TSTP Solution File: NUM848+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM848+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 2.00s 2.18s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 14 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('NUM848+2.p',unknown),
[] ).
cnf(2,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
A = A,
file('NUM848+2.p',unknown),
[] ).
cnf(6,axiom,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('NUM848+2.p',unknown),
[] ).
cnf(7,axiom,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('NUM848+2.p',unknown),
[] ).
cnf(9,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7]),6]),
[iquote('copy,7,demod,6')] ).
cnf(10,axiom,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
file('NUM848+2.p',unknown),
[] ).
cnf(11,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10]),9]),
[iquote('copy,10,demod,9')] ).
cnf(24,axiom,
vmul(A,vsucc(B)) = vplus(vmul(A,B),A),
file('NUM848+2.p',unknown),
[] ).
cnf(31,axiom,
vplus(v1,A) = vsucc(A),
file('NUM848+2.p',unknown),
[] ).
cnf(33,plain,
vsucc(A) = vplus(v1,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(41,plain,
vplus(vmul(A,B),A) = vmul(A,vplus(v1,B)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24])]),33]),
[iquote('copy,24,flip.1,demod,33')] ).
cnf(43,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))) = vmul(vd436,vplus(v1,vplus(vd437,vd439))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),33,41])]),
[iquote('back_demod,11,demod,33,41,flip.1')] ).
cnf(46,plain,
vmul(vd436,vplus(v1,vplus(vd437,vd439))) != vmul(vd436,vplus(v1,vplus(vd437,vd439))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),33,43,41,43]),
[iquote('back_demod,2,demod,33,43,41,43')] ).
cnf(47,plain,
$false,
inference(binary,[status(thm)],[46,4]),
[iquote('binary,46.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM848+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 09:55:30 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.00/2.18 ----- Otter 3.3f, August 2004 -----
% 2.00/2.18 The process was started by sandbox2 on n025.cluster.edu,
% 2.00/2.18 Wed Jul 27 09:55:30 2022
% 2.00/2.18 The command was "./otter". The process ID is 18330.
% 2.00/2.18
% 2.00/2.18 set(prolog_style_variables).
% 2.00/2.18 set(auto).
% 2.00/2.18 dependent: set(auto1).
% 2.00/2.18 dependent: set(process_input).
% 2.00/2.18 dependent: clear(print_kept).
% 2.00/2.18 dependent: clear(print_new_demod).
% 2.00/2.18 dependent: clear(print_back_demod).
% 2.00/2.18 dependent: clear(print_back_sub).
% 2.00/2.18 dependent: set(control_memory).
% 2.00/2.18 dependent: assign(max_mem, 12000).
% 2.00/2.18 dependent: assign(pick_given_ratio, 4).
% 2.00/2.18 dependent: assign(stats_level, 1).
% 2.00/2.18 dependent: assign(max_seconds, 10800).
% 2.00/2.18 clear(print_given).
% 2.00/2.18
% 2.00/2.18 formula_list(usable).
% 2.00/2.18 all A (A=A).
% 2.00/2.18 vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))!=vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))).
% 2.00/2.18 vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 2.00/2.18 vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 2.00/2.18 vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 2.00/2.18 vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 2.00/2.18 vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 2.00/2.18 vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 2.00/2.18 all Vd396 Vd397 (vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396)&vmul(Vd396,v1)=Vd396).
% 2.00/2.18 all Vd386 Vd387 (less(Vd386,vplus(Vd387,v1))->le_q(Vd386,Vd387)).
% 2.00/2.18 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 2.00/2.18 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 2.00/2.18 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 2.00/2.18 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 2.00/2.18 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 2.00/2.18 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 -------> usable clausifies to:
% 2.00/2.18
% 2.00/2.18 list(usable).
% 2.00/2.18 0 [] A=A.
% 2.00/2.18 0 [] vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))!=vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))).
% 2.00/2.18 0 [] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 0 [] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 2.00/2.18 0 [] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 2.00/2.18 0 [] vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 2.00/2.18 0 [] vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 2.00/2.18 0 [] vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 2.00/2.18 0 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 2.00/2.18 0 [] vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396).
% 2.00/2.18 0 [] vmul(Vd396,v1)=Vd396.
% 2.00/2.18 0 [] -less(Vd386,vplus(Vd387,v1))|le_q(Vd386,Vd387).
% 2.00/2.18 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 2.00/2.18 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 2.00/2.18 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 2.00/2.18 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 2.00/2.18 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 2.00/2.18 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 2.00/2.18 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 2.00/2.18
% 2.00/2.18 This ia a non-Horn set with equality. The strategy will be
% 2.00/2.18 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.00/2.18 deletion, with positive clauses in sos and nonpositive
% 2.00/2.18 clauses in usable.
% 2.00/2.18
% 2.00/2.18 dependent: set(knuth_bendix).
% 2.00/2.18 dependent: set(anl_eq).
% 2.00/2.18 dependent: set(para_from).
% 2.00/2.18 dependent: set(para_into).
% 2.00/2.18 dependent: clear(para_from_right).
% 2.00/2.18 dependent: clear(para_into_right).
% 2.00/2.18 dependent: set(para_from_vars).
% 2.00/2.18 dependent: set(eq_units_both_ways).
% 2.00/2.18 dependent: set(dynamic_demod_all).
% 2.00/2.18 dependent: set(dynamic_demod).
% 2.00/2.18 dependent: set(order_eq).
% 2.00/2.18 dependent: set(back_demod).
% 2.00/2.18 dependent: set(lrpo).
% 2.00/2.18 dependent: set(hyper_res).
% 2.00/2.18 dependent: set(unit_deletion).
% 2.00/2.18 dependent: set(factor).
% 2.00/2.18
% 2.00/2.18 ------------> process usable:
% 2.00/2.18 ** KEPT (pick-wt=18): 2 [copy,1,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))!=vplus(vmul(vd436,vd437),vplus(vmul(vd
% 2.00/2.18 -------- PROOF --------
% 2.00/2.18 436,vd439),vd436)).
% 2.00/2.18 ** KEPT (pick-wt=8): 3 [] -less(A,vplus(B,v1))|le_q(A,B).
% 2.00/2.18
% 2.00/2.18 ------------> process sos:
% 2.00/2.18 ** KEPT (pick-wt=3): 4 [] A=A.
% 2.00/2.18 ** KEPT (pick-wt=19): 5 [] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ---> New Demodulator: 6 [new_demod,5] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ** KEPT (pick-wt=17): 8 [copy,7,demod,6] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ---> New Demodulator: 9 [new_demod,8] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ** KEPT (pick-wt=16): 11 [copy,10,demod,9] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ---> New Demodulator: 12 [new_demod,11] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ** KEPT (pick-wt=16): 14 [copy,13,demod,12] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ---> New Demodulator: 15 [new_demod,14] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 2.00/2.18 ** KEPT (pick-wt=13): 17 [copy,16,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 2.00/2.18 ---> New Demodulator: 18 [new_demod,17] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 2.00/2.18 ** KEPT (pick-wt=13): 20 [copy,19,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 2.00/2.18 ---> New Demodulator: 21 [new_demod,20] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 2.00/2.18 ** KEPT (pick-wt=10): 22 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 2.00/2.18 ---> New Demodulator: 23 [new_demod,22] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 2.00/2.18 ** KEPT (pick-wt=10): 24 [] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 2.00/2.18 ** KEPT (pick-wt=5): 25 [] vmul(A,v1)=A.
% 2.00/2.18 ---> New Demodulator: 26 [new_demod,25] vmul(A,v1)=A.
% 2.00/2.18 ** KEPT (pick-wt=7): 27 [] vplus(A,B)=vplus(B,A).
% 2.00/2.18 ** KEPT (pick-wt=9): 29 [copy,28,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 2.00/2.18 ---> New Demodulator: 30 [new_demod,29] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 2.00/2.18 ** KEPT (pick-wt=6): 32 [copy,31,flip.1] vsucc(A)=vplus(v1,A).
% 2.00/2.18 ---> New Demodulator: 33 [new_demod,32] vsucc(A)=vplus(v1,A).
% 2.00/2.18 ** KEPT (pick-wt=11): 34 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 2.00/2.18 ---> New Demodulator: 35 [new_demod,34] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 2.00/2.18 ** KEPT (pick-wt=11): 37 [copy,36,demod,33,33] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 2.00/2.18 Following clause subsumed by 27 during input processing: 0 [demod,33] vplus(A,v1)=vplus(v1,A).
% 2.00/2.18 ** KEPT (pick-wt=9): 39 [copy,38,demod,33,flip.2] A=v1|vplus(v1,vskolem2(A))=A.
% 2.00/2.18 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 2.00/2.18 >>>> Starting back demodulation with 6.
% 2.00/2.18 >>>> Starting back demodulation with 9.
% 2.00/2.18 >>>> Starting back demodulation with 12.
% 2.00/2.18 >>>> Starting back demodulation with 15.
% 2.00/2.18 >>>> Starting back demodulation with 18.
% 2.00/2.18 >> back demodulating 5 with 18.
% 2.00/2.18 >>>> Starting back demodulation with 21.
% 2.00/2.18 >>>> Starting back demodulation with 23.
% 2.00/2.18 ** KEPT (pick-wt=11): 40 [copy,24,flip.1,demod,33] vplus(vmul(A,B),A)=vmul(A,vplus(v1,B)).
% 2.00/2.18 ---> New Demodulator: 41 [new_demod,40] vplus(vmul(A,B),A)=vmul(A,vplus(v1,B)).
% 2.00/2.18 24 back subsumes 22.
% 2.00/2.18 >>>> Starting back demodulation with 26.
% 2.00/2.18 >> back demodulating 20 with 26.
% 2.00/2.18 Following clause subsumed by 27 during input processing: 0 [copy,27,flip.1] vplus(A,B)=vplus(B,A).
% 2.00/2.18 >>>> Starting back demodulation with 30.
% 2.00/2.18 >> back demodulating 11 with 30.
% 2.00/2.18 >>>> Starting back demodulation with 33.
% 2.00/2.18 >> back demodulating 29 with 33.
% 2.00/2.18 >> back demodulating 24 with 33.
% 2.00/2.18 >> back demodulating 14 with 33.
% 2.00/2.18 >> back demodulating 2 with 33.
% 2.00/2.18
% 2.00/2.18 ----> UNIT CONFLICT at 0.00 sec ----> 47 [binary,46.1,4.1] $F.
% 2.00/2.18
% 2.00/2.18 Length of proof is 7. Level of proof is 4.
% 2.00/2.18
% 2.00/2.18 ---------------- PROOF ----------------
% 2.00/2.18 % SZS status Theorem
% 2.00/2.18 % SZS output start Refutation
% See solution above
% 2.00/2.18 ------------ end of proof -------------
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Search stopped by max_proofs option.
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Search stopped by max_proofs option.
% 2.00/2.18
% 2.00/2.18 ============ end of search ============
% 2.00/2.18
% 2.00/2.18 -------------- statistics -------------
% 2.00/2.18 clauses given 0
% 2.00/2.18 clauses generated 0
% 2.00/2.18 clauses kept 22
% 2.00/2.18 clauses forward subsumed 7
% 2.00/2.18 clauses back subsumed 1
% 2.00/2.18 Kbytes malloced 976
% 2.00/2.18
% 2.00/2.18 ----------- times (seconds) -----------
% 2.00/2.18 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.18 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.18
% 2.00/2.18 That finishes the proof of the theorem.
% 2.00/2.18
% 2.00/2.18 Process 18330 finished Wed Jul 27 09:55:32 2022
% 2.00/2.18 Otter interrupted
% 2.00/2.18 PROOF FOUND
%------------------------------------------------------------------------------