % 1.93/2.12 ** KEPT (pick-wt=5): 31 [] x2(A,B)!=eX. % 1.93/2.12 ** KEPT (pick-wt=5): 32 [] x2(A,B)!=eY. % 1.93/2.12 ** KEPT (pick-wt=3): 34 [copy,33,flip.1] eY!=eX. % 1.93/2.12 ** KEPT (pick-wt=10): 35 [] lin(A)!=lin(B)|assoc(A)=assoc(B). % 1.93/2.12 ** KEPT (pick-wt=7): 36 [copy,28,flip.1] x2(A,B)!=z(C,D). % 1.93/2.12 Following clause subsumed by 28 during input processing: 0 [copy,36,flip.1] z(A,B)!=x2(C,D). % 1.93/2.12 % 1.93/2.12 ------------> process sos: % 1.93/2.12 ** KEPT (pick-wt=3): 37 [] A=A. % 1.93/2.12 ** KEPT (pick-wt=6): 38 [] head(cons(A,B))=A. % 1.93/2.12 ---> New Demodulator: 39 [new_demod,38] head(cons(A,B))=A. % 1.93/2.12 ** KEPT (pick-wt=6): 40 [] tail(cons(A,B))=B. % 1.93/2.12 ---> New Demodulator: 41 [new_demod,40] tail(cons(A,B))=B. % 1.93/2.12 ** KEPT (pick-wt=6): 42 [] proj1(z(A,B))=A. % 1.93/2.12 ---> New Demodulator: 43 [new_demod,42] proj1(z(A,B))=A. % 1.93/2.12 ** KEPT (pick-wt=6): 44 [] proj2(z(A,B))=B. % 1.93/2.12 ---> New Demodulator: 45 [new_demod,44] proj2(z(A,B))=B. % 1.93/2.12 ** KEPT (pick-wt=6): 46 [] proj12(x2(A,B))=A. % 1.93/2.12 ---> New Demodulator: 47 [new_demod,46] proj12(x2(A,B))=A. % 1.93/2.12 ** KEPT (pick-wt=6): 48 [] proj22(x2(A,B))=B. % 1.93/2.12 ---> New Demodulator: 49 [new_demod,48] proj22(x2(A,B))=B. % 1.93/2.12 ** KEPT (pick-wt=18): 51 [copy,50,flip.1,flip.2] z(proj1(A),proj2(A))=A|x2(proj12(A),proj22(A))=A|assoc(A)=A. % 1.93/2.12 ** KEPT (pick-wt=17): 53 [copy,52,flip.1] z(proj1(A),proj2(A))=A|assoc(z(A,B))=z(assoc(A),assoc(B)). % 1.93/2.12 ** KEPT (pick-wt=13): 54 [] assoc(z(z(A,B),C))=assoc(z(A,z(B,C))). % 1.93/2.12 ---> New Demodulator: 55 [new_demod,54] assoc(z(z(A,B),C))=assoc(z(A,z(B,C))). % 1.93/2.12 ** KEPT (pick-wt=10): 56 [] assoc(x2(A,B))=x2(assoc(A),assoc(B)). % 1.93/2.12 ---> New Demodulator: 57 [new_demod,56] assoc(x2(A,B))=x2(assoc(A),assoc(B)). % 1.93/2.12 ** KEPT (pick-wt=5): 58 [] append(nil,A)=A. % 1.93/2.12 ---> New Demodulator: 59 [new_demod,58] append(nil,A)=A. % 1.93/2.12 ** KEPT (pick-wt=11): 61 [copy,60,flip.1] cons(A,append(B,C))=append(cons(A,B),C). % 1.93/2.12 ---> New Demodulator: 62 [new_demod,61] cons(A,append(B,C))=append(cons(A,B),C). % 1.93/2.12 ** KEPT (pick-wt=12): 64 [copy,63,flip.1] x2(proj12(A),proj22(A))=A|linTerm(A)=lin(A). % 1.93/2.12 ** KEPT (pick-wt=17): 65 [] linTerm(x2(A,B))=append(cons(c,nil),append(lin(z(A,B)),cons(d,nil))). % 1.93/2.12 ---> New Demodulator: 66 [new_demod,65] linTerm(x2(A,B))=append(cons(c,nil),append(lin(z(A,B)),cons(d,nil))). % 1.93/2.12 ** KEPT (pick-wt=14): 67 [] lin(z(A,B))=append(linTerm(A),append(cons(plus,nil),linTerm(B))). % 1.93/2.12 ** KEPT (pick-wt=14): 68 [] lin(x2(A,B))=append(lin(A),append(cons(mul,nil),lin(B))). % 1.93/2.12 ---> New Demodulator: 69 [new_demod,68] lin(x2(A,B))=append(lin(A),append(cons(mul,nil),lin(B))). % 1.93/2.12 ** KEPT (pick-wt=6): 70 [] lin(eX)=cons(x,nil). % 1.93/2.12 ---> New Demodulator: 71 [new_demod,70] lin(eX)=cons(x,nil). % 1.93/2.12 ** KEPT (pick-wt=6): 72 [] lin(eY)=cons(y,nil). % 1.93/2.12 ---> New Demodulator: 73 [new_demod,72] lin(eY)=cons(y,nil). % 1.93/2.12 Following clause subsumed by 37 during input processing: 0 [copy,37,flip.1] A=A. % 1.93/2.12 >>>> Starting back demodulation with 39. % 1.93/2.12 >>>> Starting back demodulation with 41. % 1.93/2.12 >>>> Starting back demodulation with 43. % 1.93/2.12 >>>> Starting back demodulation with 45. % 1.93/2.12 >>>> Starting back demodulation with 47. % 1.93/2.12 >>>> Starting back demodulation with 49. % 1.93/2.12 >>>> Starting back demodulation with 55. % 1.93/2.12 >>>> Starting back demodulation with 57. % 1.93/2.12 >>>> Starting back demodulation with 59. % 1.93/2.12 >>>> Starting back demodulation with 62. % 1.93/2.12 >>>> Starting back demodulation with 66. % 1.93/2.12 ** KEPT (pick-wt=14): 74 [copy,67,flip.1] append(linTerm(A),append(cons(plus,nil),linTerm(B)))=lin(z(A,B)). % 1.93/2.12 >>>> Starting back demodulation with 69. % 1.93/2.12 >>>> Starting back demodulation with 71. % 1.93/2.12 >>>> Starting back demodulation with 73. % 1.93/2.12 Following clause subsumed by 67 during input processing: 0 [copy,74,flip.1] lin(z(A,B))=append(linTerm(A),append(cons(plus,nil),linTerm(B))). % 1.93/2.12 % 1.93/2.12 ======= end of input processing ======= % 9.55/9.74 % 9.55/9.74 =========== start of search =========== % 9.55/9.74 % 9.55/9.74 % 9.55/9.74 Resetting weight limit to 12. % 9.55/9.74 % 9.55/9.74 % 9.55/9.74 Resetting weight limit to 12. % 9.55/9.74 % 9.55/9.74 sos_size=623 % 9.55/9.74 % 9.55/9.74 Search stopped because sos empty. % 9.55/9.74 % 9.55/9.74 % 9.55/9.74 Search stopped because sos empty. % 9.55/9.74 % 9.55/9.74 ============ end of search ============ % 9.55/9.74 % 9.55/9.74 -------------- statistics ------------- % 9.55/9.74 clauses given 868 % 9.55/9.74 clauses generated 459000 % 9.55/9.74 clauses kept 943 % 9.55/9.74 clauses forward subsumed 3164 % 9.55/9.74 clauses back subsumed 42 % 9.55/9.74 Kbytes malloced 7812 % 9.55/9.74 % 9.55/9.74 ----------- times (seconds) ----------- % 9.55/9.74 user CPU time 7.61 (0 hr, 0 min, 7 sec) % 9.55/9.74 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 9.55/9.74 wall-clock time 10 (0 hr, 0 min, 10 sec) % 9.55/9.74 % 9.55/9.74 Process 4034 finished Tue May 5 09:33:29 2026 % 9.55/9.74 Otter interrupted % 9.55/9.74 PROOF NOT FOUND %------------------------------------------------------------------------------