%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM836+2 : TPTP v8.1.0. Released v4.1.0.
% 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 : Wed Jul 27 13:10:03 EDT 2022
% Result : Theorem 3.16s 3.32s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 12 unt; 0 nHn; 15 RR)
% Number of literals : 26 ( 14 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 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 : 27 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ less(A,B)
| B = vplus(A,dollar_f1(B,A)) ),
file('NUM836+2.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+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ greater(A,B)
| A = vplus(B,dollar_f2(B,A)) ),
file('NUM836+2.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(10,axiom,
( A != vplus(B,C)
| B != vplus(A,D) ),
file('NUM836+2.p',unknown),
[] ).
cnf(13,plain,
vplus(A,B) != A,
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[10])]),
[iquote('factor,10.1.2,flip.1')] ).
cnf(14,axiom,
A = A,
file('NUM836+2.p',unknown),
[] ).
cnf(15,axiom,
greater(vd203,vd204),
file('NUM836+2.p',unknown),
[] ).
cnf(16,axiom,
less(vd203,vd204),
file('NUM836+2.p',unknown),
[] ).
cnf(19,axiom,
vplus(vplus(A,B),C) = vplus(A,vplus(B,C)),
file('NUM836+2.p',unknown),
[] ).
cnf(28,plain,
less(A,vplus(A,B)),
inference(hyper,[status(thm)],[14,5]),
[iquote('hyper,14,5')] ).
cnf(33,plain,
vplus(vd203,dollar_f1(vd204,vd203)) = vd204,
inference(hyper,[status(thm)],[16,4]),
[iquote('hyper,16,4')] ).
cnf(44,plain,
( less(A,B)
| ~ greater(B,A) ),
inference(para_into,[status(thm),theory(equality)],[28,7]),
[iquote('para_into,28.1.2,7.2.1')] ).
cnf(115,plain,
less(vd204,vd203),
inference(hyper,[status(thm)],[44,15]),
[iquote('hyper,44,15')] ).
cnf(133,plain,
vplus(vd204,dollar_f1(vd203,vd204)) = vd203,
inference(hyper,[status(thm)],[115,4]),
[iquote('hyper,115,4')] ).
cnf(164,plain,
vplus(vd203,vplus(dollar_f1(vd204,vd203),A)) = vplus(vd204,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,19])]),
[iquote('para_from,33.1.1,19.1.1.1,flip.1')] ).
cnf(1011,plain,
vplus(vd204,A) != vd203,
inference(para_from,[status(thm),theory(equality)],[164,13]),
[iquote('para_from,164.1.1,13.1.1')] ).
cnf(1012,plain,
$false,
inference(binary,[status(thm)],[1011,133]),
[iquote('binary,1011.1,133.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM836+2 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:56:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.13 ----- Otter 3.3f, August 2004 -----
% 1.95/2.13 The process was started by sandbox2 on n020.cluster.edu,
% 1.95/2.13 Wed Jul 27 09:56:38 2022
% 1.95/2.13 The command was "./otter". The process ID is 23537.
% 1.95/2.13
% 1.95/2.13 set(prolog_style_variables).
% 1.95/2.13 set(auto).
% 1.95/2.13 dependent: set(auto1).
% 1.95/2.13 dependent: set(process_input).
% 1.95/2.13 dependent: clear(print_kept).
% 1.95/2.13 dependent: clear(print_new_demod).
% 1.95/2.13 dependent: clear(print_back_demod).
% 1.95/2.13 dependent: clear(print_back_sub).
% 1.95/2.13 dependent: set(control_memory).
% 1.95/2.13 dependent: assign(max_mem, 12000).
% 1.95/2.13 dependent: assign(pick_given_ratio, 4).
% 1.95/2.13 dependent: assign(stats_level, 1).
% 1.95/2.13 dependent: assign(max_seconds, 10800).
% 1.95/2.13 clear(print_given).
% 1.95/2.13
% 1.95/2.13 formula_list(usable).
% 1.95/2.13 all A (A=A).
% 1.95/2.13 -(-greater(vd203,vd204)| -less(vd203,vd204)).
% 1.95/2.13 vd203!=vd204| -greater(vd203,vd204).
% 1.95/2.13 all Vd198 Vd199 (less(Vd199,Vd198)<-> (exists Vd201 (Vd198=vplus(Vd199,Vd201)))).
% 1.95/2.13 all Vd193 Vd194 (greater(Vd194,Vd193)<-> (exists Vd196 (Vd194=vplus(Vd193,Vd196)))).
% 1.95/2.13 all Vd120 Vd121 (Vd120=Vd121| (exists Vd123 (Vd120=vplus(Vd121,Vd123)))| (exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.95/2.13 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.95/2.13 all Vd120 Vd121 (-(exists Vd123 (Vd120=vplus(Vd121,Vd123)))| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.95/2.13 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd123 (Vd120=vplus(Vd121,Vd123)))).
% 1.95/2.13 all Vd104 Vd105 (Vd104!=Vd105-> (all Vd107 (vplus(Vd107,Vd104)!=vplus(Vd107,Vd105)))).
% 1.95/2.13 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 1.95/2.13 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.95/2.13 end_of_list.
% 1.95/2.13
% 1.95/2.13 -------> usable clausifies to:
% 1.95/2.13
% 1.95/2.13 list(usable).
% 1.95/2.13 0 [] A=A.
% 1.95/2.13 0 [] greater(vd203,vd204).
% 1.95/2.13 0 [] less(vd203,vd204).
% 1.95/2.13 0 [] vd203!=vd204| -greater(vd203,vd204).
% 1.95/2.13 0 [] -less(Vd199,Vd198)|Vd198=vplus(Vd199,$f1(Vd198,Vd199)).
% 1.95/2.13 0 [] less(Vd199,Vd198)|Vd198!=vplus(Vd199,Vd201).
% 1.95/2.13 0 [] -greater(Vd194,Vd193)|Vd194=vplus(Vd193,$f2(Vd193,Vd194)).
% 1.95/2.13 0 [] greater(Vd194,Vd193)|Vd194!=vplus(Vd193,Vd196).
% 1.95/2.13 0 [] Vd120=Vd121|Vd120=vplus(Vd121,$f3(Vd120,Vd121))|Vd121=vplus(Vd120,$f4(Vd120,Vd121)).
% 1.95/2.13 0 [] Vd120!=Vd121|Vd121!=vplus(Vd120,Vd125).
% 1.95/2.13 0 [] Vd120!=vplus(Vd121,Vd123)|Vd121!=vplus(Vd120,Vd125).
% 1.95/2.13 0 [] Vd120!=Vd121|Vd120!=vplus(Vd121,Vd123).
% 1.95/2.13 0 [] Vd104=Vd105|vplus(Vd107,Vd104)!=vplus(Vd107,Vd105).
% 1.95/2.13 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 1.95/2.13 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.95/2.13 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.95/2.13 end_of_list.
% 1.95/2.13
% 1.95/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.95/2.13
% 1.95/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.95/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.95/2.13 deletion, with positive clauses in sos and nonpositive
% 1.95/2.13 clauses in usable.
% 1.95/2.13
% 1.95/2.13 dependent: set(knuth_bendix).
% 1.95/2.13 dependent: set(anl_eq).
% 1.95/2.13 dependent: set(para_from).
% 1.95/2.13 dependent: set(para_into).
% 1.95/2.13 dependent: clear(para_from_right).
% 1.95/2.13 dependent: clear(para_into_right).
% 1.95/2.13 dependent: set(para_from_vars).
% 1.95/2.13 dependent: set(eq_units_both_ways).
% 1.95/2.13 dependent: set(dynamic_demod_all).
% 1.95/2.13 dependent: set(dynamic_demod).
% 1.95/2.13 dependent: set(order_eq).
% 1.95/2.13 dependent: set(back_demod).
% 1.95/2.13 dependent: set(lrpo).
% 1.95/2.13 dependent: set(hyper_res).
% 1.95/2.13 dependent: set(unit_deletion).
% 1.95/2.13 dependent: set(factor).
% 1.95/2.13
% 1.95/2.13 ------------> process usable:
% 1.95/2.13 ** KEPT (pick-wt=6): 2 [copy,1,flip.1] vd204!=vd203| -greater(vd203,vd204).
% 1.95/2.13 ** KEPT (pick-wt=10): 4 [copy,3,flip.2] -less(A,B)|vplus(A,$f1(B,A))=B.
% 1.95/2.13 ** KEPT (pick-wt=8): 5 [] less(A,B)|B!=vplus(A,C).
% 1.95/2.13 ** KEPT (pick-wt=10): 7 [copy,6,flip.2] -greater(A,B)|vplus(B,$f2(B,A))=A.
% 1.95/2.13 ** KEPT (pick-wt=8): 8 [] greater(A,B)|A!=vplus(B,C).
% 1.95/2.13 ** KEPT (pick-wt=8): 9 [] A!=B|B!=vplus(A,C).
% 1.95/2.13 ** KEPT (pick-wt=10): 10 [] A!=vplus(B,C)|B!=vplus(A,D).
% 1.95/2.13 ** KEPT (pick-wt=8): 11 [] A!=B|A!=vplus(B,C).
% 1.95/2.13 ** KEPT (pick-wt=10): 12 [] A=B|vplus(C,A)!=vplus(C,B).
% 1.95/2.13
% 1.95/2.13 ------------> process sos:
% 1.95/2.13 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.95/2.13 ** KEPT (pick-wt=3): 15 [] greater(vd203,vd204).
% 1.95/2.13 ** KEPT (pick-wt=3): 16 [] less(vd203,vd204).
% 1.95/2.13 ** KEPT (pick-wt=17): 18 [copy,17,flip.2,flip.3] A=B|vplus(B,$f3(A,B))=A|vplus(A,$f4(A,B))=B.
% 1.95/2.13 ** KEPT (pick-wt=11): 19 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.95/2.13 ---> New Demodulator: 20 [new_demod,19] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 3.16/3.32 ** KEPT (pick-wt=9): 22 [copy,21,flip.1] vsucc(vplus(A,B))=vplus(A,vsucc(B)).
% 3.16/3.32 ---> New Demodulator: 23 [new_demod,22] vsucc(vplus(A,B))=vplus(A,vsucc(B)).
% 3.16/3.32 ** KEPT (pick-wt=6): 25 [copy,24,flip.1] vsucc(A)=vplus(A,v1).
% 3.16/3.32 ---> New Demodulator: 26 [new_demod,25] vsucc(A)=vplus(A,v1).
% 3.16/3.32 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 3.16/3.32 >>>> Starting back demodulation with 20.
% 3.16/3.32 >>>> Starting back demodulation with 23.
% 3.16/3.32 >>>> Starting back demodulation with 26.
% 3.16/3.32 >> back demodulating 22 with 26.
% 3.16/3.32
% 3.16/3.32 ======= end of input processing =======
% 3.16/3.32
% 3.16/3.32 =========== start of search ===========
% 3.16/3.32
% 3.16/3.32
% 3.16/3.32 Resetting weight limit to 13.
% 3.16/3.32
% 3.16/3.32
% 3.16/3.32 Resetting weight limit to 13.
% 3.16/3.32
% 3.16/3.32 sos_size=754
% 3.16/3.32
% 3.16/3.32
% 3.16/3.32 Resetting weight limit to 10.
% 3.16/3.32
% 3.16/3.32
% 3.16/3.32 Resetting weight limit to 10.
% 3.16/3.32
% 3.16/3.32 sos_size=813
% 3.16/3.32
% 3.16/3.32 -------- PROOF --------
% 3.16/3.32
% 3.16/3.32 ----> UNIT CONFLICT at 1.19 sec ----> 1012 [binary,1011.1,133.1] $F.
% 3.16/3.32
% 3.16/3.32 Length of proof is 10. Level of proof is 4.
% 3.16/3.32
% 3.16/3.32 ---------------- PROOF ----------------
% 3.16/3.32 % SZS status Theorem
% 3.16/3.32 % SZS output start Refutation
% See solution above
% 3.16/3.32 ------------ end of proof -------------
% 3.16/3.32
% 3.16/3.32
% 3.16/3.32 Search stopped by max_proofs option.
% 3.16/3.32
% 3.16/3.32
% 3.16/3.32 Search stopped by max_proofs option.
% 3.16/3.32
% 3.16/3.32 ============ end of search ============
% 3.16/3.32
% 3.16/3.32 -------------- statistics -------------
% 3.16/3.32 clauses given 145
% 3.16/3.32 clauses generated 29186
% 3.16/3.32 clauses kept 959
% 3.16/3.32 clauses forward subsumed 1380
% 3.16/3.32 clauses back subsumed 20
% 3.16/3.32 Kbytes malloced 8789
% 3.16/3.32
% 3.16/3.32 ----------- times (seconds) -----------
% 3.16/3.32 user CPU time 1.19 (0 hr, 0 min, 1 sec)
% 3.16/3.32 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.16/3.32 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.16/3.32
% 3.16/3.32 That finishes the proof of the theorem.
% 3.16/3.32
% 3.16/3.32 Process 23537 finished Wed Jul 27 09:56:41 2022
% 3.16/3.32 Otter interrupted
% 3.16/3.32 PROOF FOUND
%------------------------------------------------------------------------------