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Otter---3.3.UNS-Ref.s

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%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : REL046-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n020.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 13:11:58 EDT 2022

% Result   : Unsatisfiable 1.97s 2.18s
% Output   : Refutation 1.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   55 (  52 unt;   0 nHn;   9 RR)
%            Number of literals    :   58 (  57 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( join(sk1,sk2) != sk2
    | join(sk1,sk3) != sk3 ),
    file('REL046-1.p',unknown),
    [] ).

cnf(2,axiom,
    A = A,
    file('REL046-1.p',unknown),
    [] ).

cnf(3,axiom,
    join(A,B) = join(B,A),
    file('REL046-1.p',unknown),
    [] ).

cnf(4,axiom,
    join(A,join(B,C)) = join(join(A,B),C),
    file('REL046-1.p',unknown),
    [] ).

cnf(6,plain,
    join(join(A,B),C) = join(A,join(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
    [iquote('copy,4,flip.1')] ).

cnf(7,axiom,
    A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
    file('REL046-1.p',unknown),
    [] ).

cnf(8,plain,
    join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
    [iquote('copy,7,flip.1')] ).

cnf(10,axiom,
    meet(A,B) = complement(join(complement(A),complement(B))),
    file('REL046-1.p',unknown),
    [] ).

cnf(12,plain,
    complement(join(complement(A),complement(B))) = meet(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
    [iquote('copy,10,flip.1')] ).

cnf(16,axiom,
    composition(A,one) = A,
    file('REL046-1.p',unknown),
    [] ).

cnf(22,axiom,
    converse(converse(A)) = A,
    file('REL046-1.p',unknown),
    [] ).

cnf(25,axiom,
    converse(composition(A,B)) = composition(converse(B),converse(A)),
    file('REL046-1.p',unknown),
    [] ).

cnf(27,axiom,
    join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
    file('REL046-1.p',unknown),
    [] ).

cnf(29,axiom,
    top = join(A,complement(A)),
    file('REL046-1.p',unknown),
    [] ).

cnf(30,plain,
    join(A,complement(A)) = top,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[29])]),
    [iquote('copy,29,flip.1')] ).

cnf(32,axiom,
    zero = meet(A,complement(A)),
    file('REL046-1.p',unknown),
    [] ).

cnf(34,plain,
    meet(A,complement(A)) = zero,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),
    [iquote('copy,32,flip.1')] ).

cnf(35,axiom,
    join(sk1,meet(sk2,sk3)) = meet(sk2,sk3),
    file('REL046-1.p',unknown),
    [] ).

cnf(37,plain,
    join(meet(A,B),complement(join(complement(A),B))) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[8]),12]),
    [iquote('back_demod,8,demod,12')] ).

cnf(39,plain,
    join(complement(A),A) = top,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,30])]),
    [iquote('para_into,3.1.1,30.1.1,flip.1')] ).

cnf(47,plain,
    complement(join(complement(A),meet(B,C))) = meet(A,join(complement(B),complement(C))),
    inference(para_into,[status(thm),theory(equality)],[12,12]),
    [iquote('para_into,11.1.1.1.2,11.1.1')] ).

cnf(51,plain,
    complement(top) = zero,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,30]),34]),
    [iquote('para_into,11.1.1.1,30.1.1,demod,34')] ).

cnf(52,plain,
    meet(A,B) = meet(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,3]),12]),
    [iquote('para_into,11.1.1.1,3.1.1,demod,12')] ).

cnf(65,plain,
    join(sk1,join(meet(sk2,sk3),A)) = join(meet(sk2,sk3),A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,35])]),
    [iquote('para_into,5.1.1.1,35.1.1,flip.1')] ).

cnf(69,plain,
    join(A,join(B,C)) = join(B,join(A,C)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,3]),6]),
    [iquote('para_into,5.1.1.1,3.1.1,demod,6')] ).

cnf(75,plain,
    complement(join(complement(A),zero)) = meet(A,top),
    inference(para_from,[status(thm),theory(equality)],[51,12]),
    [iquote('para_from,50.1.1,11.1.1.1.2')] ).

cnf(83,plain,
    complement(join(zero,complement(A))) = meet(top,A),
    inference(para_from,[status(thm),theory(equality)],[51,12]),
    [iquote('para_from,50.1.1,11.1.1.1.1')] ).

cnf(181,plain,
    composition(converse(one),converse(A)) = converse(A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,16])]),
    [iquote('para_into,25.1.1.1,16.1.1,flip.1')] ).

cnf(187,plain,
    composition(converse(one),A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[181,22]),22]),
    [iquote('para_into,181.1.1.2,21.1.1,demod,22')] ).

cnf(190,plain,
    converse(one) = one,
    inference(para_into,[status(thm),theory(equality)],[187,16]),
    [iquote('para_into,187.1.1,16.1.1')] ).

cnf(192,plain,
    composition(one,A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[187]),190]),
    [iquote('back_demod,187,demod,190')] ).

cnf(198,plain,
    join(complement(A),complement(A)) = complement(A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,190]),192,192]),
    [iquote('para_into,27.1.1.1.1,189.1.1,demod,192,192')] ).

cnf(258,plain,
    complement(complement(A)) = meet(A,A),
    inference(para_from,[status(thm),theory(equality)],[198,12]),
    [iquote('para_from,197.1.1,11.1.1.1')] ).

cnf(262,plain,
    join(complement(A),join(complement(A),B)) = join(complement(A),B),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[198,6])]),
    [iquote('para_from,197.1.1,5.1.1.1,flip.1')] ).

cnf(278,plain,
    join(zero,meet(A,A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,34]),198,258]),
    [iquote('para_into,37.1.1.1,33.1.1,demod,198,258')] ).

cnf(290,plain,
    join(meet(A,A),zero) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,39]),51]),
    [iquote('para_into,37.1.1.2.1,39.1.1,demod,51')] ).

cnf(298,plain,
    join(meet(A,complement(B)),meet(A,B)) = A,
    inference(para_into,[status(thm),theory(equality)],[37,12]),
    [iquote('para_into,37.1.1.2,11.1.1')] ).

cnf(317,plain,
    meet(top,complement(A)) = complement(A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[258,83]),278])]),
    [iquote('para_from,257.1.1,82.1.1.1.2,demod,278,flip.1')] ).

cnf(319,plain,
    meet(complement(A),top) = complement(A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[258,75]),290])]),
    [iquote('para_from,257.1.1,74.1.1.1.1,demod,290,flip.1')] ).

cnf(350,plain,
    join(complement(A),meet(top,A)) = top,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[317,37]),51,83]),
    [iquote('para_from,317.1.1,37.1.1.1,demod,51,83')] ).

cnf(475,plain,
    join(complement(A),meet(A,top)) = top,
    inference(para_into,[status(thm),theory(equality)],[350,52]),
    [iquote('para_into,350.1.1.2,52.1.1')] ).

cnf(528,plain,
    meet(A,join(complement(A),zero)) = zero,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[475,47]),51,51])]),
    [iquote('para_from,475.1.1,47.1.1.1,demod,51,51,flip.1')] ).

cnf(620,plain,
    join(zero,meet(A,top)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[528,37]),262,75]),
    [iquote('para_from,528.1.1,37.1.1.1,demod,262,75')] ).

cnf(622,plain,
    join(zero,complement(A)) = complement(A),
    inference(para_into,[status(thm),theory(equality)],[620,319]),
    [iquote('para_into,620.1.1.2,319.1.1')] ).

cnf(661,plain,
    meet(A,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[622,258]),278,258])]),
    [iquote('para_into,622.1.1.2,257.1.1,demod,278,258,flip.1')] ).

cnf(695,plain,
    complement(complement(A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[258]),661]),
    [iquote('back_demod,257,demod,661')] ).

cnf(752,plain,
    join(A,A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[695,198]),695,695]),
    [iquote('para_from,694.1.1,197.1.1.2,demod,695,695')] ).

cnf(822,plain,
    join(A,join(B,A)) = join(B,A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[69,752])]),
    [iquote('para_into,69.1.1.2,752.1.1,flip.1')] ).

cnf(1105,plain,
    join(meet(A,B),A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[298,822]),298]),
    [iquote('para_from,297.1.1,822.1.1.2,demod,298')] ).

cnf(1107,plain,
    join(meet(A,B),B) = B,
    inference(para_into,[status(thm),theory(equality)],[1105,52]),
    [iquote('para_into,1104.1.1.1,52.1.1')] ).

cnf(1111,plain,
    join(sk1,sk2) = sk2,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1105,65]),1105]),
    [iquote('para_from,1104.1.1,65.1.1.2,demod,1105')] ).

cnf(1115,plain,
    ( sk2 != sk2
    | join(sk1,sk3) != sk3 ),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),1111]),
    [iquote('back_demod,1,demod,1111')] ).

cnf(1149,plain,
    join(sk1,sk3) = sk3,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1107,65]),1107]),
    [iquote('para_from,1106.1.1,65.1.1.2,demod,1107')] ).

cnf(1152,plain,
    ( sk2 != sk2
    | sk3 != sk3 ),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1115]),1149]),
    [iquote('back_demod,1115,demod,1149')] ).

cnf(1169,plain,
    $false,
    inference(hyper,[status(thm)],[1152,2,2]),
    [iquote('hyper,1152,2,2')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : REL046-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n020.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 10:08:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.97/2.14  ----- Otter 3.3f, August 2004 -----
% 1.97/2.14  The process was started by sandbox on n020.cluster.edu,
% 1.97/2.14  Wed Jul 27 10:08:38 2022
% 1.97/2.14  The command was "./otter".  The process ID is 19123.
% 1.97/2.14  
% 1.97/2.14  set(prolog_style_variables).
% 1.97/2.14  set(auto).
% 1.97/2.14     dependent: set(auto1).
% 1.97/2.14     dependent: set(process_input).
% 1.97/2.14     dependent: clear(print_kept).
% 1.97/2.14     dependent: clear(print_new_demod).
% 1.97/2.14     dependent: clear(print_back_demod).
% 1.97/2.14     dependent: clear(print_back_sub).
% 1.97/2.14     dependent: set(control_memory).
% 1.97/2.14     dependent: assign(max_mem, 12000).
% 1.97/2.14     dependent: assign(pick_given_ratio, 4).
% 1.97/2.14     dependent: assign(stats_level, 1).
% 1.97/2.14     dependent: assign(max_seconds, 10800).
% 1.97/2.14  clear(print_given).
% 1.97/2.14  
% 1.97/2.14  list(usable).
% 1.97/2.14  0 [] A=A.
% 1.97/2.14  0 [] join(A,B)=join(B,A).
% 1.97/2.14  0 [] join(A,join(B,C))=join(join(A,B),C).
% 1.97/2.14  0 [] A=join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))).
% 1.97/2.14  0 [] meet(A,B)=complement(join(complement(A),complement(B))).
% 1.97/2.14  0 [] composition(A,composition(B,C))=composition(composition(A,B),C).
% 1.97/2.14  0 [] composition(A,one)=A.
% 1.97/2.14  0 [] composition(join(A,B),C)=join(composition(A,C),composition(B,C)).
% 1.97/2.14  0 [] converse(converse(A))=A.
% 1.97/2.14  0 [] converse(join(A,B))=join(converse(A),converse(B)).
% 1.97/2.14  0 [] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.97/2.14  0 [] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.97/2.14  0 [] top=join(A,complement(A)).
% 1.97/2.14  0 [] zero=meet(A,complement(A)).
% 1.97/2.14  0 [] join(sk1,meet(sk2,sk3))=meet(sk2,sk3).
% 1.97/2.14  0 [] join(sk1,sk2)!=sk2|join(sk1,sk3)!=sk3.
% 1.97/2.14  end_of_list.
% 1.97/2.14  
% 1.97/2.14  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.97/2.14  
% 1.97/2.14  This is a Horn set with equality.  The strategy will be
% 1.97/2.14  Knuth-Bendix and hyper_res, with positive clauses in
% 1.97/2.14  sos and nonpositive clauses in usable.
% 1.97/2.14  
% 1.97/2.14     dependent: set(knuth_bendix).
% 1.97/2.14     dependent: set(anl_eq).
% 1.97/2.14     dependent: set(para_from).
% 1.97/2.14     dependent: set(para_into).
% 1.97/2.14     dependent: clear(para_from_right).
% 1.97/2.14     dependent: clear(para_into_right).
% 1.97/2.14     dependent: set(para_from_vars).
% 1.97/2.14     dependent: set(eq_units_both_ways).
% 1.97/2.14     dependent: set(dynamic_demod_all).
% 1.97/2.14     dependent: set(dynamic_demod).
% 1.97/2.14     dependent: set(order_eq).
% 1.97/2.14     dependent: set(back_demod).
% 1.97/2.14     dependent: set(lrpo).
% 1.97/2.14     dependent: set(hyper_res).
% 1.97/2.14     dependent: clear(order_hyper).
% 1.97/2.14  
% 1.97/2.14  ------------> process usable:
% 1.97/2.14  ** KEPT (pick-wt=10): 1 [] join(sk1,sk2)!=sk2|join(sk1,sk3)!=sk3.
% 1.97/2.14  
% 1.97/2.14  ------------> process sos:
% 1.97/2.14  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.97/2.14  ** KEPT (pick-wt=7): 3 [] join(A,B)=join(B,A).
% 1.97/2.14  ** KEPT (pick-wt=11): 5 [copy,4,flip.1] join(join(A,B),C)=join(A,join(B,C)).
% 1.97/2.14  ---> New Demodulator: 6 [new_demod,5] join(join(A,B),C)=join(A,join(B,C)).
% 1.97/2.14  ** KEPT (pick-wt=14): 8 [copy,7,flip.1] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.97/2.14  ---> New Demodulator: 9 [new_demod,8] join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))=A.
% 1.97/2.14  ** KEPT (pick-wt=10): 11 [copy,10,flip.1] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.97/2.14  ---> New Demodulator: 12 [new_demod,11] complement(join(complement(A),complement(B)))=meet(A,B).
% 1.97/2.14  ** KEPT (pick-wt=11): 14 [copy,13,flip.1] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 1.97/2.14  ---> New Demodulator: 15 [new_demod,14] composition(composition(A,B),C)=composition(A,composition(B,C)).
% 1.97/2.14  ** KEPT (pick-wt=5): 16 [] composition(A,one)=A.
% 1.97/2.14  ---> New Demodulator: 17 [new_demod,16] composition(A,one)=A.
% 1.97/2.14  ** KEPT (pick-wt=13): 19 [copy,18,flip.1] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.97/2.14  ---> New Demodulator: 20 [new_demod,19] join(composition(A,B),composition(C,B))=composition(join(A,C),B).
% 1.97/2.14  ** KEPT (pick-wt=5): 21 [] converse(converse(A))=A.
% 1.97/2.14  ---> New Demodulator: 22 [new_demod,21] converse(converse(A))=A.
% 1.97/2.14  ** KEPT (pick-wt=10): 23 [] converse(join(A,B))=join(converse(A),converse(B)).
% 1.97/2.14  ---> New Demodulator: 24 [new_demod,23] converse(join(A,B))=join(converse(A),converse(B)).
% 1.97/2.14  ** KEPT (pick-wt=10): 25 [] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.97/2.14  ---> New Demodulator: 26 [new_demod,25] converse(composition(A,B))=composition(converse(B),converse(A)).
% 1.97/2.14  ** KEPT (pick-wt=13): 27 [] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.97/2.18  ---> New Demodulator: 28 [new_demod,27] join(composition(converse(A),complement(composition(A,B))),complement(B))=complement(B).
% 1.97/2.18  ** KEPT (pick-wt=6): 30 [copy,29,flip.1] join(A,complement(A))=top.
% 1.97/2.18  ---> New Demodulator: 31 [new_demod,30] join(A,complement(A))=top.
% 1.97/2.18  ** KEPT (pick-wt=6): 33 [copy,32,flip.1] meet(A,complement(A))=zero.
% 1.97/2.18  ---> New Demodulator: 34 [new_demod,33] meet(A,complement(A))=zero.
% 1.97/2.18  ** KEPT (pick-wt=9): 35 [] join(sk1,meet(sk2,sk3))=meet(sk2,sk3).
% 1.97/2.18  ---> New Demodulator: 36 [new_demod,35] join(sk1,meet(sk2,sk3))=meet(sk2,sk3).
% 1.97/2.18    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.97/2.18    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] join(A,B)=join(B,A).
% 1.97/2.18  >>>> Starting back demodulation with 6.
% 1.97/2.18  >>>> Starting back demodulation with 9.
% 1.97/2.18  >>>> Starting back demodulation with 12.
% 1.97/2.18      >> back demodulating 8 with 12.
% 1.97/2.18  >>>> Starting back demodulation with 15.
% 1.97/2.18  >>>> Starting back demodulation with 17.
% 1.97/2.18  >>>> Starting back demodulation with 20.
% 1.97/2.18  >>>> Starting back demodulation with 22.
% 1.97/2.18  >>>> Starting back demodulation with 24.
% 1.97/2.18  >>>> Starting back demodulation with 26.
% 1.97/2.18  >>>> Starting back demodulation with 28.
% 1.97/2.18  >>>> Starting back demodulation with 31.
% 1.97/2.18  >>>> Starting back demodulation with 34.
% 1.97/2.18  >>>> Starting back demodulation with 36.
% 1.97/2.18  >>>> Starting back demodulation with 38.
% 1.97/2.18  
% 1.97/2.18  ======= end of input processing =======
% 1.97/2.18  
% 1.97/2.18  =========== start of search ===========
% 1.97/2.18  
% 1.97/2.18  
% 1.97/2.18  Resetting weight limit to 10.
% 1.97/2.18  
% 1.97/2.18  
% 1.97/2.18  Resetting weight limit to 10.
% 1.97/2.18  
% 1.97/2.18  sos_size=190
% 1.97/2.18  
% 1.97/2.18  -------- PROOF -------- 
% 1.97/2.18  
% 1.97/2.18  -----> EMPTY CLAUSE at   0.04 sec ----> 1169 [hyper,1152,2,2] $F.
% 1.97/2.18  
% 1.97/2.18  Length of proof is 41.  Level of proof is 21.
% 1.97/2.18  
% 1.97/2.18  ---------------- PROOF ----------------
% 1.97/2.18  % SZS status Unsatisfiable
% 1.97/2.18  % SZS output start Refutation
% See solution above
% 1.97/2.18  ------------ end of proof -------------
% 1.97/2.18  
% 1.97/2.18  
% 1.97/2.18  Search stopped by max_proofs option.
% 1.97/2.18  
% 1.97/2.18  
% 1.97/2.18  Search stopped by max_proofs option.
% 1.97/2.18  
% 1.97/2.18  ============ end of search ============
% 1.97/2.18  
% 1.97/2.18  -------------- statistics -------------
% 1.97/2.18  clauses given                148
% 1.97/2.18  clauses generated           2661
% 1.97/2.18  clauses kept                 608
% 1.97/2.18  clauses forward subsumed    2076
% 1.97/2.18  clauses back subsumed          0
% 1.97/2.18  Kbytes malloced             4882
% 1.97/2.18  
% 1.97/2.18  ----------- times (seconds) -----------
% 1.97/2.18  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.97/2.18  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 1.97/2.18  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.97/2.18  
% 1.97/2.18  That finishes the proof of the theorem.
% 1.97/2.18  
% 1.97/2.18  Process 19123 finished Wed Jul 27 10:08:40 2022
% 1.97/2.18  Otter interrupted
% 1.97/2.18  PROOF FOUND
%------------------------------------------------------------------------------