TSTP Solution File: SWV348-2 by SOS---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SOS---2.0
% Problem  : SWV348-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : sos-script %s

% Computer : n012.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  : 600s
% DateTime : Wed Jul 20 21:38:06 EDT 2022

% Result   : Unsatisfiable 0.67s 0.88s
% Output   : Refutation 0.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV348-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : sos-script %s
% 0.13/0.34  % Computer : n012.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  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 01:59:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  ----- Otter 3.2, August 2001 -----
% 0.13/0.36  The process was started by sandbox2 on n012.cluster.edu,
% 0.13/0.36  Thu Jun 16 01:59:09 2022
% 0.13/0.36  The command was "./sos".  The process ID is 16851.
% 0.13/0.36  
% 0.13/0.36  set(prolog_style_variables).
% 0.13/0.36  set(auto).
% 0.13/0.36     dependent: set(auto1).
% 0.13/0.36     dependent: set(process_input).
% 0.13/0.36     dependent: clear(print_kept).
% 0.13/0.36     dependent: clear(print_new_demod).
% 0.13/0.36     dependent: clear(print_back_demod).
% 0.13/0.36     dependent: clear(print_back_sub).
% 0.13/0.36     dependent: set(control_memory).
% 0.13/0.36     dependent: assign(max_mem, 12000).
% 0.13/0.36     dependent: assign(pick_given_ratio, 4).
% 0.13/0.36     dependent: assign(stats_level, 1).
% 0.13/0.36     dependent: assign(pick_semantic_ratio, 3).
% 0.13/0.36     dependent: assign(sos_limit, 5000).
% 0.13/0.36     dependent: assign(max_weight, 60).
% 0.13/0.36  clear(print_given).
% 0.13/0.36  
% 0.13/0.36  list(usable).
% 0.13/0.36  
% 0.13/0.36  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 0.13/0.36  
% 0.13/0.36  This ia a non-Horn set with equality.  The strategy will be
% 0.13/0.36  Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.13/0.36  unit deletion, with positive clauses in sos and nonpositive
% 0.13/0.36  clauses in usable.
% 0.13/0.36  
% 0.13/0.36     dependent: set(knuth_bendix).
% 0.13/0.36     dependent: set(para_from).
% 0.13/0.36     dependent: set(para_into).
% 0.13/0.36     dependent: clear(para_from_right).
% 0.13/0.36     dependent: clear(para_into_right).
% 0.13/0.36     dependent: set(para_from_vars).
% 0.13/0.36     dependent: set(eq_units_both_ways).
% 0.13/0.36     dependent: set(dynamic_demod_all).
% 0.13/0.36     dependent: set(dynamic_demod).
% 0.13/0.36     dependent: set(order_eq).
% 0.13/0.36     dependent: set(back_demod).
% 0.13/0.36     dependent: set(lrpo).
% 0.13/0.36     dependent: set(hyper_res).
% 0.13/0.36     dependent: set(unit_deletion).
% 0.13/0.36     dependent: set(factor).
% 0.13/0.36  
% 0.13/0.36  ------------> process usable:
% 0.13/0.36  
% 0.13/0.36  ------------> process sos:
% 0.13/0.36    Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] {-} A=A.
% 0.13/0.36  
% 0.13/0.36  ======= end of input processing =======
% 0.42/0.62  
% 0.42/0.62  Stopped by limit on insertions
% 0.42/0.62  
% 0.42/0.62  
% 0.42/0.62  Failed to model usable list: disabling FINDER
% 0.42/0.62  
% 0.42/0.62  
% 0.42/0.62  
% 0.42/0.62  -------------- Softie stats --------------
% 0.42/0.62  
% 0.42/0.62  UPDATE_STOP: 300
% 0.42/0.62  SFINDER_TIME_LIMIT: 2
% 0.42/0.62  SHORT_CLAUSE_CUTOFF: 4
% 0.42/0.62  number of clauses in intial UL: 16
% 0.42/0.62  number of clauses initially in problem: 23
% 0.42/0.62  percentage of clauses intially in UL: 69
% 0.42/0.62  percentage of distinct symbols occuring in initial UL: 81
% 0.42/0.62  percent of all initial clauses that are short: 100
% 0.42/0.62  absolute distinct symbol count: 33
% 0.42/0.62     distinct predicate count: 2
% 0.42/0.62     distinct function count: 14
% 0.42/0.62     distinct constant count: 17
% 0.42/0.62  
% 0.42/0.62  ---------- no more Softie stats ----------
% 0.42/0.62  
% 0.42/0.62  
% 0.42/0.62  
% 0.42/0.62  =========== start of search ===========
% 0.67/0.88  
% 0.67/0.88  -------- PROOF -------- 
% 0.67/0.88  % SZS status Unsatisfiable
% 0.67/0.88  % SZS output start Refutation
% 0.67/0.88  
% 0.67/0.88  ----> UNIT CONFLICT at   0.49 sec ----> 581 [binary,580.1,15.1] {-} $F.
% 0.67/0.88  
% 0.67/0.88  Length of proof is 16.  Level of proof is 13.
% 0.67/0.88  
% 0.67/0.88  ---------------- PROOF ----------------
% 0.67/0.88  % SZS status Unsatisfiable
% 0.67/0.88  % SZS output start Refutation
% 0.67/0.88  
% 0.67/0.88  2 [] {+} -c_in(A,B,tc_Message_Omsg)|c_in(A,c_Message_Oparts(B),tc_Message_Omsg).
% 0.67/0.88  3 [] {+} -c_in(c_Message_Omsg_OMPair(A,B),c_Message_Oanalz(C),tc_Message_Omsg)|c_in(B,c_Message_Oanalz(C),tc_Message_Omsg).
% 0.67/0.88  4 [] {+} -c_in(c_Message_Omsg_OMPair(A,B),c_Message_Oanalz(C),tc_Message_Omsg)|c_in(A,c_Message_Oanalz(C),tc_Message_Omsg).
% 0.67/0.88  5 [] {+} -c_in(A,c_Event_Obad,tc_Message_Oagent)| -c_in(B,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))|c_in(c_Message_Omsg_OKey(c_Public_OshrK(A)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,B)),tc_Message_Omsg).
% 0.67/0.88  6 [] {+} -c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))| -c_in(c_Event_Oevent_OGets(B,C),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)|c_in(C,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg).
% 0.67/0.88  7 [] {+} -c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))| -c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(E,F)))),G)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)|c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(E,F))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  8 [] {+} -c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(A),B),c_Message_Oanalz(C),tc_Message_Omsg)| -c_in(c_Message_Omsg_OKey(c_Public_OshrK(A)),c_Message_Oanalz(C),tc_Message_Omsg)|c_in(B,c_Message_Oanalz(C),tc_Message_Omsg).
% 0.67/0.88  9 [] {+} -c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))| -c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(E,F)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)|c_in(B,c_Event_Obad,tc_Message_Oagent)|c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(E,F)))),c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OKey(D))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  10 [] {+} -c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))| -c_in(c_Event_Oevent_OGets(B,c_Message_Omsg_OMPair(C,c_Message_Omsg_OCrypt(c_Public_OshrK(D),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(E),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(F),G))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)| -c_in(c_Event_Oevent_OSays(H,I,c_Message_Omsg_OMPair(J,c_Message_Omsg_OCrypt(c_Public_OshrK(K),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(L),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(M),G))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)|c_in(G,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)|F=M.
% 0.67/0.88  11 [] {+} -c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))| -c_in(c_Event_Oevent_OGets(B,c_Message_Omsg_OMPair(C,c_Message_Omsg_OCrypt(c_Public_OshrK(D),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(E),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(F),G))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)| -c_in(c_Event_Oevent_OSays(H,I,c_Message_Omsg_OMPair(J,c_Message_Omsg_OCrypt(c_Public_OshrK(K),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(L),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(M),G))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)|c_in(G,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)|D=K.
% 0.67/0.88  12 [] {+} -c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))| -c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(E,F)))),c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OKey(D))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)| -c_in(c_Message_Omsg_OKey(D),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)|c_in(C,c_Event_Obad,tc_Message_Oagent)|c_in(B,c_Event_Obad,tc_Message_Oagent)|c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(E,c_Message_Omsg_OMPair(F,c_Message_Omsg_OKey(D)))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  13 [] {+} -c_in(v_B,c_Event_Obad,tc_Message_Oagent).
% 0.67/0.88  14 [] {+} -c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),A))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  15 [] {+} -c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  17 [] {-} c_Message_Oparts(c_Message_Oanalz(A))=c_Message_Oparts(A).
% 0.67/0.88  19 [] {-} c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)).
% 0.67/0.88  20 [] {-} c_in(c_Event_Oevent_OGets(v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  21 [] {-} c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  22 [] {-} c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  28 [para_from,17.1.1,2.2.2] {-} -c_in(A,c_Message_Oanalz(B),tc_Message_Omsg)|c_in(A,c_Message_Oparts(B),tc_Message_Omsg).
% 0.67/0.88  79 [hyper,20,6,19] {-} c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  144 [hyper,79,4] {-} c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  262 [hyper,144,28] {-} c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  264 [hyper,262,9,19] {-} c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)|c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  334 [hyper,264,12,19,22,factor_simp] {-} c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)|c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)|c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  335 [hyper,264,7,19] {-} c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)|c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  339 [hyper,335,11,19,21,unit_del,15] {-} c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)|v_Ba=v_B.
% 0.67/0.88  340 [hyper,335,10,19,21,unit_del,15] {-} c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)|v_NAa=v_NA.
% 0.67/0.88  358 [para_from,339.2.1,334.2.1,unit_del,13,factor_simp] {-} c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)|c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent).
% 0.67/0.88  444 [para_into,358.2.1.2.1.1,340.2.1,unit_del,14,factor_simp] {-} c_in(v_Aa,c_Event_Obad,tc_Message_Oagent).
% 0.67/0.88  445 [hyper,444,5,19] {-} c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  459 [hyper,445,8,144] {-} c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  510 [hyper,459,3] {-} c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  577 [hyper,510,3] {-} c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  580 [hyper,577,3] {-} c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg).
% 0.67/0.88  581 [binary,580.1,15.1] {-} $F.
% 0.67/0.88  
% 0.67/0.88  % SZS output end Refutation
% 0.67/0.88  ------------ end of proof -------------
% 0.67/0.88  
% 0.67/0.88  
% 0.67/0.88  Search stopped by max_proofs option.
% 0.67/0.88  
% 0.67/0.88  
% 0.67/0.88  Search stopped by max_proofs option.
% 0.67/0.88  
% 0.67/0.88  ============ end of search ============
% 0.67/0.88  
% 0.67/0.88  That finishes the proof of the theorem.
% 0.67/0.88  
% 0.67/0.88  Process 16851 finished Thu Jun 16 01:59:10 2022
%------------------------------------------------------------------------------