TSTP Solution File: NUM847+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.75s 1.95s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 2 RR)
% Number of literals : 3 ( 2 equ; 1 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 : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('NUM847+2.p',unknown),
[] ).
cnf(37,axiom,
vplus(vplus(A,B),C) = vplus(A,vplus(B,C)),
file('NUM847+2.p',unknown),
[] ).
cnf(39,plain,
$false,
inference(binary,[status(thm)],[37,1]),
[iquote('binary,37.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:02:16 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.75/1.95 ----- Otter 3.3f, August 2004 -----
% 1.75/1.95 The process was started by sandbox on n018.cluster.edu,
% 1.75/1.95 Wed Jul 27 10:02:16 2022
% 1.75/1.95 The command was "./otter". The process ID is 13894.
% 1.75/1.95
% 1.75/1.95 set(prolog_style_variables).
% 1.75/1.95 set(auto).
% 1.75/1.95 dependent: set(auto1).
% 1.75/1.95 dependent: set(process_input).
% 1.75/1.95 dependent: clear(print_kept).
% 1.75/1.95 dependent: clear(print_new_demod).
% 1.75/1.95 dependent: clear(print_back_demod).
% 1.75/1.95 dependent: clear(print_back_sub).
% 1.75/1.95 dependent: set(control_memory).
% 1.75/1.95 dependent: assign(max_mem, 12000).
% 1.75/1.95 dependent: assign(pick_given_ratio, 4).
% 1.75/1.95 dependent: assign(stats_level, 1).
% 1.75/1.95 dependent: assign(max_seconds, 10800).
% 1.75/1.95 clear(print_given).
% 1.75/1.95
% 1.75/1.95 formula_list(usable).
% 1.75/1.95 all A (A=A).
% 1.75/1.95 vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)!=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.75/1.95 vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 1.75/1.95 vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 1.75/1.95 vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 1.75/1.95 vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 1.75/1.95 vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.75/1.95 vmul(vd436,vplus(vd437,v1))=vmul(vd436,vsucc(vd437)).
% 1.75/1.95 all Vd400 (vmul(v1,Vd400)=Vd400).
% 1.75/1.95 all Vd396 Vd397 (vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396)&vmul(Vd396,v1)=Vd396).
% 1.75/1.95 all Vd386 Vd387 (less(Vd386,vplus(Vd387,v1))->le_q(Vd386,Vd387)).
% 1.75/1.95 all Vd375 Vd376 (greater(Vd375,Vd376)->ge_q(Vd375,vplus(Vd376,v1))).
% 1.75/1.95 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 1.75/1.95 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 1.75/1.95 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 1.75/1.95 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 1.75/1.95 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.75/1.95 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 1.75/1.95 all Vd16 (vsucc(Vd16)!=Vd16).
% 1.75/1.95 end_of_list.
% 1.75/1.95
% 1.75/1.95 -------> usable clausifies to:
% 1.75/1.95
% 1.75/1.95 list(usable).
% 1.75/1.95 0 [] A=A.
% 1.75/1.95 0 [] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)!=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.75/1.95 0 [] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 1.75/1.95 0 [] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 0 [] vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 1.75/1.95 0 [] vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 1.75/1.95 0 [] vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 1.75/1.95 0 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.75/1.95 0 [] vmul(vd436,vplus(vd437,v1))=vmul(vd436,vsucc(vd437)).
% 1.75/1.95 0 [] vmul(v1,Vd400)=Vd400.
% 1.75/1.95 0 [] vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396).
% 1.75/1.95 0 [] vmul(Vd396,v1)=Vd396.
% 1.75/1.95 0 [] -less(Vd386,vplus(Vd387,v1))|le_q(Vd386,Vd387).
% 1.75/1.95 0 [] -greater(Vd375,Vd376)|ge_q(Vd375,vplus(Vd376,v1)).
% 1.75/1.95 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 1.75/1.95 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 1.75/1.95 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 1.75/1.95 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 1.75/1.95 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.75/1.95 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.75/1.95 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 1.75/1.95 0 [] vsucc(Vd16)!=Vd16.
% 1.75/1.95 end_of_list.
% 1.75/1.95
% 1.75/1.95 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 1.75/1.95
% 1.75/1.95 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.95 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.95 deletion, with positive clauses in sos and nonpositive
% 1.75/1.95 clauses in usable.
% 1.75/1.95
% 1.75/1.95 dependent: set(knuth_bendix).
% 1.75/1.95 dependent: set(anl_eq).
% 1.75/1.95 dependent: set(para_from).
% 1.75/1.95 dependent: set(para_into).
% 1.75/1.95 dependent: clear(para_from_right).
% 1.75/1.95 dependent: clear(para_into_right).
% 1.75/1.95 dependent: set(para_from_vars).
% 1.75/1.95 dependent: set(eq_units_both_ways).
% 1.75/1.95 dependent: set(dynamic_demod_all).
% 1.75/1.95 dependent: set(dynamic_demod).
% 1.75/1.95 dependent: set(order_eq).
% 1.75/1.95 dependent: set(back_demod).
% 1.75/1.95 dependent: set(lrpo).
% 1.75/1.95 dependent: set(hyper_res).
% 1.75/1.95 dependent: set(unit_deletion).
% 1.75/1.95 dependent: set(factor).
% 1.75/1.95
% 1.75/1.95 ------------> process usa
% 1.75/1.95 -------- PROOF --------
% 1.75/1.95 ble:
% 1.75/1.95 ** KEPT (pick-wt=19): 1 [] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)!=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.75/1.95 ** KEPT (pick-wt=8): 2 [] -less(A,vplus(B,v1))|le_q(A,B).
% 1.75/1.95 ** KEPT (pick-wt=8): 3 [] -greater(A,B)|ge_q(A,vplus(B,v1)).
% 1.75/1.95 ** KEPT (pick-wt=4): 4 [] vsucc(A)!=A.
% 1.75/1.95
% 1.75/1.95 ------------> process sos:
% 1.75/1.95 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.75/1.95 ** KEPT (pick-wt=17): 7 [copy,6,flip.1] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 ---> New Demodulator: 8 [new_demod,7] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 ** KEPT (pick-wt=14): 9 [] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 ---> New Demodulator: 10 [new_demod,9] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 ** KEPT (pick-wt=14): 12 [copy,11,demod,10] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 ---> New Demodulator: 13 [new_demod,12] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.75/1.95 ** KEPT (pick-wt=13): 15 [copy,14,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 1.75/1.95 ---> New Demodulator: 16 [new_demod,15] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 1.75/1.95 ** KEPT (pick-wt=13): 18 [copy,17,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 1.75/1.95 ---> New Demodulator: 19 [new_demod,18] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 1.75/1.95 ** KEPT (pick-wt=10): 20 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.75/1.95 ---> New Demodulator: 21 [new_demod,20] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.75/1.95 ** KEPT (pick-wt=11): 23 [copy,22,demod,21,flip.1] vplus(vmul(vd436,vd437),vd436)=vmul(vd436,vplus(vd437,v1)).
% 1.75/1.95 ---> New Demodulator: 24 [new_demod,23] vplus(vmul(vd436,vd437),vd436)=vmul(vd436,vplus(vd437,v1)).
% 1.75/1.95 ** KEPT (pick-wt=5): 25 [] vmul(v1,A)=A.
% 1.75/1.95 ---> New Demodulator: 26 [new_demod,25] vmul(v1,A)=A.
% 1.75/1.95 ** KEPT (pick-wt=10): 27 [] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 1.75/1.95 ** KEPT (pick-wt=5): 28 [] vmul(A,v1)=A.
% 1.75/1.95 ---> New Demodulator: 29 [new_demod,28] vmul(A,v1)=A.
% 1.75/1.95 ** KEPT (pick-wt=7): 30 [] vplus(A,B)=vplus(B,A).
% 1.75/1.95 ** KEPT (pick-wt=9): 32 [copy,31,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.75/1.95 ---> New Demodulator: 33 [new_demod,32] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.75/1.95 ** KEPT (pick-wt=6): 35 [copy,34,flip.1] vsucc(A)=vplus(v1,A).
% 1.75/1.95 ---> New Demodulator: 36 [new_demod,35] vsucc(A)=vplus(v1,A).
% 1.75/1.95 ** KEPT (pick-wt=11): 37 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.75/1.95 ---> New Demodulator: 38 [new_demod,37] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.75/1.95
% 1.75/1.95 ----> UNIT CONFLICT at 0.00 sec ----> 39 [binary,37.1,1.1] $F.
% 1.75/1.95
% 1.75/1.95 Length of proof is 0. Level of proof is 0.
% 1.75/1.95
% 1.75/1.95 ---------------- PROOF ----------------
% 1.75/1.95 % SZS status Theorem
% 1.75/1.95 % SZS output start Refutation
% See solution above
% 1.75/1.95 ------------ end of proof -------------
% 1.75/1.95
% 1.75/1.95
% 1.75/1.95 Search stopped by max_proofs option.
% 1.75/1.95
% 1.75/1.95
% 1.75/1.95 Search stopped by max_proofs option.
% 1.75/1.95
% 1.75/1.95 ============ end of search ============
% 1.75/1.95
% 1.75/1.95 -------------- statistics -------------
% 1.75/1.95 clauses given 0
% 1.75/1.95 clauses generated 0
% 1.75/1.95 clauses kept 19
% 1.75/1.95 clauses forward subsumed 0
% 1.75/1.95 clauses back subsumed 0
% 1.75/1.95 Kbytes malloced 976
% 1.75/1.95
% 1.75/1.95 ----------- times (seconds) -----------
% 1.75/1.95 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.95
% 1.75/1.95 That finishes the proof of the theorem.
% 1.75/1.95
% 1.75/1.95 Process 13894 finished Wed Jul 27 10:02:18 2022
% 1.75/1.95 Otter interrupted
% 1.75/1.95 PROOF FOUND
%------------------------------------------------------------------------------