%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWX199-1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n019.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 1.93s 2.19s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWX199-1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.12 % Command : otter-tptp-script %s % 0.16/0.33 % Computer : n019.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 11:13:44 EDT 2026 % 0.16/0.33 % CPUTime : % 1.81/2.04 ----- Otter 3.3f, August 2004 ----- % 1.81/2.04 The process was started by sandbox2 on n019.cluster.edu, % 1.81/2.04 Tue May 5 11:13:44 2026 % 1.81/2.04 The command was "./otter". The process ID is 28456. % 1.81/2.04 % 1.81/2.04 set(prolog_style_variables). % 1.81/2.04 set(auto). % 1.81/2.04 dependent: set(auto1). % 1.81/2.04 dependent: set(process_input). % 1.81/2.04 dependent: clear(print_kept). % 1.81/2.04 dependent: clear(print_new_demod). % 1.81/2.04 dependent: clear(print_back_demod). % 1.81/2.04 dependent: clear(print_back_sub). % 1.81/2.04 dependent: set(control_memory). % 1.81/2.04 dependent: assign(max_mem, 12000). % 1.81/2.04 dependent: assign(pick_given_ratio, 4). % 1.81/2.04 dependent: assign(stats_level, 1). % 1.81/2.04 dependent: assign(max_seconds, 10800). % 1.81/2.04 clear(print_given). % 1.81/2.04 % 1.81/2.04 list(usable). % 1.81/2.04 0 [] A=A. % 1.81/2.04 0 [] aux(Z,Xs,Y2,Ys,btrue)=cons(Z,merge(Xs,cons(Y2,Ys))). % 1.81/2.04 0 [] aux(Z,Xs,Y2,Ys,bfalse)=cons(Y2,merge(cons(Z,Xs),Ys)). % 1.81/2.04 0 [] le_qNat(z,Y)=btrue. % 1.81/2.04 0 [] le_qNat(s(Z),z)=bfalse. % 1.81/2.04 0 [] le_qNat(s(Z),s(M))=le_qNat(Z,M). % 1.81/2.04 0 [] merge(nil,Y)=Y. % 1.81/2.04 0 [] merge(cons(Z,Xs),nil)=cons(Z,Xs). % 1.81/2.04 0 [] merge(cons(Z,Xs),cons(Y2,Ys))=aux(Z,Xs,Y2,Ys,le_qNat(Z,Y2)). % 1.81/2.04 0 [] impl(btrue,Q)=Q. % 1.81/2.04 0 [] impl(bfalse,Q)=btrue. % 1.81/2.04 0 [] prop_merge_comm(X,Y,Z)=impl(e_q(merge(X,Y),merge(Y,X)),impl(e_q(merge(X,Z),merge(Z,X)),e_q(merge(Y,Z),merge(Z,Y)))). % 1.81/2.04 0 [] e_q3(bfalse,btrue)=bfalse. % 1.81/2.04 0 [] e_q3(btrue,bfalse)=bfalse. % 1.81/2.04 0 [] e_q2(s(X),s(Y))=e_q2(X,Y). % 1.81/2.04 0 [] e_q2(z,s(X))=bfalse. % 1.81/2.04 0 [] e_q2(s(X),z)=bfalse. % 1.81/2.04 0 [] e_q(X,X)=btrue. % 1.81/2.04 0 [] e_q2(X,X)=btrue. % 1.81/2.04 0 [] e_q3(X,X)=btrue. % 1.81/2.04 0 [] e_q2(X,Z)!=bfalse|e_q(cons(X,Y),cons(Z,X2))=bfalse. % 1.81/2.04 0 [] e_q2(X,Z)!=btrue|e_q(cons(X,Y),cons(Z,X2))=e_q(Y,X2). % 1.81/2.04 0 [] e_q(nil,cons(X,Y))=bfalse. % 1.81/2.04 0 [] e_q(cons(X,Y),nil)=bfalse. % 1.81/2.04 0 [] e_q3(prop_merge_comm(X,Y,Z),bfalse)!=btrue. % 1.81/2.04 end_of_list. % 1.81/2.04 % 1.81/2.04 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2. % 1.81/2.04 % 1.81/2.04 This is a Horn set with equality. The strategy will be % 1.81/2.04 Knuth-Bendix and hyper_res, with positive clauses in % 1.81/2.04 sos and nonpositive clauses in usable. % 1.81/2.04 % 1.81/2.04 dependent: set(knuth_bendix). % 1.81/2.04 dependent: set(anl_eq). % 1.81/2.04 dependent: set(para_from). % 1.81/2.04 dependent: set(para_into). % 1.81/2.04 dependent: clear(para_from_right). % 1.81/2.04 dependent: clear(para_into_right). % 1.81/2.04 dependent: set(para_from_vars). % 1.81/2.04 dependent: set(eq_units_both_ways). % 1.81/2.04 dependent: set(dynamic_demod_all). % 1.81/2.04 dependent: set(dynamic_demod). % 1.81/2.04 dependent: set(order_eq). % 1.81/2.04 dependent: set(back_demod). % 1.81/2.04 dependent: set(lrpo). % 1.81/2.04 dependent: set(hyper_res). % 1.81/2.04 dependent: clear(order_hyper). % 1.81/2.04 % 1.81/2.04 ------------> process usable: % 1.81/2.04 ** KEPT (pick-wt=14): 1 [] e_q2(A,B)!=bfalse|e_q(cons(A,C),cons(B,D))=bfalse. % 1.81/2.04 ** KEPT (pick-wt=16): 2 [] e_q2(A,B)!=btrue|e_q(cons(A,C),cons(B,D))=e_q(C,D). % 1.81/2.04 ** KEPT (pick-wt=8): 3 [] e_q3(prop_merge_comm(A,B,C),bfalse)!=btrue. % 1.81/2.04 % 1.81/2.04 ------------> process sos: % 1.81/2.04 ** KEPT (pick-wt=3): 4 [] A=A. % 1.81/2.04 ** KEPT (pick-wt=14): 6 [copy,5,flip.1] cons(A,merge(B,cons(C,D)))=aux(A,B,C,D,btrue). % 1.81/2.04 ---> New Demodulator: 7 [new_demod,6] cons(A,merge(B,cons(C,D)))=aux(A,B,C,D,btrue). % 1.81/2.04 ** KEPT (pick-wt=14): 9 [copy,8,flip.1] cons(A,merge(cons(B,C),D))=aux(B,C,A,D,bfalse). % 1.81/2.04 ---> New Demodulator: 10 [new_demod,9] cons(A,merge(cons(B,C),D))=aux(B,C,A,D,bfalse). % 1.81/2.04 ** KEPT (pick-wt=5): 11 [] le_qNat(z,A)=btrue. % 1.81/2.04 ---> New Demodulator: 12 [new_demod,11] le_qNat(z,A)=btrue. % 1.81/2.04 ** KEPT (pick-wt=6): 13 [] le_qNat(s(A),z)=bfalse. % 1.81/2.04 ---> New Demodulator: 14 [new_demod,13] le_qNat(s(A),z)=bfalse. % 1.81/2.04 ** KEPT (pick-wt=9): 15 [] le_qNat(s(A),s(B))=le_qNat(A,B). % 1.81/2.04 ---> New Demodulator: 16 [new_demod,15] le_qNat(s(A),s(B))=le_qNat(A,B). % 1.81/2.04 ** KEPT (pick-wt=5): 17 [] merge(nil,A)=A. % 1.81/2.04 ---> New Demodulator: 18 [new_demod,17] merge(nil,A)=A. % 1.81/2.04 ** KEPT (pick-wt=9): 19 [] merge(cons(A,B),nil)=cons(A,B). % 1.81/2.04 ---> New Demodulator: 20 [new_demod,19] merge(cons(A,B),nil)=cons(A,B). % 1.81/2.04 ** KEPT (pick-wt=16): 21 [] merge(cons(A,B),cons(C,D))=aux(A,B,C,D,le_qNat(A,C)). % 1.81/2.04 ---> New Demodulator: 22 [new_demod,21] merge(cons(A,B),cons(C,D))=aux(A,B,C,D,le_qNat(A,C)). % 1.81/2.04 ** KEPT (pick-wt=5): 23 [] impl(btrue,A)=A. % 1.81/2.04 ---> New Demodulator: 24 [new_demod,23] impl(btrue,A)=A. % 1.81/2.04 ** KEPT (pick-wt=5): 25 [] impl(bfalse,A)=btrue. % 1.81/2.04 ---> New Demodulator: 26 [new_demod,25] impl(bfalse,A)=btrue. % 1.81/2.04 ** KEPT (pick-wt=28): 28 [copy,27,flip.1] impl(e_q(merge(A,B),merge(B,A)),impl(e_q(merge(A,C),merge(C,A)),e_q(merge(B,C),merge(C,B))))=prop_merge_comm(A,B,C). % 1.93/2.19 ---> New Demodulator: 29 [new_demod,28] impl(e_q(merge(A,B),merge(B,A)),impl(e_q(merge(A,C),merge(C,A)),e_q(merge(B,C),merge(C,B))))=prop_merge_comm(A,B,C). % 1.93/2.19 ** KEPT (pick-wt=5): 30 [] e_q3(bfalse,btrue)=bfalse. % 1.93/2.19 ---> New Demodulator: 31 [new_demod,30] e_q3(bfalse,btrue)=bfalse. % 1.93/2.19 ** KEPT (pick-wt=5): 32 [] e_q3(btrue,bfalse)=bfalse. % 1.93/2.19 ---> New Demodulator: 33 [new_demod,32] e_q3(btrue,bfalse)=bfalse. % 1.93/2.19 ** KEPT (pick-wt=9): 34 [] e_q2(s(A),s(B))=e_q2(A,B). % 1.93/2.19 ---> New Demodulator: 35 [new_demod,34] e_q2(s(A),s(B))=e_q2(A,B). % 1.93/2.19 ** KEPT (pick-wt=6): 36 [] e_q2(z,s(A))=bfalse. % 1.93/2.19 ---> New Demodulator: 37 [new_demod,36] e_q2(z,s(A))=bfalse. % 1.93/2.19 ** KEPT (pick-wt=6): 38 [] e_q2(s(A),z)=bfalse. % 1.93/2.19 ---> New Demodulator: 39 [new_demod,38] e_q2(s(A),z)=bfalse. % 1.93/2.19 ** KEPT (pick-wt=5): 40 [] e_q(A,A)=btrue. % 1.93/2.19 ---> New Demodulator: 41 [new_demod,40] e_q(A,A)=btrue. % 1.93/2.19 ** KEPT (pick-wt=5): 42 [] e_q2(A,A)=btrue. % 1.93/2.19 ---> New Demodulator: 43 [new_demod,42] e_q2(A,A)=btrue. % 1.93/2.19 ** KEPT (pick-wt=5): 44 [] e_q3(A,A)=btrue. % 1.93/2.19 ---> New Demodulator: 45 [new_demod,44] e_q3(A,A)=btrue. % 1.93/2.19 ** KEPT (pick-wt=7): 46 [] e_q(nil,cons(A,B))=bfalse. % 1.93/2.19 ---> New Demodulator: 47 [new_demod,46] e_q(nil,cons(A,B))=bfalse. % 1.93/2.19 ** KEPT (pick-wt=7): 48 [] e_q(cons(A,B),nil)=bfalse. % 1.93/2.19 ---> New Demodulator: 49 [new_demod,48] e_q(cons(A,B),nil)=bfalse. % 1.93/2.19 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A. % 1.93/2.19 >>>> Starting back demodulation with 7. % 1.93/2.19 >>>> Starting back demodulation with 10. % 1.93/2.19 >>>> Starting back demodulation with 12. % 1.93/2.19 >>>> Starting back demodulation with 14. % 1.93/2.19 >>>> Starting back demodulation with 16. % 1.93/2.19 >>>> Starting back demodulation with 18. % 1.93/2.19 >>>> Starting back demodulation with 20. % 1.93/2.19 >>>> Starting back demodulation with 22. % 1.93/2.19 >>>> Starting back demodulation with 24. % 1.93/2.19 >>>> Starting back demodulation with 26. % 1.93/2.19 >>>> Starting back demodulation with 29. % 1.93/2.19 >>>> Starting back demodulation with 31. % 1.93/2.19 >>>> Starting back demodulation with 33. % 1.93/2.19 >>>> Starting back demodulation with 35. % 1.93/2.19 >>>> Starting back demodulation with 37. % 1.93/2.19 >>>> Starting back demodulation with 39. % 1.93/2.19 >>>> Starting back demodulation with 41. % 1.93/2.19 >>>> Starting back demodulation with 43. % 1.93/2.19 >>>> Starting back demodulation with 45. % 1.93/2.19 >>>> Starting back demodulation with 47. % 1.93/2.19 >>>> Starting back demodulation with 49. % 1.93/2.19 % 1.93/2.19 ======= end of input processing ======= % 1.93/2.19 % 1.93/2.19 =========== start of search =========== % 1.93/2.19 % 1.93/2.19 % 1.93/2.19 Resetting weight limit to 16. % 1.93/2.19 % 1.93/2.19 % 1.93/2.19 Resetting weight limit to 16. % 1.93/2.19 % 1.93/2.19 sos_size=157 % 1.93/2.19 % 1.93/2.19 Search stopped because sos empty. % 1.93/2.19 % 1.93/2.19 % 1.93/2.19 Search stopped because sos empty. % 1.93/2.19 % 1.93/2.19 ============ end of search ============ % 1.93/2.19 % 1.93/2.19 -------------- statistics ------------- % 1.93/2.19 clauses given 265 % 1.93/2.19 clauses generated 13091 % 1.93/2.19 clauses kept 318 % 1.93/2.19 clauses forward subsumed 2729 % 1.93/2.19 clauses back subsumed 21 % 1.93/2.19 Kbytes malloced 7812 % 1.93/2.19 % 1.93/2.19 ----------- times (seconds) ----------- % 1.93/2.19 user CPU time 0.15 (0 hr, 0 min, 0 sec) % 1.93/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec) % 1.93/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec) % 1.93/2.19 % 1.93/2.19 Process 28456 finished Tue May 5 11:13:46 2026 % 1.93/2.19 Otter interrupted % 1.93/2.19 PROOF NOT FOUND %------------------------------------------------------------------------------