TSTP Solution File: GEO648+1 by SOS---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SOS---2.0
% Problem  : GEO648+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : sos-script %s

% Computer : n017.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 : Sat Jul 16 06:21:19 EDT 2022

% Result   : Theorem 20.22s 20.40s
% Output   : Refutation 20.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO648+1 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13  % Command  : sos-script %s
% 0.13/0.34  % Computer : n017.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 : Fri Jun 17 17:24:11 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.38  ----- Otter 3.2, August 2001 -----
% 0.20/0.38  The process was started by sandbox2 on n017.cluster.edu,
% 0.20/0.38  Fri Jun 17 17:24:12 2022
% 0.20/0.38  The command was "./sos".  The process ID is 29331.
% 0.20/0.38  
% 0.20/0.38  set(prolog_style_variables).
% 0.20/0.38  set(auto).
% 0.20/0.38     dependent: set(auto1).
% 0.20/0.38     dependent: set(process_input).
% 0.20/0.38     dependent: clear(print_kept).
% 0.20/0.38     dependent: clear(print_new_demod).
% 0.20/0.38     dependent: clear(print_back_demod).
% 0.20/0.38     dependent: clear(print_back_sub).
% 0.20/0.38     dependent: set(control_memory).
% 0.20/0.38     dependent: assign(max_mem, 12000).
% 0.20/0.38     dependent: assign(pick_given_ratio, 4).
% 0.20/0.38     dependent: assign(stats_level, 1).
% 0.20/0.38     dependent: assign(pick_semantic_ratio, 3).
% 0.20/0.38     dependent: assign(sos_limit, 5000).
% 0.20/0.38     dependent: assign(max_weight, 60).
% 0.20/0.38  clear(print_given).
% 0.20/0.38  
% 0.20/0.38  formula_list(usable).
% 0.20/0.38  
% 0.20/0.38  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 0.20/0.38  
% 0.20/0.38  This ia a non-Horn set with equality.  The strategy will be
% 0.20/0.38  Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.20/0.38  unit deletion, with positive clauses in sos and nonpositive
% 0.20/0.38  clauses in usable.
% 0.20/0.38  
% 0.20/0.38     dependent: set(knuth_bendix).
% 0.20/0.38     dependent: set(para_from).
% 0.20/0.38     dependent: set(para_into).
% 0.20/0.38     dependent: clear(para_from_right).
% 0.20/0.38     dependent: clear(para_into_right).
% 0.20/0.38     dependent: set(para_from_vars).
% 0.20/0.38     dependent: set(eq_units_both_ways).
% 0.20/0.38     dependent: set(dynamic_demod_all).
% 0.20/0.38     dependent: set(dynamic_demod).
% 0.20/0.38     dependent: set(order_eq).
% 0.20/0.38     dependent: set(back_demod).
% 0.20/0.38     dependent: set(lrpo).
% 0.20/0.38     dependent: set(hyper_res).
% 0.20/0.38     dependent: set(unit_deletion).
% 0.20/0.38     dependent: set(factor).
% 0.20/0.38  
% 0.20/0.38  ------------> process usable:
% 0.20/0.38    Following clause subsumed by 72 during input processing: 0 [] {-} -eqangle(A,B,C,D,C,D,A,B)|perp(A,B,C,D)|para(A,B,C,D).
% 0.20/0.38  
% 0.20/0.38  ------------> process sos:
% 0.20/0.38    Following clause subsumed by 165 during input processing: 0 [copy,165,flip.1] {-} A=A.
% 0.20/0.38  165 back subsumes 146.
% 0.20/0.38  165 back subsumes 145.
% 0.20/0.38  165 back subsumes 144.
% 0.20/0.38  165 back subsumes 143.
% 0.20/0.38  
% 0.20/0.38  ======= end of input processing =======
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Failed to model usable list: disabling FINDER
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  -------------- Softie stats --------------
% 0.20/0.44  
% 0.20/0.44  UPDATE_STOP: 300
% 0.20/0.44  SFINDER_TIME_LIMIT: 2
% 0.20/0.44  SHORT_CLAUSE_CUTOFF: 4
% 0.20/0.44  number of clauses in intial UL: 154
% 0.20/0.44  number of clauses initially in problem: 161
% 0.20/0.44  percentage of clauses intially in UL: 95
% 0.20/0.44  percentage of distinct symbols occuring in initial UL: 87
% 0.20/0.44  percent of all initial clauses that are short: 100
% 0.20/0.44  absolute distinct symbol count: 41
% 0.20/0.44     distinct predicate count: 12
% 0.20/0.44     distinct function count: 20
% 0.20/0.44     distinct constant count: 9
% 0.20/0.44  
% 0.20/0.44  ---------- no more Softie stats ----------
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  =========== start of search ===========
% 5.81/6.00  
% 5.81/6.00  
% 5.81/6.00  Changing weight limit from 60 to 56.
% 5.81/6.00  
% 5.81/6.00  Resetting weight limit to 56 after 195 givens.
% 5.81/6.00  
% 6.88/7.11  
% 6.88/7.11  
% 6.88/7.11  Changing weight limit from 56 to 55.
% 6.88/7.11  
% 6.88/7.11  Resetting weight limit to 55 after 200 givens.
% 6.88/7.11  
% 7.86/8.04  
% 7.86/8.04  
% 7.86/8.04  Changing weight limit from 55 to 54.
% 7.86/8.04  
% 7.86/8.04  Resetting weight limit to 54 after 205 givens.
% 7.86/8.04  
% 8.92/9.16  
% 8.92/9.16  
% 8.92/9.16  Changing weight limit from 54 to 52.
% 8.92/9.16  
% 8.92/9.16  Resetting weight limit to 52 after 210 givens.
% 8.92/9.16  
% 9.66/9.88  
% 9.66/9.88  
% 9.66/9.88  Changing weight limit from 52 to 51.
% 9.66/9.88  
% 9.66/9.88  Resetting weight limit to 51 after 215 givens.
% 9.66/9.88  
% 11.39/11.56  
% 11.39/11.56  
% 11.39/11.56  Changing weight limit from 51 to 50.
% 11.39/11.56  
% 11.39/11.56  Resetting weight limit to 50 after 225 givens.
% 11.39/11.56  
% 12.92/13.10  
% 12.92/13.10  
% 12.92/13.10  Changing weight limit from 50 to 46.
% 12.92/13.10  
% 12.92/13.10  Resetting weight limit to 46 after 235 givens.
% 12.92/13.10  
% 13.34/13.54  
% 13.34/13.54  
% 13.34/13.54  Changing weight limit from 46 to 45.
% 13.34/13.54  
% 13.34/13.54  Resetting weight limit to 45 after 240 givens.
% 13.34/13.54  
% 13.76/13.98  
% 13.76/13.98  
% 13.76/13.98  Changing weight limit from 45 to 34.
% 13.76/13.98  
% 13.76/13.98  Resetting weight limit to 34 after 245 givens.
% 13.76/13.98  
% 14.21/14.40  
% 14.21/14.40  
% 14.21/14.40  Changing weight limit from 34 to 33.
% 14.21/14.40  
% 14.21/14.40  Resetting weight limit to 33 after 265 givens.
% 14.21/14.40  
% 14.57/14.75  
% 14.57/14.75  
% 14.57/14.75  Changing weight limit from 33 to 31.
% 14.57/14.75  
% 14.57/14.75  Modelling stopped after 300 given clauses and 0.00 seconds
% 14.57/14.75  
% 14.57/14.75  
% 14.57/14.75  Resetting weight limit to 31 after 325 givens.
% 14.57/14.75  
% 14.83/15.00  
% 14.83/15.00  
% 14.83/15.00  Changing weight limit from 31 to 30.
% 14.83/15.00  
% 14.83/15.00  Resetting weight limit to 30 after 385 givens.
% 14.83/15.00  
% 15.44/15.67  
% 15.44/15.67  
% 15.44/15.67  Changing weight limit from 30 to 29.
% 15.44/15.67  
% 15.44/15.67  Resetting weight limit to 29 after 540 givens.
% 15.44/15.67  
% 15.81/16.00  
% 15.81/16.00  
% 15.81/16.00  Changing weight limit from 29 to 26.
% 15.81/16.00  
% 15.81/16.00  Resetting weight limit to 26 after 595 givens.
% 15.81/16.00  
% 15.81/16.06  
% 15.81/16.06  
% 15.81/16.06  Changing weight limit from 26 to 21.
% 15.81/16.06  
% 15.81/16.06  Resetting weight limit to 21 after 635 givens.
% 15.81/16.06  
% 15.92/16.08  
% 15.92/16.08  
% 15.92/16.08  Changing weight limit from 21 to 18.
% 15.92/16.08  
% 15.92/16.08  Resetting weight limit to 18 after 650 givens.
% 15.92/16.08  
% 16.26/16.51  
% 16.26/16.51  
% 16.26/16.51  Changing weight limit from 18 to 17.
% 16.26/16.51  
% 16.26/16.51  Resetting weight limit to 17 after 945 givens.
% 16.26/16.51  
% 16.36/16.59  
% 16.36/16.59  
% 16.36/16.59  Changing weight limit from 17 to 16.
% 16.36/16.59  
% 16.36/16.59  Resetting weight limit to 16 after 950 givens.
% 16.36/16.59  
% 16.43/16.64  
% 16.43/16.64  
% 16.43/16.64  Changing weight limit from 16 to 15.
% 16.43/16.64  
% 16.43/16.64  Resetting weight limit to 15 after 990 givens.
% 16.43/16.64  
% 16.43/16.64  
% 16.43/16.64  
% 16.43/16.64  Changing weight limit from 15 to 14.
% 16.43/16.64  
% 16.43/16.64  Resetting weight limit to 14 after 995 givens.
% 16.43/16.64  
% 17.06/17.26  
% 17.06/17.26  
% 17.06/17.26  Changing weight limit from 14 to 12.
% 17.06/17.26  
% 17.06/17.26  Resetting weight limit to 12 after 1060 givens.
% 17.06/17.26  
% 17.11/17.33  
% 17.11/17.33  
% 17.11/17.33  Changing weight limit from 12 to 11.
% 17.11/17.33  
% 17.11/17.33  Resetting weight limit to 11 after 1100 givens.
% 17.11/17.33  
% 17.58/17.75  
% 17.58/17.75  
% 17.58/17.75  Changing weight limit from 11 to 10.
% 17.58/17.75  
% 17.58/17.75  Resetting weight limit to 10 after 1460 givens.
% 17.58/17.75  
% 18.93/19.12  
% 18.93/19.12  
% 18.93/19.12  Changing weight limit from 10 to 9.
% 18.93/19.12  
% 18.93/19.12  Resetting weight limit to 9 after 1650 givens.
% 18.93/19.12  
% 20.22/20.40  
% 20.22/20.40  -- HEY sandbox2, WE HAVE A PROOF!! -- 
% 20.22/20.40  
% 20.22/20.40  ----> UNIT CONFLICT at  19.89 sec ----> 36169 [binary,36168.1,113.1] {-} $F.
% 20.22/20.40  
% 20.22/20.40  Length of proof is 75.  Level of proof is 17.
% 20.22/20.40  
% 20.22/20.40  ---------------- PROOF ----------------
% 20.22/20.40  % SZS status Theorem
% 20.22/20.40  % SZS output start Refutation
% 20.22/20.40  
% 20.22/20.40  1 [] {+} -coll(A,B,C)|coll(A,C,B).
% 20.22/20.40  2 [] {+} -coll(A,B,C)|coll(B,A,C).
% 20.22/20.40  3 [] {+} -coll(A,B,C)| -coll(A,B,D)|coll(C,D,A).
% 20.22/20.40  7 [] {+} -perp(A,B,C,D)|perp(A,B,D,C).
% 20.22/20.40  8 [] {+} -perp(A,B,C,D)|perp(C,D,A,B).
% 20.22/20.40  9 [] {+} -perp(A,B,C,D)| -perp(C,D,E,F)|para(A,B,E,F).
% 20.22/20.40  10 [] {+} -para(A,B,C,D)| -perp(C,D,E,F)|perp(A,B,E,F).
% 20.22/20.40  14 [] {+} -cyclic(A,B,C,D)|cyclic(A,B,D,C).
% 20.22/20.40  15 [] {+} -cyclic(A,B,C,D)|cyclic(A,C,B,D).
% 20.22/20.40  16 [] {+} -cyclic(A,B,C,D)|cyclic(B,A,C,D).
% 20.22/20.40  17 [] {+} -cyclic(A,B,C,D)| -cyclic(A,B,C,E)|cyclic(B,C,D,E).
% 20.22/20.40  40 [] {+} -para(A,B,C,D)|eqangle(A,B,E,F,C,D,E,F).
% 20.22/20.40  43 [] {+} -eqangle(A,B,A,C,D,B,D,C)| -coll(A,D,C)|cyclic(B,C,A,D).
% 20.22/20.40  44 [] {+} -cyclic(A,B,C,D)| -cyclic(A,B,C,E)| -cyclic(A,B,C,F)| -eqangle(C,A,C,B,F,D,F,E)|cong(A,B,D,E).
% 20.22/20.40  45 [] {+} -midp(A,B,C)| -midp(D,B,E)|para(A,D,C,E).
% 20.22/20.40  46 [] {+} -midp(A,B,C)| -para(A,D,C,E)| -coll(D,B,E)|midp(D,B,E).
% 20.22/20.40  57 [] {+} -cong(A,B,C,B)| -cong(A,D,C,D)|perp(A,C,B,D).
% 20.22/20.40  58 [] {+} -cong(A,B,C,B)| -cong(A,D,C,D)| -cyclic(A,C,B,D)|perp(B,A,A,D).
% 20.22/20.40  65 [] {+} -midp(A,B,C)| -para(B,D,C,E)| -para(B,E,C,D)|midp(A,D,E).
% 20.22/20.40  67 [] {+} -para(A,B,A,C)|coll(A,B,C).
% 20.22/20.40  68 [] {+} -cong(A,B,A,C)| -coll(A,B,C)|midp(A,B,C).
% 20.22/20.40  69 [] {+} -midp(A,B,C)|cong(A,B,A,C).
% 20.22/20.40  113 [] {+} -para($c9,$c6,$c8,$c5).
% 20.22/20.40  114 [factor,3.1.2] {+} -coll(A,B,C)|coll(C,C,A).
% 20.22/20.40  120 [factor,17.1.2] {+} -cyclic(A,B,C,D)|cyclic(B,C,D,D).
% 20.22/20.40  121 [factor,44.1.2] {+} -cyclic(A,B,C,D)| -cyclic(A,B,C,E)| -eqangle(C,A,C,B,E,D,E,D)|cong(A,B,D,D).
% 20.22/20.40  123 [factor,44.2.3] {+} -cyclic(A,B,C,D)| -cyclic(A,B,C,E)| -eqangle(C,A,C,B,E,D,E,E)|cong(A,B,D,E).
% 20.22/20.40  129 [factor,65.2.3] {+} -midp(A,B,C)| -para(B,D,C,D)|midp(A,D,D).
% 20.22/20.40  161 [] {-} perp($c9,$c7,$c7,$c6).
% 20.22/20.40  162 [] {-} perp($c9,$c8,$c8,$c6).
% 20.22/20.40  163 [] {-} coll($c7,$c9,$c5).
% 20.22/20.40  183 [hyper,163,114] {-} coll($c5,$c5,$c7).
% 20.22/20.40  184 [hyper,163,2] {-} coll($c9,$c7,$c5).
% 20.22/20.40  185 [hyper,163,1] {-} coll($c7,$c5,$c9).
% 20.22/20.40  198 [hyper,183,114] {-} coll($c7,$c7,$c5).
% 20.22/20.40  212 [hyper,184,114] {-} coll($c5,$c5,$c9).
% 20.22/20.40  213 [hyper,184,1] {-} coll($c9,$c5,$c7).
% 20.22/20.40  243 [hyper,185,114] {-} coll($c9,$c9,$c7).
% 20.22/20.40  257 [hyper,198,1] {-} coll($c7,$c5,$c7).
% 20.22/20.40  284 [hyper,212,114] {-} coll($c9,$c9,$c5).
% 20.22/20.40  298 [hyper,161,8] {-} perp($c7,$c6,$c9,$c7).
% 20.22/20.40  316 [hyper,213,114] {-} coll($c7,$c7,$c9).
% 20.22/20.40  330 [hyper,243,1] {-} coll($c9,$c7,$c9).
% 20.22/20.40  356 [hyper,257,114] {-} coll($c7,$c7,$c7).
% 20.22/20.40  374 [hyper,162,8] {-} perp($c8,$c6,$c9,$c8).
% 20.22/20.40  483 [hyper,330,114] {-} coll($c9,$c9,$c9).
% 20.22/20.40  485 [hyper,330,2] {-} coll($c7,$c9,$c9).
% 20.22/20.40  858 [hyper,298,9,161] {-} para($c9,$c7,$c9,$c7).
% 20.22/20.40  859 [hyper,298,9,161] {-} para($c7,$c6,$c7,$c6).
% 20.22/20.40  860 [hyper,298,7] {-} perp($c7,$c6,$c7,$c9).
% 20.22/20.40  895 [hyper,374,9,162] {-} para($c9,$c8,$c9,$c8).
% 20.22/20.40  1053 [hyper,858,40] {-} eqangle($c9,$c7,A,B,$c9,$c7,A,B).
% 20.22/20.40  1071 [hyper,859,67] {-} coll($c7,$c6,$c6).
% 20.22/20.40  1072 [hyper,859,40] {-} eqangle($c7,$c6,A,B,$c7,$c6,A,B).
% 20.22/20.40  1089 [hyper,1071,114] {-} coll($c6,$c6,$c7).
% 20.22/20.40  1104 [hyper,1089,114] {-} coll($c7,$c7,$c6).
% 20.22/20.40  1245 [hyper,1104,3,356] {-} coll($c6,$c7,$c7).
% 20.22/20.40  1246 [hyper,1104,3,316] {-} coll($c6,$c9,$c7).
% 20.22/20.40  1427 [hyper,1246,1] {-} coll($c6,$c7,$c9).
% 20.22/20.40  1585 [hyper,1427,114] {-} coll($c9,$c9,$c6).
% 20.22/20.40  2362 [hyper,860,8] {-} perp($c7,$c9,$c7,$c6).
% 20.22/20.40  4579 [hyper,2362,9,860] {-} para($c7,$c9,$c7,$c9).
% 20.22/20.40  15104 [hyper,1053,43,1585] {-} cyclic($c7,$c6,$c9,$c9).
% 20.22/20.40  15106 [hyper,1053,43,483] {-} cyclic($c7,$c9,$c9,$c9).
% 20.22/20.40  15107 [hyper,1053,43,284] {-} cyclic($c7,$c5,$c9,$c9).
% 20.22/20.40  15108 [hyper,1053,43,243] {-} cyclic($c7,$c7,$c9,$c9).
% 20.22/20.40  15115 [hyper,15104,16] {-} cyclic($c6,$c7,$c9,$c9).
% 20.22/20.40  15121 [hyper,15107,15] {-} cyclic($c7,$c9,$c5,$c9).
% 20.22/20.40  15132 [hyper,1072,43,1104] {-} cyclic($c6,$c6,$c7,$c7).
% 20.22/20.40  15134 [hyper,1072,43,356] {-} cyclic($c6,$c7,$c7,$c7).
% 20.22/20.40  15135 [hyper,1072,43,316] {-} cyclic($c6,$c9,$c7,$c7).
% 20.22/20.40  15139 [hyper,15108,15] {-} cyclic($c7,$c9,$c7,$c9).
% 20.22/20.40  15150 [hyper,15115,15] {-} cyclic($c6,$c9,$c7,$c9).
% 20.22/20.40  15164 [hyper,15121,16] {-} cyclic($c9,$c7,$c5,$c9).
% 20.22/20.40  15173 [hyper,15132,15] {-} cyclic($c6,$c7,$c6,$c7).
% 20.22/20.40  15176 [hyper,15135,120] {-} cyclic($c9,$c7,$c7,$c7).
% 20.22/20.40  15197 [hyper,15139,16] {-} cyclic($c9,$c7,$c7,$c9).
% 20.22/20.40  15198 [hyper,15139,14] {-} cyclic($c7,$c9,$c9,$c7).
% 20.22/20.40  15226 [hyper,15150,17,15135] {-} cyclic($c9,$c7,$c9,$c7).
% 20.22/20.40  15282 [hyper,15164,14] {-} cyclic($c9,$c7,$c9,$c5).
% 20.22/20.40  15302 [hyper,15173,14] {-} cyclic($c6,$c7,$c7,$c6).
% 20.22/20.40  15337 [hyper,15197,17,15176] {-} cyclic($c7,$c7,$c9,$c7).
% 20.22/20.40  15351 [hyper,15198,123,15106,1053] {-} cong($c7,$c9,$c7,$c9).
% 20.22/20.40  15453 [hyper,15282,120] {-} cyclic($c7,$c9,$c5,$c5).
% 20.22/20.40  15459 [hyper,15282,17,15226] {-} cyclic($c7,$c9,$c5,$c7).
% 20.22/20.40  15518 [hyper,15302,123,15134,1072] {-} cong($c6,$c7,$c6,$c7).
% 20.22/20.40  15578 [hyper,15337,121,15108,1053] {-} cong($c7,$c7,$c7,$c7).
% 20.22/20.40  15605 [hyper,15351,68,485] {-} midp($c7,$c9,$c9).
% 20.22/20.40  15614 [hyper,15605,129,895] {-} midp($c7,$c8,$c8).
% 20.22/20.40  15615 [hyper,15605,129,858] {-} midp($c7,$c7,$c7).
% 20.22/20.40  15632 [hyper,15614,69] {-} cong($c7,$c8,$c7,$c8).
% 20.22/20.40  15656 [hyper,15615,46,4579,330] {-} midp($c9,$c7,$c9).
% 20.22/20.40  16388 [hyper,15453,15] {-} cyclic($c7,$c5,$c9,$c5).
% 20.22/20.40  16416 [hyper,15459,15] {-} cyclic($c7,$c5,$c9,$c7).
% 20.22/20.40  16700 [hyper,15518,68,1245] {-} midp($c6,$c7,$c7).
% 20.22/20.40  16818 [hyper,16700,45,15656] {-} para($c9,$c6,$c9,$c7).
% 20.22/20.40  18409 [hyper,15578,58,15351,15337] {-} perp($c9,$c7,$c7,$c7).
% 20.22/20.40  19847 [hyper,16416,44,16388,15107,1053] {-} cong($c7,$c5,$c7,$c5).
% 20.22/20.40  27153 [hyper,18409,10,16818] {-} perp($c9,$c6,$c7,$c7).
% 20.22/20.40  30844 [hyper,19847,57,15632] {-} perp($c7,$c7,$c8,$c5).
% 20.22/20.40  36168 [hyper,30844,9,27153] {-} para($c9,$c6,$c8,$c5).
% 20.22/20.40  36169 [binary,36168.1,113.1] {-} $F.
% 20.22/20.40  
% 20.22/20.40  % SZS output end Refutation
% 20.22/20.40  ------------ end of proof -------------
% 20.22/20.40  
% 20.22/20.40  
% 20.22/20.40  Search stopped by max_proofs option.
% 20.22/20.40  
% 20.22/20.40  
% 20.22/20.40  Search stopped by max_proofs option.
% 20.22/20.40  
% 20.22/20.40  ============ end of search ============
% 20.22/20.40  
% 20.22/20.40  That finishes the proof of the theorem.
% 20.22/20.40  
% 20.22/20.40  Process 29331 finished Fri Jun 17 17:24:32 2022
%------------------------------------------------------------------------------