TSTP Solution File: NUM846+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM846+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 13:10:05 EDT 2022
% Result : Theorem 1.76s 1.98s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 6 RR)
% Number of literals : 7 ( 6 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 1 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('NUM846+2.p',unknown),
[] ).
cnf(2,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(7,axiom,
A = A,
file('NUM846+2.p',unknown),
[] ).
cnf(13,axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
file('NUM846+2.p',unknown),
[] ).
cnf(15,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vd439)) = vmul(vd436,vplus(vd437,vd439)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(44,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),15]),
[iquote('back_demod,2,demod,15')] ).
cnf(45,plain,
$false,
inference(binary,[status(thm)],[44,7]),
[iquote('binary,44.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM846+2 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n027.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 09:50:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.76/1.98 ----- Otter 3.3f, August 2004 -----
% 1.76/1.98 The process was started by sandbox2 on n027.cluster.edu,
% 1.76/1.98 Wed Jul 27 09:50:22 2022
% 1.76/1.98 The command was "./otter". The process ID is 13214.
% 1.76/1.98
% 1.76/1.98 set(prolog_style_variables).
% 1.76/1.98 set(auto).
% 1.76/1.98 dependent: set(auto1).
% 1.76/1.98 dependent: set(process_input).
% 1.76/1.98 dependent: clear(print_kept).
% 1.76/1.98 dependent: clear(print_new_demod).
% 1.76/1.98 dependent: clear(print_back_demod).
% 1.76/1.98 dependent: clear(print_back_sub).
% 1.76/1.98 dependent: set(control_memory).
% 1.76/1.98 dependent: assign(max_mem, 12000).
% 1.76/1.98 dependent: assign(pick_given_ratio, 4).
% 1.76/1.98 dependent: assign(stats_level, 1).
% 1.76/1.98 dependent: assign(max_seconds, 10800).
% 1.76/1.98 clear(print_given).
% 1.76/1.98
% 1.76/1.98 formula_list(usable).
% 1.76/1.98 all A (A=A).
% 1.76/1.98 vplus(vmul(vd436,vplus(vd437,vd439)),vd436)!=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 1.76/1.98 vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.76/1.98 vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 1.76/1.98 vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 1.76/1.98 vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 1.76/1.98 vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.76/1.98 vmul(vd436,vplus(vd437,v1))=vmul(vd436,vsucc(vd437)).
% 1.76/1.98 all Vd418 Vd419 (vmul(Vd418,Vd419)=vmul(Vd419,Vd418)).
% 1.76/1.98 all Vd400 (vmul(v1,Vd400)=Vd400).
% 1.76/1.98 all Vd396 Vd397 (vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396)&vmul(Vd396,v1)=Vd396).
% 1.76/1.98 all Vd386 Vd387 (less(Vd386,vplus(Vd387,v1))->le_q(Vd386,Vd387)).
% 1.76/1.98 all Vd375 Vd376 (greater(Vd375,Vd376)->ge_q(Vd375,vplus(Vd376,v1))).
% 1.76/1.98 all Vd369 ge_q(Vd369,v1).
% 1.76/1.98 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 1.76/1.98 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 1.76/1.98 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 1.76/1.98 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 1.76/1.98 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.76/1.98 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 1.76/1.98 all Vd16 (vsucc(Vd16)!=Vd16).
% 1.76/1.98 all Vd7 Vd8 (Vd7!=Vd8->vsucc(Vd7)!=vsucc(Vd8)).
% 1.76/1.98 end_of_list.
% 1.76/1.98
% 1.76/1.98 -------> usable clausifies to:
% 1.76/1.98
% 1.76/1.98 list(usable).
% 1.76/1.98 0 [] A=A.
% 1.76/1.98 0 [] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)!=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 1.76/1.98 0 [] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.76/1.98 0 [] vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 1.76/1.98 0 [] vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 1.76/1.98 0 [] vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 1.76/1.98 0 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.76/1.98 0 [] vmul(vd436,vplus(vd437,v1))=vmul(vd436,vsucc(vd437)).
% 1.76/1.98 0 [] vmul(Vd418,Vd419)=vmul(Vd419,Vd418).
% 1.76/1.98 0 [] vmul(v1,Vd400)=Vd400.
% 1.76/1.98 0 [] vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396).
% 1.76/1.98 0 [] vmul(Vd396,v1)=Vd396.
% 1.76/1.98 0 [] -less(Vd386,vplus(Vd387,v1))|le_q(Vd386,Vd387).
% 1.76/1.98 0 [] -greater(Vd375,Vd376)|ge_q(Vd375,vplus(Vd376,v1)).
% 1.76/1.98 0 [] ge_q(Vd369,v1).
% 1.76/1.98 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 1.76/1.98 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 1.76/1.98 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 1.76/1.98 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 1.76/1.98 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.76/1.98 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.76/1.98 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 1.76/1.98 0 [] vsucc(Vd16)!=Vd16.
% 1.76/1.98 0 [] Vd7=Vd8|vsucc(Vd7)!=vsucc(Vd8).
% 1.76/1.98 end_of_list.
% 1.76/1.98
% 1.76/1.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.76/1.98
% 1.76/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.76/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.76/1.98 deletion, with positive clauses in sos and nonpositive
% 1.76/1.98 clauses in usable.
% 1.76/1.98
% 1.76/1.98 dependent: set(knuth_bendix).
% 1.76/1.98 dependent: set(anl_eq).
% 1.76/1.98 dependent: set(para_from).
% 1.76/1.98 dependent: set(para_into).
% 1.76/1.98 dependent: clear(para_from_right).
% 1.76/1.98 dependent: clear(para_into_right).
% 1.76/1.98 dependent: set(para_from_vars).
% 1.76/1.98 dependent: set(eq_units_both_ways).
% 1.76/1.98 dependent: set(dynamic_demod_all).
% 1.76/1.98 dependent: set(dynamic_demod).
% 1.76/1.98 dependent: set(order_eq).
% 1.76/1.98 dependent: set(back_demod).
% 1.76/1.98 dependent: set(lrpo).
% 1.76/1.98 dependent: set(hyper_res).
% 1.76/1.98 dependent: set(unit_deletion).
% 1.76/1.98 dependent: set(factor).
% 1.76/1.98
% 1.76/1.98 ------------> process usab
% 1.76/1.98 -------- PROOF --------
% 1.76/1.98 le:
% 1.76/1.98 ** KEPT (pick-wt=17): 2 [copy,1,flip.1] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)!=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.76/1.98 ** KEPT (pick-wt=8): 3 [] -less(A,vplus(B,v1))|le_q(A,B).
% 1.76/1.98 ** KEPT (pick-wt=8): 4 [] -greater(A,B)|ge_q(A,vplus(B,v1)).
% 1.76/1.98 ** KEPT (pick-wt=4): 5 [] vsucc(A)!=A.
% 1.76/1.98 ** KEPT (pick-wt=8): 6 [] A=B|vsucc(A)!=vsucc(B).
% 1.76/1.98
% 1.76/1.98 ------------> process sos:
% 1.76/1.98 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.76/1.98 ** KEPT (pick-wt=14): 8 [] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.76/1.98 ---> New Demodulator: 9 [new_demod,8] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.76/1.98 ** KEPT (pick-wt=14): 11 [copy,10,demod,9] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.76/1.98 ---> New Demodulator: 12 [new_demod,11] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.76/1.98 ** KEPT (pick-wt=13): 14 [copy,13,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 1.76/1.98 ---> New Demodulator: 15 [new_demod,14] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 1.76/1.98 ** KEPT (pick-wt=13): 17 [copy,16,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 1.76/1.98 ---> New Demodulator: 18 [new_demod,17] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 1.76/1.98 ** KEPT (pick-wt=10): 19 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.76/1.98 ---> New Demodulator: 20 [new_demod,19] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.76/1.98 ** KEPT (pick-wt=11): 22 [copy,21,demod,20,flip.1] vplus(vmul(vd436,vd437),vd436)=vmul(vd436,vplus(vd437,v1)).
% 1.76/1.98 ---> New Demodulator: 23 [new_demod,22] vplus(vmul(vd436,vd437),vd436)=vmul(vd436,vplus(vd437,v1)).
% 1.76/1.98 ** KEPT (pick-wt=7): 24 [] vmul(A,B)=vmul(B,A).
% 1.76/1.98 ** KEPT (pick-wt=5): 25 [] vmul(v1,A)=A.
% 1.76/1.98 ---> New Demodulator: 26 [new_demod,25] vmul(v1,A)=A.
% 1.76/1.98 ** KEPT (pick-wt=10): 27 [] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 1.76/1.98 ** KEPT (pick-wt=5): 28 [] vmul(A,v1)=A.
% 1.76/1.98 ---> New Demodulator: 29 [new_demod,28] vmul(A,v1)=A.
% 1.76/1.98 ** KEPT (pick-wt=3): 30 [] ge_q(A,v1).
% 1.76/1.98 ** KEPT (pick-wt=7): 31 [] vplus(A,B)=vplus(B,A).
% 1.76/1.98 ** KEPT (pick-wt=9): 33 [copy,32,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.76/1.98 ---> New Demodulator: 34 [new_demod,33] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.76/1.98 ** KEPT (pick-wt=6): 36 [copy,35,flip.1] vsucc(A)=vplus(v1,A).
% 1.76/1.98 ---> New Demodulator: 37 [new_demod,36] vsucc(A)=vplus(v1,A).
% 1.76/1.98 ** KEPT (pick-wt=11): 38 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.76/1.98 ---> New Demodulator: 39 [new_demod,38] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.76/1.98 ** KEPT (pick-wt=11): 41 [copy,40,demod,37,37] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.76/1.98 Following clause subsumed by 31 during input processing: 0 [demod,37] vplus(A,v1)=vplus(v1,A).
% 1.76/1.98 ** KEPT (pick-wt=9): 43 [copy,42,demod,37,flip.2] A=v1|vplus(v1,vskolem2(A))=A.
% 1.76/1.98 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.76/1.98 >>>> Starting back demodulation with 9.
% 1.76/1.98 >>>> Starting back demodulation with 12.
% 1.76/1.98 >>>> Starting back demodulation with 15.
% 1.76/1.98 >> back demodulating 2 with 15.
% 1.76/1.98
% 1.76/1.98 ----> UNIT CONFLICT at 0.00 sec ----> 45 [binary,44.1,7.1] $F.
% 1.76/1.98
% 1.76/1.98 Length of proof is 3. Level of proof is 2.
% 1.76/1.98
% 1.76/1.98 ---------------- PROOF ----------------
% 1.76/1.98 % SZS status Theorem
% 1.76/1.98 % SZS output start Refutation
% See solution above
% 1.76/1.98 ------------ end of proof -------------
% 1.76/1.98
% 1.76/1.98
% 1.76/1.98 Search stopped by max_proofs option.
% 1.76/1.98
% 1.76/1.98
% 1.76/1.98 Search stopped by max_proofs option.
% 1.76/1.98
% 1.76/1.98 ============ end of search ============
% 1.76/1.98
% 1.76/1.98 -------------- statistics -------------
% 1.76/1.98 clauses given 0
% 1.76/1.98 clauses generated 0
% 1.76/1.98 clauses kept 24
% 1.76/1.98 clauses forward subsumed 2
% 1.76/1.98 clauses back subsumed 0
% 1.76/1.98 Kbytes malloced 976
% 1.76/1.98
% 1.76/1.98 ----------- times (seconds) -----------
% 1.76/1.98 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.76/1.98
% 1.76/1.98 That finishes the proof of the theorem.
% 1.76/1.98
% 1.76/1.98 Process 13214 finished Wed Jul 27 09:50:23 2022
% 1.76/1.98 Otter interrupted
% 1.76/1.98 PROOF FOUND
%------------------------------------------------------------------------------