TSTP Solution File: NUM835+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 1.81s 2.01s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 9 unt; 3 nHn; 8 RR)
% Number of literals : 22 ( 17 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
vd165 != vplus(vd151,A),
file('NUM835+2.p',unknown),
[] ).
cnf(2,plain,
vplus(vd151,A) != vd165,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
vd151 != vplus(vd165,A),
file('NUM835+2.p',unknown),
[] ).
cnf(4,plain,
vplus(vd165,A) != vd151,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(5,axiom,
vd151 != vd165,
file('NUM835+2.p',unknown),
[] ).
cnf(6,plain,
vd165 != vd151,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(7,axiom,
( ~ m(A)
| B = A
| B = vplus(A,dollar_f1(B,A))
| A = vplus(B,dollar_f2(B,A)) ),
file('NUM835+2.p',unknown),
[] ).
cnf(8,plain,
( ~ m(A)
| B = A
| vplus(A,dollar_f1(B,A)) = B
| vplus(B,dollar_f2(B,A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])])]),
[iquote('copy,7,flip.3,flip.4')] ).
cnf(10,axiom,
( m(A)
| B != vplus(A,C) ),
file('NUM835+2.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('NUM835+2.p',unknown),
[] ).
cnf(30,plain,
m(A),
inference(hyper,[status(thm)],[13,10]),
[iquote('hyper,13,10')] ).
cnf(31,plain,
( A = B
| vplus(B,dollar_f1(A,B)) = A
| vplus(A,dollar_f2(A,B)) = B ),
inference(hyper,[status(thm)],[30,8]),
[iquote('hyper,30,8')] ).
cnf(123,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[31,6]),2,4]),
[iquote('hyper,31,6,unit_del,2,4')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n010.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 09:35:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.81/2.00 ----- Otter 3.3f, August 2004 -----
% 1.81/2.00 The process was started by sandbox on n010.cluster.edu,
% 1.81/2.00 Wed Jul 27 09:35:25 2022
% 1.81/2.00 The command was "./otter". The process ID is 16207.
% 1.81/2.00
% 1.81/2.00 set(prolog_style_variables).
% 1.81/2.00 set(auto).
% 1.81/2.00 dependent: set(auto1).
% 1.81/2.00 dependent: set(process_input).
% 1.81/2.00 dependent: clear(print_kept).
% 1.81/2.00 dependent: clear(print_new_demod).
% 1.81/2.00 dependent: clear(print_back_demod).
% 1.81/2.00 dependent: clear(print_back_sub).
% 1.81/2.00 dependent: set(control_memory).
% 1.81/2.00 dependent: assign(max_mem, 12000).
% 1.81/2.00 dependent: assign(pick_given_ratio, 4).
% 1.81/2.00 dependent: assign(stats_level, 1).
% 1.81/2.00 dependent: assign(max_seconds, 10800).
% 1.81/2.00 clear(print_given).
% 1.81/2.00
% 1.81/2.00 formula_list(usable).
% 1.81/2.00 all A (A=A).
% 1.81/2.00 -((exists Vd180 (vd165=vplus(vd151,Vd180)))| (exists Vd170 (vd151=vplus(vd165,Vd170)))|vd151=vd165).
% 1.81/2.00 all Vd180 (vd165=vplus(vd151,Vd180)->m(vsucc(vd165))).
% 1.81/2.00 all Vd180 (vd165=vplus(vd151,Vd180)->vsucc(vplus(vd151,Vd180))=vplus(vd151,vsucc(Vd180))).
% 1.81/2.00 all Vd180 (vd165=vplus(vd151,Vd180)->vsucc(vd165)=vsucc(vplus(vd151,Vd180))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170!=v1->m(vsucc(vd165)))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170!=v1->vplus(vplus(vd165,v1),vskolem3)=vplus(vsucc(vd165),vskolem3))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170!=v1->vplus(vd165,vplus(v1,vskolem3))=vplus(vplus(vd165,v1),vskolem3))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170!=v1->vd151=vplus(vd165,vplus(v1,vskolem3)))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170!=v1->vsucc(vskolem3)=vplus(v1,vskolem3))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170!=v1->Vd170=vsucc(vskolem3))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170=v1->m(vsucc(vd165)))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170=v1->vplus(vd165,v1)=vsucc(vd165))).
% 1.81/2.00 all Vd170 (vd151=vplus(vd165,Vd170)-> (Vd170=v1->vd151=vplus(vd165,v1))).
% 1.81/2.00 vd151=vd165->m(vsucc(vd165)).
% 1.81/2.00 vd151=vd165->vplus(vd165,v1)=vplus(vd151,v1).
% 1.81/2.00 vd151=vd165->vsucc(vd165)=vplus(vd165,v1).
% 1.81/2.00 all Vd151 Vd152 (m(Vd152)<->Vd151=Vd152| (exists Vd155 (Vd151=vplus(Vd152,Vd155)))| (exists Vd157 (Vd152=vplus(Vd151,Vd157)))).
% 1.81/2.00 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 1.81/2.00 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 1.81/2.00 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 1.81/2.00 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 1.81/2.00 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.81/2.00 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 1.81/2.00 all Vd16 (vsucc(Vd16)!=Vd16).
% 1.81/2.00 end_of_list.
% 1.81/2.00
% 1.81/2.00 -------> usable clausifies to:
% 1.81/2.00
% 1.81/2.00 list(usable).
% 1.81/2.00 0 [] A=A.
% 1.81/2.00 0 [] vd165!=vplus(vd151,Vd180).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170).
% 1.81/2.00 0 [] vd151!=vd165.
% 1.81/2.00 0 [] vd165!=vplus(vd151,Vd180)|m(vsucc(vd165)).
% 1.81/2.00 0 [] vd165!=vplus(vd151,Vd180)|vsucc(vplus(vd151,Vd180))=vplus(vd151,vsucc(Vd180)).
% 1.81/2.00 0 [] vd165!=vplus(vd151,Vd180)|vsucc(vd165)=vsucc(vplus(vd151,Vd180)).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170=v1|m(vsucc(vd165)).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170=v1|vplus(vplus(vd165,v1),vskolem3)=vplus(vsucc(vd165),vskolem3).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170=v1|vplus(vd165,vplus(v1,vskolem3))=vplus(vplus(vd165,v1),vskolem3).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170=v1|vd151=vplus(vd165,vplus(v1,vskolem3)).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170=v1|vsucc(vskolem3)=vplus(v1,vskolem3).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170=v1|Vd170=vsucc(vskolem3).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170!=v1|m(vsucc(vd165)).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170!=v1|vplus(vd165,v1)=vsucc(vd165).
% 1.81/2.00 0 [] vd151!=vplus(vd165,Vd170)|Vd170!=v1|vd151=vplus(vd165,v1).
% 1.81/2.00 0 [] vd151!=vd165|m(vsucc(vd165)).
% 1.81/2.00 0 [] vd151!=vd165|vplus(vd165,v1)=vplus(vd151,v1).
% 1.81/2.00 0 [] vd151!=vd165|vsucc(vd165)=vplus(vd165,v1).
% 1.81/2.00 0 [] -m(Vd152)|Vd151=Vd152|Vd151=vplus(Vd152,$f1(Vd151,Vd152))|Vd152=vplus(Vd151,$f2(Vd151,Vd152)).
% 1.81/2.00 0 [] m(Vd152)|Vd151!=Vd152.
% 1.81/2.00 0 [] m(Vd152)|Vd151!=vplus(Vd152,Vd155).
% 1.81/2.00 0 [] m(Vd152)|Vd152!=vplus(Vd151,Vd157).
% 1.81/2.00 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 1.81/2.00 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 1.81/2.00 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 1.81/2.00 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 1.81/2.00 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.81/2.00 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.81/2.00 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 1.81/2.00 0 [] vsucc(Vd16)!=Vd16.
% 1.81/2.00 end_of_list.
% 1.81/2.00
% 1.81/2.00 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.81/2.00
% 1.81/2.00 This ia a non-Horn set with equality. The strategy will be
% 1.81/2.00 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.81/2.00 deletion, with positive clauses in sos and nonpositive
% 1.81/2.00 clauses in usable.
% 1.81/2.00
% 1.81/2.00 dependent: set(knuth_bendix).
% 1.81/2.00 dependent: set(anl_eq).
% 1.81/2.00 dependent: set(para_from).
% 1.81/2.00 dependent: set(para_into).
% 1.81/2.00 dependent: clear(para_from_right).
% 1.81/2.00 dependent: clear(para_into_right).
% 1.81/2.00 dependent: set(para_from_vars).
% 1.81/2.00 dependent: set(eq_units_both_ways).
% 1.81/2.00 dependent: set(dynamic_demod_all).
% 1.81/2.00 dependent: set(dynamic_demod).
% 1.81/2.00 dependent: set(order_eq).
% 1.81/2.00 dependent: set(back_demod).
% 1.81/2.00 dependent: set(lrpo).
% 1.81/2.00 dependent: set(hyper_res).
% 1.81/2.00 dependent: set(unit_deletion).
% 1.81/2.00 dependent: set(factor).
% 1.81/2.00
% 1.81/2.00 ------------> process usable:
% 1.81/2.00 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] vplus(vd151,A)!=vd165.
% 1.81/2.00 ** KEPT (pick-wt=5): 4 [copy,3,flip.1] vplus(vd165,A)!=vd151.
% 1.81/2.00 ** KEPT (pick-wt=3): 6 [copy,5,flip.1] vd165!=vd151.
% 1.81/2.00 Following clause subsumed by 2 during input processing: 0 [flip.1] vplus(vd151,A)!=vd165|m(vsucc(vd165)).
% 1.81/2.00 Following clause subsumed by 2 during input processing: 0 [flip.1] vplus(vd151,A)!=vd165|vsucc(vplus(vd151,A))=vplus(vd151,vsucc(A)).
% 1.81/2.00 Following clause subsumed by 2 during input processing: 0 [flip.1,flip.2] vplus(vd151,A)!=vd165|vsucc(vplus(vd151,A))=vsucc(vd165).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [flip.1] vplus(vd165,A)!=vd151|A=v1|m(vsucc(vd165)).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [flip.1,flip.3] vplus(vd165,A)!=vd151|A=v1|vplus(vsucc(vd165),vskolem3)=vplus(vplus(vd165,v1),vskolem3).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [flip.1,flip.3] vplus(vd165,A)!=vd151|A=v1|vplus(vplus(vd165,v1),vskolem3)=vplus(vd165,vplus(v1,vskolem3)).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [unit_del,4,flip.1] vplus(vd165,A)!=vd151|A=v1.
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [flip.1] vplus(vd165,A)!=vd151|A=v1|vsucc(vskolem3)=vplus(v1,vskolem3).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [flip.1] vplus(vd165,A)!=vd151|A=v1|A=vsucc(vskolem3).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [flip.1] vplus(vd165,A)!=vd151|A!=v1|m(vsucc(vd165)).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [flip.1,flip.3] vplus(vd165,A)!=vd151|A!=v1|vsucc(vd165)=vplus(vd165,v1).
% 1.81/2.00 Following clause subsumed by 4 during input processing: 0 [unit_del,4,flip.1] vplus(vd165,A)!=vd151|A!=v1.
% 1.81/2.00 Following clause subsumed by 6 during input processing: 0 [flip.1] vd165!=vd151|m(vsucc(vd165)).
% 1.81/2.00 Following clause subsumed by 6 during input processing: 0 [flip.1] vd165!=vd151|vplus(vd165,v1)=vplus(vd151,v1).
% 1.81/2.00 Following clause subsumed by 6 during input processing: 0 [flip.1] vd165!=vd151|vsucc(vd165)=vplus(vd165,v1).
% 1.81/2.00 ** KEPT (pick-wt=19): 8 [copy,7,flip.3,flip.4] -m(A)|B=A|vplus(A,$f1(B,A))=B|vplus(B,$f2(B,A))=A.
% 1.81/2.00 ** KEPT (pick-wt=5): 9 [] m(A)|B!=A.
% 1.81/2.00 ** KEPT (pick-wt=7): 10 [] m(A)|B!=vplus(A,C).
% 1.81/2.00 ** KEPT (pick-wt=7): 11 [] m(A)|A!=vplus(B,C).
% 1.81/2.00 ** KEPT (pick-wt=4): 12 [] vsucc(A)!=A.
% 1.81/2.00
% 1.81/2.00 ------------> process sos:
% 1.81/2.00 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.81/2.00 ** KEPT (pick-wt=7): 14 [] vplus(A,B)=vplus(B,A).
% 1.81/2.00 ** KEPT (pick-wt=9): 16 [copy,15,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.81/2.00 ---> New Demodulator: 17 [new_demod,16] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.81/2.00 ** KEPT (pick-wt=6): 19 [copy,18,flip.1] vsucc(A)=vplus(v1,A).
% 1.81/2.00 ---> New Demodulator: 20 [new_demod,19] vsucc(A)=vplus(v1,A).
% 1.81/2.00 ** KEPT (pick-wt=11): 21 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.81/2.00 ---> New Demodulator: 22 [new_demod,21] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.81/2.00 ** KEPT (pick-wt=11): 24 [copy,23,demod,20,20] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.81/2.00 Following clause subsumed by 14 during input processing: 0 [demod,20] vplus(A,v1)=vplus(v1,A).
% 1.81/2.00 ** KEPT (pick-wt=9): 26 [copy,25,demod,20,flip.2] A=v1|vplus(v1,vskolem2(A))=A.
% 1.81/2.00 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.81/2.00 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] vplus(A,B)=vplus(B,A).
% 1.81/2.01 >>>> Starting back demodulation with 17.
% 1.81/2.01 >>>> Starting back demodulation with 20.
% 1.81/2.01 >> back demodulating 16 with 20.
% 1.81/2.01 >> back demodulating 12 with 20.
% 1.81/2.01 >>>> Starting back demodulation with 22.
% 1.81/2.01 ** KEPT (pick-wt=11): 28 [copy,24,flip.1] vplus(v1,vplus(A,B))=vplus(A,vplus(v1,B)).
% 1.81/2.01 Following clause subsumed by 24 during input processing: 0 [copy,28,flip.1] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.81/2.01
% 1.81/2.01 ======= end of input processing =======
% 1.81/2.01
% 1.81/2.01 =========== start of search ===========
% 1.81/2.01
% 1.81/2.01 -------- PROOF --------
% 1.81/2.01
% 1.81/2.01 -----> EMPTY CLAUSE at 0.00 sec ----> 123 [hyper,31,6,unit_del,2,4] $F.
% 1.81/2.01
% 1.81/2.01 Length of proof is 6. Level of proof is 2.
% 1.81/2.01
% 1.81/2.01 ---------------- PROOF ----------------
% 1.81/2.01 % SZS status Theorem
% 1.81/2.01 % SZS output start Refutation
% See solution above
% 1.81/2.01 ------------ end of proof -------------
% 1.81/2.01
% 1.81/2.01
% 1.81/2.01 Search stopped by max_proofs option.
% 1.81/2.01
% 1.81/2.01
% 1.81/2.01 Search stopped by max_proofs option.
% 1.81/2.01
% 1.81/2.01 ============ end of search ============
% 1.81/2.01
% 1.81/2.01 -------------- statistics -------------
% 1.81/2.01 clauses given 16
% 1.81/2.01 clauses generated 129
% 1.81/2.01 clauses kept 104
% 1.81/2.01 clauses forward subsumed 64
% 1.81/2.01 clauses back subsumed 7
% 1.81/2.01 Kbytes malloced 976
% 1.81/2.01
% 1.81/2.01 ----------- times (seconds) -----------
% 1.81/2.01 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.81/2.01 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.01 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.81/2.01
% 1.81/2.01 That finishes the proof of the theorem.
% 1.81/2.01
% 1.81/2.01 Process 16207 finished Wed Jul 27 09:35:26 2022
% 1.81/2.01 Otter interrupted
% 1.81/2.01 PROOF FOUND
%------------------------------------------------------------------------------