TSTP Solution File: NUM837+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM837+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 : Wed Jul 27 13:10:03 EDT 2022
% Result : Theorem 1.80s 2.00s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 5 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
vd269 != vplus(vd268,A),
file('NUM837+1.p',unknown),
[] ).
cnf(2,plain,
vplus(vd268,A) != vd269,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(16,axiom,
( ~ less(A,B)
| B = vplus(A,dollar_f1(B,A)) ),
file('NUM837+1.p',unknown),
[] ).
cnf(17,plain,
( ~ less(A,B)
| vplus(A,dollar_f1(B,A)) = B ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
[iquote('copy,16,flip.2')] ).
cnf(34,axiom,
less(vd268,vd269),
file('NUM837+1.p',unknown),
[] ).
cnf(66,plain,
vplus(vd268,dollar_f1(vd269,vd268)) = vd269,
inference(hyper,[status(thm)],[34,17]),
[iquote('hyper,34,17')] ).
cnf(68,plain,
$false,
inference(binary,[status(thm)],[66,2]),
[iquote('binary,66.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM837+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 09:58:31 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.80/2.00 ----- Otter 3.3f, August 2004 -----
% 1.80/2.00 The process was started by sandbox on n018.cluster.edu,
% 1.80/2.00 Wed Jul 27 09:58:31 2022
% 1.80/2.00 The command was "./otter". The process ID is 25480.
% 1.80/2.00
% 1.80/2.00 set(prolog_style_variables).
% 1.80/2.00 set(auto).
% 1.80/2.00 dependent: set(auto1).
% 1.80/2.00 dependent: set(process_input).
% 1.80/2.00 dependent: clear(print_kept).
% 1.80/2.00 dependent: clear(print_new_demod).
% 1.80/2.00 dependent: clear(print_back_demod).
% 1.80/2.00 dependent: clear(print_back_sub).
% 1.80/2.00 dependent: set(control_memory).
% 1.80/2.00 dependent: assign(max_mem, 12000).
% 1.80/2.00 dependent: assign(pick_given_ratio, 4).
% 1.80/2.00 dependent: assign(stats_level, 1).
% 1.80/2.00 dependent: assign(max_seconds, 10800).
% 1.80/2.00 clear(print_given).
% 1.80/2.00
% 1.80/2.00 formula_list(usable).
% 1.80/2.00 all A (A=A).
% 1.80/2.00 -(exists Vd273 (vd269=vplus(vd268,Vd273))).
% 1.80/2.00 less(vd269,vd271).
% 1.80/2.00 less(vd268,vd269).
% 1.80/2.00 all Vd258 Vd259 (le_q(Vd258,Vd259)->ge_q(Vd259,Vd258)).
% 1.80/2.00 all Vd254 Vd255 (ge_q(Vd254,Vd255)->le_q(Vd255,Vd254)).
% 1.80/2.00 all Vd249 Vd250 (le_q(Vd250,Vd249)<->less(Vd250,Vd249)|Vd250=Vd249).
% 1.80/2.00 all Vd244 Vd245 (ge_q(Vd245,Vd244)<->greater(Vd245,Vd244)|Vd245=Vd244).
% 1.80/2.00 all Vd226 Vd227 (less(Vd226,Vd227)->greater(Vd227,Vd226)).
% 1.80/2.00 all Vd208 Vd209 (greater(Vd208,Vd209)->less(Vd209,Vd208)).
% 1.80/2.00 all Vd203 Vd204 (Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204)).
% 1.80/2.00 all Vd203 Vd204 (Vd203!=Vd204| -less(Vd203,Vd204)).
% 1.80/2.00 all Vd203 Vd204 (-greater(Vd203,Vd204)| -less(Vd203,Vd204)).
% 1.80/2.00 all Vd203 Vd204 (Vd203!=Vd204| -greater(Vd203,Vd204)).
% 1.80/2.00 all Vd198 Vd199 (less(Vd199,Vd198)<-> (exists Vd201 (Vd198=vplus(Vd199,Vd201)))).
% 1.80/2.00 all Vd193 Vd194 (greater(Vd194,Vd193)<-> (exists Vd196 (Vd194=vplus(Vd193,Vd196)))).
% 1.80/2.00 all Vd120 Vd121 (Vd120=Vd121| (exists Vd123 (Vd120=vplus(Vd121,Vd123)))| (exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.80/2.00 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.80/2.00 all Vd120 Vd121 (-(exists Vd123 (Vd120=vplus(Vd121,Vd123)))| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.80/2.00 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd123 (Vd120=vplus(Vd121,Vd123)))).
% 1.80/2.00 all Vd104 Vd105 (Vd104!=Vd105-> (all Vd107 (vplus(Vd107,Vd104)!=vplus(Vd107,Vd105)))).
% 1.80/2.00 all Vd92 Vd93 (Vd93!=vplus(Vd92,Vd93)).
% 1.80/2.00 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 1.80/2.00 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 1.80/2.00 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 1.80/2.00 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 1.80/2.00 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.80/2.00 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 1.80/2.00 all Vd16 (vsucc(Vd16)!=Vd16).
% 1.80/2.00 all Vd7 Vd8 (Vd7!=Vd8->vsucc(Vd7)!=vsucc(Vd8)).
% 1.80/2.00 all Vd3 Vd4 (vsucc(Vd3)=vsucc(Vd4)->Vd3=Vd4).
% 1.80/2.00 all Vd1 (vsucc(Vd1)!=v1).
% 1.80/2.00 end_of_list.
% 1.80/2.00
% 1.80/2.00 -------> usable clausifies to:
% 1.80/2.00
% 1.80/2.00 list(usable).
% 1.80/2.00 0 [] A=A.
% 1.80/2.00 0 [] vd269!=vplus(vd268,Vd273).
% 1.80/2.00 0 [] less(vd269,vd271).
% 1.80/2.00 0 [] less(vd268,vd269).
% 1.80/2.00 0 [] -le_q(Vd258,Vd259)|ge_q(Vd259,Vd258).
% 1.80/2.00 0 [] -ge_q(Vd254,Vd255)|le_q(Vd255,Vd254).
% 1.80/2.00 0 [] -le_q(Vd250,Vd249)|less(Vd250,Vd249)|Vd250=Vd249.
% 1.80/2.00 0 [] le_q(Vd250,Vd249)| -less(Vd250,Vd249).
% 1.80/2.00 0 [] le_q(Vd250,Vd249)|Vd250!=Vd249.
% 1.80/2.00 0 [] -ge_q(Vd245,Vd244)|greater(Vd245,Vd244)|Vd245=Vd244.
% 1.80/2.00 0 [] ge_q(Vd245,Vd244)| -greater(Vd245,Vd244).
% 1.80/2.00 0 [] ge_q(Vd245,Vd244)|Vd245!=Vd244.
% 1.80/2.00 0 [] -less(Vd226,Vd227)|greater(Vd227,Vd226).
% 1.80/2.00 0 [] -greater(Vd208,Vd209)|less(Vd209,Vd208).
% 1.80/2.00 0 [] Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204).
% 1.80/2.00 0 [] Vd203!=Vd204| -less(Vd203,Vd204).
% 1.80/2.00 0 [] -greater(Vd203,Vd204)| -less(Vd203,Vd204).
% 1.80/2.00 0 [] Vd203!=Vd204| -greater(Vd203,Vd204).
% 1.80/2.00 0 [] -less(Vd199,Vd198)|Vd198=vplus(Vd199,$f1(Vd198,Vd199)).
% 1.80/2.00 0 [] less(Vd199,Vd198)|Vd198!=vplus(Vd199,Vd201).
% 1.80/2.00 0 [] -greater(Vd194,Vd193)|Vd194=vplus(Vd193,$f2(Vd193,Vd194)).
% 1.80/2.00 0 [] greater(Vd194,Vd193)|Vd194!=vplus(Vd193,Vd196).
% 1.80/2.00 0 [] Vd120=Vd121|Vd120=vplus(Vd121,$f3(Vd120,Vd121))|Vd121=vplus(Vd120,$f4(Vd120,Vd121)).
% 1.80/2.00 0 [] Vd120!=Vd121|Vd121!=vplus(Vd120,Vd125).
% 1.80/2.00 0 [] Vd120!=vplus(Vd121,Vd123)|Vd121!=vplus(Vd120,Vd125).
% 1.80/2.00 0 [] Vd120!=Vd121|Vd120!=vplus(Vd121,Vd123).
% 1.80/2.00 0 [] Vd104=Vd105|vplus(Vd107,Vd104)!=vplus(Vd107,Vd105).
% 1.80/2.00 0 [] Vd93!=vplus(Vd92,Vd93).
% 1.80/2.00 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 1.80/2.00 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 1.80/2.00 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 1.80/2.00 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 1.80/2.00 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.80/2.00 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.80/2.00 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 1.80/2.00 0 [] vsucc(Vd16)!=Vd16.
% 1.80/2.00 0 [] Vd7=Vd8|vsucc(Vd7)!=vsucc(Vd8).
% 1.80/2.00 0 [] vsucc(Vd3)!=vsucc(Vd4)|Vd3=Vd4.
% 1.80/2.00 0 [] vsucc(Vd1)!=v1.
% 1.80/2.00 end_of_list.
% 1.80/2.00
% 1.80/2.00 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.80/2.00
% 1.80/2.00 This ia a non-Horn set with equality. The strategy will be
% 1.80/2.00 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.80/2.00 deletion, with positive clauses in sos and nonpositive
% 1.80/2.00 clauses in usable.
% 1.80/2.00
% 1.80/2.00 dependent: set(knuth_bendix).
% 1.80/2.00 dependent: set(anl_eq).
% 1.80/2.00 dependent: set(para_from).
% 1.80/2.00 dependent: set(para_into).
% 1.80/2.00 dependent: clear(para_from_right).
% 1.80/2.00 dependent: clear(para_into_right).
% 1.80/2.00 dependent: set(para_from_vars).
% 1.80/2.00 dependent: set(eq_units_both_ways).
% 1.80/2.00 dependent: set(dynamic_demod_all).
% 1.80/2.00 dependent: set(dynamic_demod).
% 1.80/2.00 dependent: set(order_eq).
% 1.80/2.00 dependent: set(back_demod).
% 1.80/2.00 dependent: set(lrpo).
% 1.80/2.00 dependent: set(hyper_res).
% 1.80/2.00 dependent: set(unit_deletion).
% 1.80/2.00 dependent: set(factor).
% 1.80/2.00
% 1.80/2.00 ------------> process usable:
% 1.80/2.00 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] vplus(vd268,A)!=vd269.
% 1.80/2.00 ** KEPT (pick-wt=6): 3 [] -le_q(A,B)|ge_q(B,A).
% 1.80/2.00 ** KEPT (pick-wt=6): 4 [] -ge_q(A,B)|le_q(B,A).
% 1.80/2.00 ** KEPT (pick-wt=9): 5 [] -le_q(A,B)|less(A,B)|A=B.
% 1.80/2.00 ** KEPT (pick-wt=6): 6 [] le_q(A,B)| -less(A,B).
% 1.80/2.00 ** KEPT (pick-wt=6): 7 [] le_q(A,B)|A!=B.
% 1.80/2.00 ** KEPT (pick-wt=9): 8 [] -ge_q(A,B)|greater(A,B)|A=B.
% 1.80/2.00 ** KEPT (pick-wt=6): 9 [] ge_q(A,B)| -greater(A,B).
% 1.80/2.00 ** KEPT (pick-wt=6): 10 [] ge_q(A,B)|A!=B.
% 1.80/2.00 ** KEPT (pick-wt=6): 11 [] -less(A,B)|greater(B,A).
% 1.80/2.00 ** KEPT (pick-wt=6): 12 [] -greater(A,B)|less(B,A).
% 1.80/2.00 ** KEPT (pick-wt=6): 13 [] A!=B| -less(A,B).
% 1.80/2.00 ** KEPT (pick-wt=6): 14 [] -greater(A,B)| -less(A,B).
% 1.80/2.00 ** KEPT (pick-wt=6): 15 [] A!=B| -greater(A,B).
% 1.80/2.00 ** KEPT (pick-wt=10): 17 [copy,16,flip.2] -less(A,B)|vplus(A,$f1(B,A))=B.
% 1.80/2.00 ** KEPT (pick-wt=8): 18 [] less(A,B)|B!=vplus(A,C).
% 1.80/2.00 ** KEPT (pick-wt=10): 20 [copy,19,flip.2] -greater(A,B)|vplus(B,$f2(B,A))=A.
% 1.80/2.00 ** KEPT (pick-wt=8): 21 [] greater(A,B)|A!=vplus(B,C).
% 1.80/2.00 ** KEPT (pick-wt=8): 22 [] A!=B|B!=vplus(A,C).
% 1.80/2.00 ** KEPT (pick-wt=10): 23 [] A!=vplus(B,C)|B!=vplus(A,D).
% 1.80/2.00 ** KEPT (pick-wt=8): 24 [] A!=B|A!=vplus(B,C).
% 1.80/2.00 ** KEPT (pick-wt=10): 25 [] A=B|vplus(C,A)!=vplus(C,B).
% 1.80/2.00 ** KEPT (pick-wt=5): 27 [copy,26,flip.1] vplus(A,B)!=B.
% 1.80/2.00 ** KEPT (pick-wt=4): 28 [] vsucc(A)!=A.
% 1.80/2.00 ** KEPT (pick-wt=8): 29 [] A=B|vsucc(A)!=vsucc(B).
% 1.80/2.00 Following clause subsumed by 29 during input processing: 0 [] vsucc(A)!=vsucc(B)|A=B.
% 1.80/2.00 ** KEPT (pick-wt=4): 30 [] vsucc(A)!=v1.
% 1.80/2.00
% 1.80/2.00 ------------> process sos:
% 1.80/2.00 ** KEPT (pick-wt=3): 32 [] A=A.
% 1.80/2.00 ** KEPT (pick-wt=3): 33 [] less(vd269,vd271).
% 1.80/2.00 ** KEPT (pick-wt=3): 34 [] less(vd268,vd269).
% 1.80/2.00 ** KEPT (pick-wt=9): 35 [] A=B|greater(A,B)|less(A,B).
% 1.80/2.00 ** KEPT (pick-wt=17): 37 [copy,36,flip.2,flip.3] A=B|vplus(B,$f3(A,B))=A|vplus(A,$f4(A,B))=B.
% 1.80/2.00 ** KEPT (pick-wt=7): 38 [] vplus(A,B)=vplus(B,A).
% 1.80/2.00 ** KEPT (pick-wt=9): 40 [copy,39,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.80/2.00 ---> New Demodulator: 41 [new_demod,40] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.80/2.00 ** KEPT (pick-wt=6): 43 [copy,42,flip.1] vsucc(A)=vplus(v1,A).
% 1.80/2.00 ---> New Demodulator: 44 [new_demod,43] vsucc(A)=vplus(v1,A).
% 1.80/2.00 ** KEPT (pick-wt=11): 45 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.80/2.00 ---> New Demodulator: 46 [new_demod,45] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.80/2.00 ** KEPT (pick-wt=11): 48 [copy,47,demod,44,44] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.80/2.00 Following clause subsumed by 38 during input processing: 0 [demod,44] vplus(A,v1)=vplus(v1,A).
% 1.80/2.00 ** KEPT (pick-wt=9): 50 [copy,49,demod,44,flip.2] A=v1|vplus(v1,vskolem2(A))=A.
% 1.80/2.00 Following clause subsumed by 32 during input processing: 0 [copy,32,flip.1] A=A.
% 1.80/2.00 Following clause subsumed by 38 during input processing: 0 [copy,38,flip.1] vplus(A,B)=vplus(B,A).
% 1.80/2.00 >>>> Starting back demodulation with 41.
% 1.80/2.00 >>>> Starting back demodulation with 44.
% 1.80/2.00 >> back demodulating 40 with 44.
% 1.80/2.00 >> back demodulating 30 with 44.
% 1.80/2.00 >> back demodulating 29 with 44.
% 1.80/2.00 >> back demodulating 28 with 44.
% 1.80/2.00 >>>> Starting back demodulation with 46.
% 1.80/2.00 ** KEPT (pick-wt=11): 51 [copy,48,flip.1] vplus(v1,vplus(A,B))=vplus(A,vplus(v1,B)).
% 1.80/2.00 Following clause subsumed by 48 during input processing: 0 [copy,51,flip.1] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.80/2.00
% 1.80/2.00 ======= end of input processing =======
% 1.80/2.00
% 1.80/2.00 =========== start of search ===========
% 1.80/2.00
% 1.80/2.00 -------- PROOF --------
% 1.80/2.00
% 1.80/2.00 ----> UNIT CONFLICT at 0.00 sec ----> 68 [binary,66.1,2.1] $F.
% 1.80/2.00
% 1.80/2.00 Length of proof is 3. Level of proof is 2.
% 1.80/2.00
% 1.80/2.00 ---------------- PROOF ----------------
% 1.80/2.00 % SZS status Theorem
% 1.80/2.00 % SZS output start Refutation
% See solution above
% 1.80/2.00 ------------ end of proof -------------
% 1.80/2.00
% 1.80/2.00
% 1.80/2.00 Search stopped by max_proofs option.
% 1.80/2.00
% 1.80/2.00
% 1.80/2.00 Search stopped by max_proofs option.
% 1.80/2.00
% 1.80/2.00 ============ end of search ============
% 1.80/2.00
% 1.80/2.00 -------------- statistics -------------
% 1.80/2.00 clauses given 3
% 1.80/2.00 clauses generated 16
% 1.80/2.00 clauses kept 53
% 1.80/2.00 clauses forward subsumed 10
% 1.80/2.00 clauses back subsumed 0
% 1.80/2.00 Kbytes malloced 976
% 1.80/2.00
% 1.80/2.00 ----------- times (seconds) -----------
% 1.80/2.00 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/2.00
% 1.80/2.00 That finishes the proof of the theorem.
% 1.80/2.00
% 1.80/2.00 Process 25480 finished Wed Jul 27 09:58:33 2022
% 1.80/2.00 Otter interrupted
% 1.80/2.00 PROOF FOUND
%------------------------------------------------------------------------------