%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM836+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 1.92s 2.11s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 16 unt; 0 nHn; 18 RR)
% Number of literals : 28 ( 16 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ less(A,B)
| B = vplus(A,dollar_f1(B,A)) ),
file('NUM836+1.p',unknown),
[] ).
cnf(4,plain,
( ~ less(A,B)
| vplus(A,dollar_f1(B,A)) = B ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.2')] ).
cnf(5,axiom,
( less(A,B)
| B != vplus(A,C) ),
file('NUM836+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ greater(A,B)
| A = vplus(B,dollar_f2(B,A)) ),
file('NUM836+1.p',unknown),
[] ).
cnf(7,plain,
( ~ greater(A,B)
| vplus(B,dollar_f2(B,A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.2')] ).
cnf(13,axiom,
A != vplus(B,A),
file('NUM836+1.p',unknown),
[] ).
cnf(14,plain,
vplus(A,B) != B,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(19,axiom,
A = A,
file('NUM836+1.p',unknown),
[] ).
cnf(20,axiom,
greater(vd203,vd204),
file('NUM836+1.p',unknown),
[] ).
cnf(21,axiom,
less(vd203,vd204),
file('NUM836+1.p',unknown),
[] ).
cnf(24,axiom,
vplus(A,B) = vplus(B,A),
file('NUM836+1.p',unknown),
[] ).
cnf(31,axiom,
vplus(vplus(A,B),C) = vplus(A,vplus(B,C)),
file('NUM836+1.p',unknown),
[] ).
cnf(39,plain,
less(A,vplus(A,B)),
inference(hyper,[status(thm)],[19,5]),
[iquote('hyper,19,5')] ).
cnf(44,plain,
vplus(vd203,dollar_f1(vd204,vd203)) = vd204,
inference(hyper,[status(thm)],[21,4]),
[iquote('hyper,21,4')] ).
cnf(55,plain,
( less(A,B)
| ~ greater(B,A) ),
inference(para_into,[status(thm),theory(equality)],[39,7]),
[iquote('para_into,39.1.2,7.2.1')] ).
cnf(130,plain,
less(vd204,vd203),
inference(hyper,[status(thm)],[55,20]),
[iquote('hyper,55,20')] ).
cnf(143,plain,
vplus(vd204,dollar_f1(vd203,vd204)) = vd203,
inference(hyper,[status(thm)],[130,4]),
[iquote('hyper,130,4')] ).
cnf(204,plain,
vplus(A,vplus(B,C)) != C,
inference(para_from,[status(thm),theory(equality)],[31,14]),
[iquote('para_from,31.1.1,14.1.1')] ).
cnf(566,plain,
vplus(dollar_f1(vd204,vd203),vd203) = vd204,
inference(para_into,[status(thm),theory(equality)],[44,24]),
[iquote('para_into,44.1.1,24.1.1')] ).
cnf(858,plain,
vplus(dollar_f1(vd203,vd204),vd204) = vd203,
inference(para_into,[status(thm),theory(equality)],[143,24]),
[iquote('para_into,143.1.1,24.1.1')] ).
cnf(998,plain,
vplus(A,vd204) != vd203,
inference(para_from,[status(thm),theory(equality)],[566,204]),
[iquote('para_from,566.1.1,204.1.1.2')] ).
cnf(999,plain,
$false,
inference(binary,[status(thm)],[998,858]),
[iquote('binary,998.1,858.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM836+1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:34:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.84/2.03 ----- Otter 3.3f, August 2004 -----
% 1.84/2.03 The process was started by sandbox on n014.cluster.edu,
% 1.84/2.03 Wed Jul 27 09:34:39 2022
% 1.84/2.03 The command was "./otter". The process ID is 3166.
% 1.84/2.03
% 1.84/2.03 set(prolog_style_variables).
% 1.84/2.03 set(auto).
% 1.84/2.03 dependent: set(auto1).
% 1.84/2.03 dependent: set(process_input).
% 1.84/2.03 dependent: clear(print_kept).
% 1.84/2.03 dependent: clear(print_new_demod).
% 1.84/2.03 dependent: clear(print_back_demod).
% 1.84/2.03 dependent: clear(print_back_sub).
% 1.84/2.03 dependent: set(control_memory).
% 1.84/2.03 dependent: assign(max_mem, 12000).
% 1.84/2.03 dependent: assign(pick_given_ratio, 4).
% 1.84/2.03 dependent: assign(stats_level, 1).
% 1.84/2.03 dependent: assign(max_seconds, 10800).
% 1.84/2.03 clear(print_given).
% 1.84/2.03
% 1.84/2.03 formula_list(usable).
% 1.84/2.03 all A (A=A).
% 1.84/2.03 -(-greater(vd203,vd204)| -less(vd203,vd204)).
% 1.84/2.03 vd203!=vd204| -greater(vd203,vd204).
% 1.84/2.03 all Vd198 Vd199 (less(Vd199,Vd198)<-> (exists Vd201 (Vd198=vplus(Vd199,Vd201)))).
% 1.84/2.03 all Vd193 Vd194 (greater(Vd194,Vd193)<-> (exists Vd196 (Vd194=vplus(Vd193,Vd196)))).
% 1.84/2.03 all Vd120 Vd121 (Vd120=Vd121| (exists Vd123 (Vd120=vplus(Vd121,Vd123)))| (exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.84/2.03 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.84/2.03 all Vd120 Vd121 (-(exists Vd123 (Vd120=vplus(Vd121,Vd123)))| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.84/2.03 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd123 (Vd120=vplus(Vd121,Vd123)))).
% 1.84/2.03 all Vd104 Vd105 (Vd104!=Vd105-> (all Vd107 (vplus(Vd107,Vd104)!=vplus(Vd107,Vd105)))).
% 1.84/2.03 all Vd92 Vd93 (Vd93!=vplus(Vd92,Vd93)).
% 1.84/2.03 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 1.84/2.03 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 1.84/2.03 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 1.84/2.03 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 1.84/2.03 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.84/2.03 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 1.84/2.03 all Vd16 (vsucc(Vd16)!=Vd16).
% 1.84/2.03 all Vd7 Vd8 (Vd7!=Vd8->vsucc(Vd7)!=vsucc(Vd8)).
% 1.84/2.03 all Vd3 Vd4 (vsucc(Vd3)=vsucc(Vd4)->Vd3=Vd4).
% 1.84/2.03 all Vd1 (vsucc(Vd1)!=v1).
% 1.84/2.03 end_of_list.
% 1.84/2.03
% 1.84/2.03 -------> usable clausifies to:
% 1.84/2.03
% 1.84/2.03 list(usable).
% 1.84/2.03 0 [] A=A.
% 1.84/2.03 0 [] greater(vd203,vd204).
% 1.84/2.03 0 [] less(vd203,vd204).
% 1.84/2.03 0 [] vd203!=vd204| -greater(vd203,vd204).
% 1.84/2.03 0 [] -less(Vd199,Vd198)|Vd198=vplus(Vd199,$f1(Vd198,Vd199)).
% 1.84/2.03 0 [] less(Vd199,Vd198)|Vd198!=vplus(Vd199,Vd201).
% 1.84/2.03 0 [] -greater(Vd194,Vd193)|Vd194=vplus(Vd193,$f2(Vd193,Vd194)).
% 1.84/2.03 0 [] greater(Vd194,Vd193)|Vd194!=vplus(Vd193,Vd196).
% 1.84/2.03 0 [] Vd120=Vd121|Vd120=vplus(Vd121,$f3(Vd120,Vd121))|Vd121=vplus(Vd120,$f4(Vd120,Vd121)).
% 1.84/2.03 0 [] Vd120!=Vd121|Vd121!=vplus(Vd120,Vd125).
% 1.84/2.03 0 [] Vd120!=vplus(Vd121,Vd123)|Vd121!=vplus(Vd120,Vd125).
% 1.84/2.03 0 [] Vd120!=Vd121|Vd120!=vplus(Vd121,Vd123).
% 1.84/2.03 0 [] Vd104=Vd105|vplus(Vd107,Vd104)!=vplus(Vd107,Vd105).
% 1.84/2.03 0 [] Vd93!=vplus(Vd92,Vd93).
% 1.84/2.03 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 1.84/2.03 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 1.84/2.03 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 1.84/2.03 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 1.84/2.03 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.84/2.03 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.84/2.03 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 1.84/2.03 0 [] vsucc(Vd16)!=Vd16.
% 1.84/2.03 0 [] Vd7=Vd8|vsucc(Vd7)!=vsucc(Vd8).
% 1.84/2.03 0 [] vsucc(Vd3)!=vsucc(Vd4)|Vd3=Vd4.
% 1.84/2.03 0 [] vsucc(Vd1)!=v1.
% 1.84/2.03 end_of_list.
% 1.84/2.03
% 1.84/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.84/2.03
% 1.84/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.84/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.84/2.03 deletion, with positive clauses in sos and nonpositive
% 1.84/2.03 clauses in usable.
% 1.84/2.03
% 1.84/2.03 dependent: set(knuth_bendix).
% 1.84/2.03 dependent: set(anl_eq).
% 1.84/2.03 dependent: set(para_from).
% 1.84/2.03 dependent: set(para_into).
% 1.84/2.03 dependent: clear(para_from_right).
% 1.84/2.03 dependent: clear(para_into_right).
% 1.84/2.03 dependent: set(para_from_vars).
% 1.84/2.03 dependent: set(eq_units_both_ways).
% 1.84/2.03 dependent: set(dynamic_demod_all).
% 1.84/2.03 dependent: set(dynamic_demod).
% 1.84/2.03 dependent: set(order_eq).
% 1.84/2.03 dependent: set(back_demod).
% 1.84/2.03 dependent: set(lrpo).
% 1.84/2.03 dependent: set(hyper_res).
% 1.84/2.03 dependent: set(unit_deletion).
% 1.84/2.03 dependent: set(factor).
% 1.84/2.03
% 1.84/2.03 ------------> process usable:
% 1.84/2.03 ** KEPT (pick-wt=6): 2 [copy,1,flip.1] vd204!=vd203| -greater(vd203,vd204).
% 1.84/2.03 ** KEPT (pick-wt=10): 4 [copy,3,flip.2] -less(A,B)|vplus(A,$f1(B,A))=B.
% 1.84/2.03 ** KEPT (pick-wt=8): 5 [] less(A,B)|B!=vplus(A,C).
% 1.92/2.11 ** KEPT (pick-wt=10): 7 [copy,6,flip.2] -greater(A,B)|vplus(B,$f2(B,A))=A.
% 1.92/2.11 ** KEPT (pick-wt=8): 8 [] greater(A,B)|A!=vplus(B,C).
% 1.92/2.11 ** KEPT (pick-wt=8): 9 [] A!=B|B!=vplus(A,C).
% 1.92/2.11 ** KEPT (pick-wt=10): 10 [] A!=vplus(B,C)|B!=vplus(A,D).
% 1.92/2.11 ** KEPT (pick-wt=8): 11 [] A!=B|A!=vplus(B,C).
% 1.92/2.11 ** KEPT (pick-wt=10): 12 [] A=B|vplus(C,A)!=vplus(C,B).
% 1.92/2.11 ** KEPT (pick-wt=5): 14 [copy,13,flip.1] vplus(A,B)!=B.
% 1.92/2.11 ** KEPT (pick-wt=4): 15 [] vsucc(A)!=A.
% 1.92/2.11 ** KEPT (pick-wt=8): 16 [] A=B|vsucc(A)!=vsucc(B).
% 1.92/2.11 Following clause subsumed by 16 during input processing: 0 [] vsucc(A)!=vsucc(B)|A=B.
% 1.92/2.11 ** KEPT (pick-wt=4): 17 [] vsucc(A)!=v1.
% 1.92/2.11
% 1.92/2.11 ------------> process sos:
% 1.92/2.11 ** KEPT (pick-wt=3): 19 [] A=A.
% 1.92/2.11 ** KEPT (pick-wt=3): 20 [] greater(vd203,vd204).
% 1.92/2.11 ** KEPT (pick-wt=3): 21 [] less(vd203,vd204).
% 1.92/2.11 ** KEPT (pick-wt=17): 23 [copy,22,flip.2,flip.3] A=B|vplus(B,$f3(A,B))=A|vplus(A,$f4(A,B))=B.
% 1.92/2.11 ** KEPT (pick-wt=7): 24 [] vplus(A,B)=vplus(B,A).
% 1.92/2.11 ** KEPT (pick-wt=9): 26 [copy,25,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.92/2.11 ---> New Demodulator: 27 [new_demod,26] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.92/2.11 ** KEPT (pick-wt=6): 29 [copy,28,flip.1] vsucc(A)=vplus(v1,A).
% 1.92/2.11 ---> New Demodulator: 30 [new_demod,29] vsucc(A)=vplus(v1,A).
% 1.92/2.11 ** KEPT (pick-wt=11): 31 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.92/2.11 ---> New Demodulator: 32 [new_demod,31] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.92/2.11 ** KEPT (pick-wt=11): 34 [copy,33,demod,30,30] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.92/2.11 Following clause subsumed by 24 during input processing: 0 [demod,30] vplus(A,v1)=vplus(v1,A).
% 1.92/2.11 ** KEPT (pick-wt=9): 36 [copy,35,demod,30,flip.2] A=v1|vplus(v1,vskolem2(A))=A.
% 1.92/2.11 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] A=A.
% 1.92/2.11 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] vplus(A,B)=vplus(B,A).
% 1.92/2.11 >>>> Starting back demodulation with 27.
% 1.92/2.11 >>>> Starting back demodulation with 30.
% 1.92/2.11 >> back demodulating 26 with 30.
% 1.92/2.11 >> back demodulating 17 with 30.
% 1.92/2.11 >> back demodulating 16 with 30.
% 1.92/2.11 >> back demodulating 15 with 30.
% 1.92/2.11 >>>> Starting back demodulation with 32.
% 1.92/2.11 ** KEPT (pick-wt=11): 37 [copy,34,flip.1] vplus(v1,vplus(A,B))=vplus(A,vplus(v1,B)).
% 1.92/2.11 Following clause subsumed by 34 during input processing: 0 [copy,37,flip.1] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.92/2.11
% 1.92/2.11 ======= end of input processing =======
% 1.92/2.11
% 1.92/2.11 =========== start of search ===========
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Resetting weight limit to 8.
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Resetting weight limit to 8.
% 1.92/2.11
% 1.92/2.11 sos_size=740
% 1.92/2.11
% 1.92/2.11 -------- PROOF --------
% 1.92/2.11
% 1.92/2.11 ----> UNIT CONFLICT at 0.08 sec ----> 999 [binary,998.1,858.1] $F.
% 1.92/2.11
% 1.92/2.11 Length of proof is 12. Level of proof is 5.
% 1.92/2.11
% 1.92/2.11 ---------------- PROOF ----------------
% 1.92/2.11 % SZS status Theorem
% 1.92/2.11 % SZS output start Refutation
% See solution above
% 1.92/2.11 ------------ end of proof -------------
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Search stopped by max_proofs option.
% 1.92/2.11
% 1.92/2.11
% 1.92/2.11 Search stopped by max_proofs option.
% 1.92/2.11
% 1.92/2.11 ============ end of search ============
% 1.92/2.11
% 1.92/2.11 -------------- statistics -------------
% 1.92/2.11 clauses given 67
% 1.92/2.11 clauses generated 2115
% 1.92/2.11 clauses kept 939
% 1.92/2.11 clauses forward subsumed 728
% 1.92/2.11 clauses back subsumed 12
% 1.92/2.11 Kbytes malloced 4882
% 1.92/2.11
% 1.92/2.11 ----------- times (seconds) -----------
% 1.92/2.11 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.92/2.11 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.92/2.11 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.11
% 1.92/2.11 That finishes the proof of the theorem.
% 1.92/2.11
% 1.92/2.11 Process 3166 finished Wed Jul 27 09:34:41 2022
% 1.92/2.11 Otter interrupted
% 1.92/2.11 PROOF FOUND
%------------------------------------------------------------------------------