TSTP Solution File: NUM849+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:10:06 EDT 2022
% Result : Theorem 1.88s 2.11s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 13 unt; 0 nHn; 9 RR)
% Number of literals : 21 ( 20 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
vmul(vmul(vd448,vd449),vsucc(dollar_c1)) != vmul(vd448,vmul(vd449,vsucc(dollar_c1))),
file('NUM849+2.p',unknown),
[] ).
cnf(5,axiom,
( vmul(vmul(vd448,vd449),A) != vmul(vd448,vmul(vd449,A))
| vplus(vmul(vmul(vd448,vd449),A),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,A)),vmul(vd448,vd449)) ),
file('NUM849+2.p',unknown),
[] ).
cnf(7,axiom,
A = A,
file('NUM849+2.p',unknown),
[] ).
cnf(8,axiom,
vmul(vmul(vd448,vd449),dollar_c1) = vmul(vd448,vmul(vd449,dollar_c1)),
file('NUM849+2.p',unknown),
[] ).
cnf(13,axiom,
vmul(A,vplus(B,C)) = vplus(vmul(A,B),vmul(A,C)),
file('NUM849+2.p',unknown),
[] ).
cnf(15,plain,
vplus(vmul(A,B),vmul(A,C)) = vmul(A,vplus(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(16,axiom,
vmul(A,B) = vmul(B,A),
file('NUM849+2.p',unknown),
[] ).
cnf(18,axiom,
vmul(A,vsucc(B)) = vplus(vmul(A,B),A),
file('NUM849+2.p',unknown),
[] ).
cnf(25,axiom,
vplus(A,v1) = vsucc(A),
file('NUM849+2.p',unknown),
[] ).
cnf(27,plain,
vsucc(A) = vplus(A,v1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.1')] ).
cnf(28,plain,
( vmul(vmul(vd448,vd449),A) != vmul(vd448,vmul(vd449,A))
| vplus(vmul(vmul(vd448,vd449),A),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,A),vd449)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),15]),
[iquote('back_demod,5,demod,15')] ).
cnf(32,plain,
vplus(vmul(A,B),A) = vmul(A,vplus(B,v1)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18])]),27]),
[iquote('copy,18,flip.1,demod,27')] ).
cnf(35,plain,
vmul(vmul(vd448,vd449),vplus(dollar_c1,v1)) != vmul(vd448,vmul(vd449,vplus(dollar_c1,v1))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),27,27]),
[iquote('back_demod,1,demod,27,27')] ).
cnf(36,plain,
( vmul(vmul(vd448,vd449),A) != vmul(vd448,vmul(vd449,A))
| vmul(vmul(vd448,vd449),vplus(A,v1)) = vmul(vd448,vmul(vd449,vplus(A,v1))) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),32,32]),
[iquote('back_demod,28,demod,32,32')] ).
cnf(42,plain,
vmul(vd448,vmul(vd449,dollar_c1)) = vmul(dollar_c1,vmul(vd448,vd449)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,16])]),
[iquote('para_into,8.1.1,16.1.1,flip.1')] ).
cnf(159,plain,
( vmul(vd448,vmul(vd449,vplus(dollar_c1,v1))) != vmul(vd448,vmul(vd449,vplus(dollar_c1,v1)))
| vmul(vmul(vd448,vd449),dollar_c1) != vmul(dollar_c1,vmul(vd448,vd449)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[36,35]),42]),
[iquote('para_from,36.2.1,35.1.1,demod,42')] ).
cnf(2376,plain,
$false,
inference(hyper,[status(thm)],[159,7,16]),
[iquote('hyper,159,7,16')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 10:12:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.91 ----- Otter 3.3f, August 2004 -----
% 1.70/1.91 The process was started by sandbox2 on n027.cluster.edu,
% 1.70/1.91 Wed Jul 27 10:12:22 2022
% 1.70/1.91 The command was "./otter". The process ID is 23334.
% 1.70/1.91
% 1.70/1.91 set(prolog_style_variables).
% 1.70/1.91 set(auto).
% 1.70/1.91 dependent: set(auto1).
% 1.70/1.91 dependent: set(process_input).
% 1.70/1.91 dependent: clear(print_kept).
% 1.70/1.91 dependent: clear(print_new_demod).
% 1.70/1.91 dependent: clear(print_back_demod).
% 1.70/1.91 dependent: clear(print_back_sub).
% 1.70/1.91 dependent: set(control_memory).
% 1.70/1.91 dependent: assign(max_mem, 12000).
% 1.70/1.91 dependent: assign(pick_given_ratio, 4).
% 1.70/1.91 dependent: assign(stats_level, 1).
% 1.70/1.91 dependent: assign(max_seconds, 10800).
% 1.70/1.91 clear(print_given).
% 1.70/1.91
% 1.70/1.91 formula_list(usable).
% 1.70/1.91 all A (A=A).
% 1.70/1.91 -(all Vd454 (vmul(vmul(vd448,vd449),Vd454)=vmul(vd448,vmul(vd449,Vd454))->vmul(vmul(vd448,vd449),vsucc(Vd454))=vmul(vd448,vmul(vd449,vsucc(Vd454))))).
% 1.70/1.91 all Vd451 (vmul(vmul(vd448,vd449),Vd451)=vmul(vd448,vmul(vd449,Vd451))->vmul(vd448,vplus(vmul(vd449,Vd451),vd449))=vmul(vd448,vmul(vd449,vsucc(Vd451)))).
% 1.70/1.91 all Vd451 (vmul(vmul(vd448,vd449),Vd451)=vmul(vd448,vmul(vd449,Vd451))->vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449))=vmul(vd448,vplus(vmul(vd449,Vd451),vd449))).
% 1.70/1.91 all Vd451 (vmul(vmul(vd448,vd449),Vd451)=vmul(vd448,vmul(vd449,Vd451))->vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449))=vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449))).
% 1.70/1.91 all Vd451 (vmul(vmul(vd448,vd449),Vd451)=vmul(vd448,vmul(vd449,Vd451))->vmul(vmul(vd448,vd449),vsucc(Vd451))=vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449))).
% 1.70/1.91 vmul(vd448,vd449)=vmul(vd448,vmul(vd449,v1)).
% 1.70/1.91 all Vd432 Vd433 Vd434 (vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434))).
% 1.70/1.91 all Vd418 Vd419 (vmul(Vd418,Vd419)=vmul(Vd419,Vd418)).
% 1.70/1.91 all Vd408 Vd409 (vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409)).
% 1.70/1.91 all Vd396 Vd397 (vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396)&vmul(Vd396,v1)=Vd396).
% 1.70/1.91 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 1.70/1.91 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 -------> usable clausifies to:
% 1.70/1.91
% 1.70/1.91 list(usable).
% 1.70/1.91 0 [] A=A.
% 1.70/1.91 0 [] vmul(vmul(vd448,vd449),$c1)=vmul(vd448,vmul(vd449,$c1)).
% 1.70/1.91 0 [] vmul(vmul(vd448,vd449),vsucc($c1))!=vmul(vd448,vmul(vd449,vsucc($c1))).
% 1.70/1.91 0 [] vmul(vmul(vd448,vd449),Vd451)!=vmul(vd448,vmul(vd449,Vd451))|vmul(vd448,vplus(vmul(vd449,Vd451),vd449))=vmul(vd448,vmul(vd449,vsucc(Vd451))).
% 1.70/1.91 0 [] vmul(vmul(vd448,vd449),Vd451)!=vmul(vd448,vmul(vd449,Vd451))|vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449))=vmul(vd448,vplus(vmul(vd449,Vd451),vd449)).
% 1.70/1.91 0 [] vmul(vmul(vd448,vd449),Vd451)!=vmul(vd448,vmul(vd449,Vd451))|vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449))=vplus(vmul(vd448,vmul(vd449,Vd451)),vmul(vd448,vd449)).
% 1.70/1.91 0 [] vmul(vmul(vd448,vd449),Vd451)!=vmul(vd448,vmul(vd449,Vd451))|vmul(vmul(vd448,vd449),vsucc(Vd451))=vplus(vmul(vmul(vd448,vd449),Vd451),vmul(vd448,vd449)).
% 1.70/1.91 0 [] vmul(vd448,vd449)=vmul(vd448,vmul(vd449,v1)).
% 1.70/1.91 0 [] vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)).
% 1.70/1.91 0 [] vmul(Vd418,Vd419)=vmul(Vd419,Vd418).
% 1.70/1.91 0 [] vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409).
% 1.70/1.91 0 [] vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396).
% 1.70/1.91 0 [] vmul(Vd396,v1)=Vd396.
% 1.70/1.91 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 1.70/1.91 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.70/1.91 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.70/1.91 end_of_list.
% 1.70/1.91
% 1.70/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.70/1.91
% 1.70/1.91 This is a Horn set with equality. The strategy will be
% 1.70/1.91 Knuth-Bendix and hyper_res, with positive clauses in
% 1.70/1.91 sos and nonpositive clauses in usable.
% 1.70/1.91
% 1.70/1.91 dependent: set(knuth_bendix).
% 1.70/1.91 dependent: set(anl_eq).
% 1.70/1.91 dependent: set(para_from).
% 1.70/1.91 dependent: set(para_into).
% 1.70/1.91 dependent: clear(para_from_right).
% 1.70/1.91 dependent: clear(para_into_right).
% 1.70/1.91 dependent: set(para_from_vars).
% 1.70/1.91 dependent: set(eq_units_both_ways).
% 1.70/1.91 dependent: set(dynamic_demod_all).
% 1.70/1.91 dependent: set(dynamic_demod).
% 1.70/1.91 dependent: set(order_eq).
% 1.70/1.91 dependent: set(back_demod).
% 1.70/1.91 dependent: set(lrpo).
% 1.70/1.91 dependent: set(hyper_res).
% 1.70/1.91 dependent: clear(order_hyper).
% 1.70/1.91
% 1.70/1.91 ------------> process usable:
% 1.70/1.91 ** KEPT (pick-wt=13): 1 [] vmul(vmul(vd448,vd449),vsucc($c1))!=vmul(vd448,vmul(vd449,vsucc($c1))).
% 1.88/2.11 ** KEPT (pick-wt=25): 3 [copy,2,flip.2] vmul(vmul(vd448,vd449),A)!=vmul(vd448,vmul(vd449,A))|vmul(vd448,vmul(vd449,vsucc(A)))=vmul(vd448,vplus(vmul(vd449,A),vd449)).
% 1.88/2.11 ** KEPT (pick-wt=28): 4 [] vmul(vmul(vd448,vd449),A)!=vmul(vd448,vmul(vd449,A))|vplus(vmul(vd448,vmul(vd449,A)),vmul(vd448,vd449))=vmul(vd448,vplus(vmul(vd449,A),vd449)).
% 1.88/2.11 ** KEPT (pick-wt=30): 5 [] vmul(vmul(vd448,vd449),A)!=vmul(vd448,vmul(vd449,A))|vplus(vmul(vmul(vd448,vd449),A),vmul(vd448,vd449))=vplus(vmul(vd448,vmul(vd449,A)),vmul(vd448,vd449)).
% 1.88/2.11 ** KEPT (pick-wt=27): 6 [] vmul(vmul(vd448,vd449),A)!=vmul(vd448,vmul(vd449,A))|vmul(vmul(vd448,vd449),vsucc(A))=vplus(vmul(vmul(vd448,vd449),A),vmul(vd448,vd449)).
% 1.88/2.11
% 1.88/2.11 ------------> process sos:
% 1.88/2.11 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.88/2.11 ** KEPT (pick-wt=11): 8 [] vmul(vmul(vd448,vd449),$c1)=vmul(vd448,vmul(vd449,$c1)).
% 1.88/2.11 ---> New Demodulator: 9 [new_demod,8] vmul(vmul(vd448,vd449),$c1)=vmul(vd448,vmul(vd449,$c1)).
% 1.88/2.11 ** KEPT (pick-wt=9): 11 [copy,10,flip.1] vmul(vd448,vmul(vd449,v1))=vmul(vd448,vd449).
% 1.88/2.11 ---> New Demodulator: 12 [new_demod,11] vmul(vd448,vmul(vd449,v1))=vmul(vd448,vd449).
% 1.88/2.11 ** KEPT (pick-wt=13): 14 [copy,13,flip.1] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 1.88/2.11 ---> New Demodulator: 15 [new_demod,14] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 1.88/2.11 ** KEPT (pick-wt=7): 16 [] vmul(A,B)=vmul(B,A).
% 1.88/2.11 ** KEPT (pick-wt=10): 17 [] vmul(vsucc(A),B)=vplus(vmul(A,B),B).
% 1.88/2.11 ** KEPT (pick-wt=10): 18 [] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 1.88/2.11 ** KEPT (pick-wt=5): 19 [] vmul(A,v1)=A.
% 1.88/2.11 ---> New Demodulator: 20 [new_demod,19] vmul(A,v1)=A.
% 1.88/2.11 ** KEPT (pick-wt=7): 21 [] vplus(A,B)=vplus(B,A).
% 1.88/2.11 ** KEPT (pick-wt=9): 23 [copy,22,flip.1] vsucc(vplus(A,B))=vplus(A,vsucc(B)).
% 1.88/2.11 ---> New Demodulator: 24 [new_demod,23] vsucc(vplus(A,B))=vplus(A,vsucc(B)).
% 1.88/2.11 ** KEPT (pick-wt=6): 26 [copy,25,flip.1] vsucc(A)=vplus(A,v1).
% 1.88/2.11 ---> New Demodulator: 27 [new_demod,26] vsucc(A)=vplus(A,v1).
% 1.88/2.11 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.88/2.11 >>>> Starting back demodulation with 9.
% 1.88/2.11 >>>> Starting back demodulation with 12.
% 1.88/2.11 >>>> Starting back demodulation with 15.
% 1.88/2.11 >> back demodulating 5 with 15.
% 1.88/2.11 >> back demodulating 4 with 15.
% 1.88/2.11 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] vmul(A,B)=vmul(B,A).
% 1.88/2.11 ** KEPT (pick-wt=11): 29 [copy,17,flip.1,demod,27] vplus(vmul(A,B),B)=vmul(vplus(A,v1),B).
% 1.88/2.11 ---> New Demodulator: 30 [new_demod,29] vplus(vmul(A,B),B)=vmul(vplus(A,v1),B).
% 1.88/2.11 ** KEPT (pick-wt=11): 31 [copy,18,flip.1,demod,27] vplus(vmul(A,B),A)=vmul(A,vplus(B,v1)).
% 1.88/2.11 ---> New Demodulator: 32 [new_demod,31] vplus(vmul(A,B),A)=vmul(A,vplus(B,v1)).
% 1.88/2.11 18 back subsumes 6.
% 1.88/2.11 >>>> Starting back demodulation with 20.
% 1.88/2.11 >> back demodulating 11 with 20.
% 1.88/2.11 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] vplus(A,B)=vplus(B,A).
% 1.88/2.11 >>>> Starting back demodulation with 24.
% 1.88/2.11 >>>> Starting back demodulation with 27.
% 1.88/2.11 >> back demodulating 23 with 27.
% 1.88/2.11 >> back demodulating 18 with 27.
% 1.88/2.11 >> back demodulating 17 with 27.
% 1.88/2.11 >> back demodulating 3 with 27.
% 1.88/2.11 >> back demodulating 1 with 27.
% 1.88/2.11 >>>> Starting back demodulation with 30.
% 1.88/2.11 >>>> Starting back demodulation with 32.
% 1.88/2.11 >> back demodulating 28 with 32.
% 1.88/2.11 >>>> Starting back demodulation with 34.
% 1.88/2.11
% 1.88/2.11 ======= end of input processing =======
% 1.88/2.11
% 1.88/2.11 =========== start of search ===========
% 1.88/2.11
% 1.88/2.11
% 1.88/2.11 Resetting weight limit to 15.
% 1.88/2.11
% 1.88/2.11
% 1.88/2.11 Resetting weight limit to 15.
% 1.88/2.11
% 1.88/2.11 sos_size=1289
% 1.88/2.11
% 1.88/2.11 -------- PROOF --------
% 1.88/2.11
% 1.88/2.11 -----> EMPTY CLAUSE at 0.20 sec ----> 2376 [hyper,159,7,16] $F.
% 1.88/2.11
% 1.88/2.11 Length of proof is 8. Level of proof is 4.
% 1.88/2.11
% 1.88/2.11 ---------------- PROOF ----------------
% 1.88/2.11 % SZS status Theorem
% 1.88/2.11 % SZS output start Refutation
% See solution above
% 1.88/2.11 ------------ end of proof -------------
% 1.88/2.11
% 1.88/2.11
% 1.88/2.11 Search stopped by max_proofs option.
% 1.88/2.11
% 1.88/2.11
% 1.88/2.11 Search stopped by max_proofs option.
% 1.88/2.11
% 1.88/2.11 ============ end of search ============
% 1.88/2.11
% 1.88/2.11 -------------- statistics -------------
% 1.88/2.11 clauses given 181
% 1.88/2.11 clauses generated 17031
% 1.88/2.11 clauses kept 1991
% 1.88/2.11 clauses forward subsumed 8945
% 1.88/2.11 clauses back subsumed 237
% 1.88/2.11 Kbytes malloced 4882
% 1.88/2.11
% 1.88/2.11 ----------- times (seconds) -----------
% 1.88/2.11 user CPU time 0.20 (0 hr, 0 min, 0 sec)
% 1.88/2.11 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.88/2.11 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.88/2.11
% 1.88/2.11 That finishes the proof of the theorem.
% 1.88/2.11
% 1.88/2.11 Process 23334 finished Wed Jul 27 10:12:23 2022
% 1.95/2.11 Otter interrupted
% 1.95/2.11 PROOF FOUND
%------------------------------------------------------------------------------