TSTP Solution File: SEU118+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n021.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 13:14:48 EDT 2022

% Result   : Theorem 1.57s 2.07s
% Output   : Refutation 1.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   17 (  12 unt;   0 nHn;  13 RR)
%            Number of literals    :   27 (   2 equ;  11 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   16 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    ( ~ finite(A)
    | ~ element(B,powerset(A))
    | finite(B) ),
    file('SEU118+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ preboolean(A)
    | A != finite_subsets(B)
    | in(C,A)
    | ~ subset(C,B)
    | ~ finite(C) ),
    file('SEU118+1.p',unknown),
    [] ).

cnf(25,axiom,
    ~ element(dollar_c5,finite_subsets(dollar_c6)),
    file('SEU118+1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ element(A,powerset(B))
    | subset(A,B) ),
    file('SEU118+1.p',unknown),
    [] ).

cnf(27,axiom,
    ( element(A,powerset(B))
    | ~ subset(A,B) ),
    file('SEU118+1.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ in(A,B)
    | ~ element(B,powerset(C))
    | element(A,C) ),
    file('SEU118+1.p',unknown),
    [] ).

cnf(35,axiom,
    A = A,
    file('SEU118+1.p',unknown),
    [] ).

cnf(36,axiom,
    preboolean(finite_subsets(A)),
    file('SEU118+1.p',unknown),
    [] ).

cnf(67,axiom,
    subset(A,A),
    file('SEU118+1.p',unknown),
    [] ).

cnf(68,axiom,
    element(dollar_c5,powerset(dollar_c6)),
    file('SEU118+1.p',unknown),
    [] ).

cnf(69,axiom,
    finite(dollar_c6),
    file('SEU118+1.p',unknown),
    [] ).

cnf(162,plain,
    element(A,powerset(A)),
    inference(hyper,[status(thm)],[67,27]),
    [iquote('hyper,67,27')] ).

cnf(188,plain,
    subset(dollar_c5,dollar_c6),
    inference(hyper,[status(thm)],[68,26]),
    [iquote('hyper,68,26')] ).

cnf(190,plain,
    finite(dollar_c5),
    inference(hyper,[status(thm)],[68,5,69]),
    [iquote('hyper,68,5,69')] ).

cnf(206,plain,
    in(dollar_c5,finite_subsets(dollar_c6)),
    inference(hyper,[status(thm)],[188,10,36,35,190]),
    [iquote('hyper,188,10,36,35,190')] ).

cnf(418,plain,
    element(dollar_c5,finite_subsets(dollar_c6)),
    inference(hyper,[status(thm)],[206,28,162]),
    [iquote('hyper,206,28,162')] ).

cnf(419,plain,
    $false,
    inference(binary,[status(thm)],[418,25]),
    [iquote('binary,418.1,25.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14  % Command  : otter-tptp-script %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.21/0.35  % DateTime : Wed Jul 27 07:27:53 EDT 2022
% 0.21/0.35  % CPUTime  : 
% 1.57/2.06  ----- Otter 3.3f, August 2004 -----
% 1.57/2.06  The process was started by sandbox on n021.cluster.edu,
% 1.57/2.06  Wed Jul 27 07:27:53 2022
% 1.57/2.06  The command was "./otter".  The process ID is 7180.
% 1.57/2.06  
% 1.57/2.06  set(prolog_style_variables).
% 1.57/2.06  set(auto).
% 1.57/2.06     dependent: set(auto1).
% 1.57/2.06     dependent: set(process_input).
% 1.57/2.06     dependent: clear(print_kept).
% 1.57/2.06     dependent: clear(print_new_demod).
% 1.57/2.06     dependent: clear(print_back_demod).
% 1.57/2.06     dependent: clear(print_back_sub).
% 1.57/2.06     dependent: set(control_memory).
% 1.57/2.06     dependent: assign(max_mem, 12000).
% 1.57/2.06     dependent: assign(pick_given_ratio, 4).
% 1.57/2.06     dependent: assign(stats_level, 1).
% 1.57/2.06     dependent: assign(max_seconds, 10800).
% 1.57/2.06  clear(print_given).
% 1.57/2.06  
% 1.57/2.06  formula_list(usable).
% 1.57/2.06  all A (A=A).
% 1.57/2.06  all A B (in(A,B)-> -in(B,A)).
% 1.57/2.06  all A (empty(A)->finite(A)).
% 1.57/2.06  all A (preboolean(A)->cup_closed(A)&diff_closed(A)).
% 1.57/2.06  all A (finite(A)-> (all B (element(B,powerset(A))->finite(B)))).
% 1.57/2.06  all A (cup_closed(A)&diff_closed(A)->preboolean(A)).
% 1.57/2.06  all A B (element(B,finite_subsets(A))->finite(B)).
% 1.57/2.06  all A B (preboolean(B)-> (B=finite_subsets(A)<-> (all C (in(C,B)<->subset(C,A)&finite(C))))).
% 1.57/2.06  all A preboolean(finite_subsets(A)).
% 1.57/2.06  all A exists B element(B,A).
% 1.57/2.06  all A (-empty(powerset(A))&cup_closed(powerset(A))&diff_closed(powerset(A))&preboolean(powerset(A))).
% 1.57/2.06  all A (-empty(powerset(A))).
% 1.57/2.06  empty(empty_set).
% 1.57/2.06  all A (-empty(finite_subsets(A))&cup_closed(finite_subsets(A))&diff_closed(finite_subsets(A))&preboolean(finite_subsets(A))).
% 1.57/2.06  exists A (-empty(A)&finite(A)).
% 1.57/2.06  exists A (-empty(A)&cup_closed(A)&cap_closed(A)&diff_closed(A)&preboolean(A)).
% 1.57/2.06  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.57/2.06  exists A empty(A).
% 1.57/2.06  all A exists B (element(B,powerset(A))&empty(B)&relation(B)&function(B)&one_to_one(B)&epsilon_transitive(B)&epsilon_connected(B)&ordinal(B)&natural(B)&finite(B)).
% 1.57/2.06  all A exists B (element(B,powerset(A))&empty(B)).
% 1.57/2.06  exists A (-empty(A)).
% 1.57/2.06  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 1.57/2.06  all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)&finite(B)))).
% 1.57/2.06  all A B subset(A,A).
% 1.57/2.06  all A B (subset(A,B)&finite(B)->finite(A)).
% 1.57/2.06  all A B (in(A,B)->element(A,B)).
% 1.57/2.06  all A B (element(A,B)->empty(B)|in(A,B)).
% 1.57/2.06  -(all A B (element(B,powerset(A))-> (finite(A)->element(B,finite_subsets(A))))).
% 1.57/2.06  all A B (element(A,powerset(B))<->subset(A,B)).
% 1.57/2.06  all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.57/2.06  all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.57/2.06  all A (empty(A)->A=empty_set).
% 1.57/2.06  all A B (-(in(A,B)&empty(B))).
% 1.57/2.06  all A B (-(empty(A)&A!=B&empty(B))).
% 1.57/2.06  end_of_list.
% 1.57/2.06  
% 1.57/2.06  -------> usable clausifies to:
% 1.57/2.06  
% 1.57/2.06  list(usable).
% 1.57/2.06  0 [] A=A.
% 1.57/2.06  0 [] -in(A,B)| -in(B,A).
% 1.57/2.06  0 [] -empty(A)|finite(A).
% 1.57/2.06  0 [] -preboolean(A)|cup_closed(A).
% 1.57/2.06  0 [] -preboolean(A)|diff_closed(A).
% 1.57/2.06  0 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 1.57/2.06  0 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 1.57/2.06  0 [] -element(B,finite_subsets(A))|finite(B).
% 1.57/2.06  0 [] -preboolean(B)|B!=finite_subsets(A)| -in(C,B)|subset(C,A).
% 1.57/2.06  0 [] -preboolean(B)|B!=finite_subsets(A)| -in(C,B)|finite(C).
% 1.57/2.06  0 [] -preboolean(B)|B!=finite_subsets(A)|in(C,B)| -subset(C,A)| -finite(C).
% 1.57/2.06  0 [] -preboolean(B)|B=finite_subsets(A)|in($f1(A,B),B)|subset($f1(A,B),A).
% 1.57/2.06  0 [] -preboolean(B)|B=finite_subsets(A)|in($f1(A,B),B)|finite($f1(A,B)).
% 1.57/2.06  0 [] -preboolean(B)|B=finite_subsets(A)| -in($f1(A,B),B)| -subset($f1(A,B),A)| -finite($f1(A,B)).
% 1.57/2.06  0 [] preboolean(finite_subsets(A)).
% 1.57/2.06  0 [] element($f2(A),A).
% 1.57/2.06  0 [] -empty(powerset(A)).
% 1.57/2.06  0 [] cup_closed(powerset(A)).
% 1.57/2.06  0 [] diff_closed(powerset(A)).
% 1.57/2.06  0 [] preboolean(powerset(A)).
% 1.57/2.06  0 [] -empty(powerset(A)).
% 1.57/2.06  0 [] empty(empty_set).
% 1.57/2.06  0 [] -empty(finite_subsets(A)).
% 1.57/2.06  0 [] cup_closed(finite_subsets(A)).
% 1.57/2.06  0 [] diff_closed(finite_subsets(A)).
% 1.57/2.06  0 [] preboolean(finite_subsets(A)).
% 1.57/2.06  0 [] -empty($c1).
% 1.57/2.06  0 [] finite($c1).
% 1.57/2.06  0 [] -empty($c2).
% 1.57/2.06  0 [] cup_closed($c2).
% 1.57/2.06  0 [] cap_closed($c2).
% 1.57/2.06  0 [] diff_closed($c2).
% 1.57/2.06  0 [] preboolean($c2).
% 1.57/2.06  0 [] empty(A)|element($f3(A),powerset(A)).
% 1.57/2.06  0 [] empty(A)| -empty($f3(A)).
% 1.57/2.06  0 [] empty($c3).
% 1.57/2.06  0 [] element($f4(A),powerset(A)).
% 1.57/2.06  0 [] empty($f4(A)).
% 1.57/2.06  0 [] relation($f4(A)).
% 1.57/2.06  0 [] function($f4(A)).
% 1.57/2.06  0 [] one_to_one($f4(A)).
% 1.57/2.06  0 [] epsilon_transitive($f4(A)).
% 1.57/2.06  0 [] epsilon_connected($f4(A)).
% 1.57/2.06  0 [] ordinal($f4(A)).
% 1.57/2.06  0 [] natural($f4(A)).
% 1.57/2.06  0 [] finite($f4(A)).
% 1.57/2.06  0 [] element($f5(A),powerset(A)).
% 1.57/2.06  0 [] empty($f5(A)).
% 1.57/2.06  0 [] -empty($c4).
% 1.57/2.06  0 [] empty(A)|element($f6(A),powerset(A)).
% 1.57/2.06  0 [] empty(A)| -empty($f6(A)).
% 1.57/2.06  0 [] empty(A)|finite($f6(A)).
% 1.57/2.06  0 [] empty(A)|element($f7(A),powerset(A)).
% 1.57/2.06  0 [] empty(A)| -empty($f7(A)).
% 1.57/2.06  0 [] empty(A)|finite($f7(A)).
% 1.57/2.06  0 [] subset(A,A).
% 1.57/2.06  0 [] -subset(A,B)| -finite(B)|finite(A).
% 1.57/2.06  0 [] -in(A,B)|element(A,B).
% 1.57/2.06  0 [] -element(A,B)|empty(B)|in(A,B).
% 1.57/2.06  0 [] element($c5,powerset($c6)).
% 1.57/2.06  0 [] finite($c6).
% 1.57/2.06  0 [] -element($c5,finite_subsets($c6)).
% 1.57/2.06  0 [] -element(A,powerset(B))|subset(A,B).
% 1.57/2.06  0 [] element(A,powerset(B))| -subset(A,B).
% 1.57/2.06  0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.57/2.06  0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.57/2.06  0 [] -empty(A)|A=empty_set.
% 1.57/2.06  0 [] -in(A,B)| -empty(B).
% 1.57/2.06  0 [] -empty(A)|A=B| -empty(B).
% 1.57/2.06  end_of_list.
% 1.57/2.06  
% 1.57/2.06  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.57/2.06  
% 1.57/2.06  This ia a non-Horn set with equality.  The strategy will be
% 1.57/2.06  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.57/2.06  deletion, with positive clauses in sos and nonpositive
% 1.57/2.06  clauses in usable.
% 1.57/2.06  
% 1.57/2.06     dependent: set(knuth_bendix).
% 1.57/2.06     dependent: set(anl_eq).
% 1.57/2.06     dependent: set(para_from).
% 1.57/2.06     dependent: set(para_into).
% 1.57/2.06     dependent: clear(para_from_right).
% 1.57/2.06     dependent: clear(para_into_right).
% 1.57/2.06     dependent: set(para_from_vars).
% 1.57/2.06     dependent: set(eq_units_both_ways).
% 1.57/2.06     dependent: set(dynamic_demod_all).
% 1.57/2.06     dependent: set(dynamic_demod).
% 1.57/2.06     dependent: set(order_eq).
% 1.57/2.06     dependent: set(back_demod).
% 1.57/2.06     dependent: set(lrpo).
% 1.57/2.06     dependent: set(hyper_res).
% 1.57/2.06     dependent: set(unit_deletion).
% 1.57/2.06     dependent: set(factor).
% 1.57/2.06  
% 1.57/2.06  ------------> process usable:
% 1.57/2.06  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.57/2.06  ** KEPT (pick-wt=4): 2 [] -empty(A)|finite(A).
% 1.57/2.06  ** KEPT (pick-wt=4): 3 [] -preboolean(A)|cup_closed(A).
% 1.57/2.06  ** KEPT (pick-wt=4): 4 [] -preboolean(A)|diff_closed(A).
% 1.57/2.06  ** KEPT (pick-wt=8): 5 [] -finite(A)| -element(B,powerset(A))|finite(B).
% 1.57/2.06  ** KEPT (pick-wt=6): 6 [] -cup_closed(A)| -diff_closed(A)|preboolean(A).
% 1.57/2.06  ** KEPT (pick-wt=6): 7 [] -element(A,finite_subsets(B))|finite(A).
% 1.57/2.06  ** KEPT (pick-wt=12): 8 [] -preboolean(A)|A!=finite_subsets(B)| -in(C,A)|subset(C,B).
% 1.57/2.06  ** KEPT (pick-wt=11): 9 [] -preboolean(A)|A!=finite_subsets(B)| -in(C,A)|finite(C).
% 1.57/2.06  ** KEPT (pick-wt=14): 10 [] -preboolean(A)|A!=finite_subsets(B)|in(C,A)| -subset(C,B)| -finite(C).
% 1.57/2.06  ** KEPT (pick-wt=16): 11 [] -preboolean(A)|A=finite_subsets(B)|in($f1(B,A),A)|subset($f1(B,A),B).
% 1.57/2.06  ** KEPT (pick-wt=15): 12 [] -preboolean(A)|A=finite_subsets(B)|in($f1(B,A),A)|finite($f1(B,A)).
% 1.57/2.06  ** KEPT (pick-wt=20): 13 [] -preboolean(A)|A=finite_subsets(B)| -in($f1(B,A),A)| -subset($f1(B,A),B)| -finite($f1(B,A)).
% 1.57/2.06  ** KEPT (pick-wt=3): 14 [] -empty(powerset(A)).
% 1.57/2.06    Following clause subsumed by 14 during input processing: 0 [] -empty(powerset(A)).
% 1.57/2.06  ** KEPT (pick-wt=3): 15 [] -empty(finite_subsets(A)).
% 1.57/2.06  ** KEPT (pick-wt=2): 16 [] -empty($c1).
% 1.57/2.06  ** KEPT (pick-wt=2): 17 [] -empty($c2).
% 1.57/2.06  ** KEPT (pick-wt=5): 18 [] empty(A)| -empty($f3(A)).
% 1.57/2.06  ** KEPT (pick-wt=2): 19 [] -empty($c4).
% 1.57/2.06  ** KEPT (pick-wt=5): 20 [] empty(A)| -empty($f6(A)).
% 1.57/2.06  ** KEPT (pick-wt=5): 21 [] empty(A)| -empty($f7(A)).
% 1.57/2.06  ** KEPT (pick-wt=7): 22 [] -subset(A,B)| -finite(B)|finite(A).
% 1.57/2.06  ** KEPT (pick-wt=6): 23 [] -in(A,B)|element(A,B).
% 1.57/2.06  ** KEPT (pick-wt=8): 24 [] -element(A,B)|empty(B)|in(A,B).
% 1.57/2.06  ** KEPT (pick-wt=4): 25 [] -element($c5,finite_subsets($c6)).
% 1.57/2.06  ** KEPT (pick-wt=7): 26 [] -element(A,powerset(B))|subset(A,B).
% 1.57/2.06  ** KEPT (pick-wt=7): 27 [] element(A,powerset(B))| -subset(A,B).
% 1.57/2.06  ** KEPT (pick-wt=10): 28 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.57/2.06  ** KEPT (pick-wt=9): 29 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.57/2.06  ** KEPT (pick-wt=5): 30 [] -empty(A)|A=empty_set.
% 1.57/2.06  ** KEPT (pick-wt=5): 31 [] -in(A,B)| -empty(B).
% 1.57/2.06  ** KEPT (pick-wt=7): 32 [] -empty(A)|A=B| -empty(B).
% 1.57/2.06  
% 1.57/2.06  ------------> process sos:
% 1.57/2.06  ** KEPT (pick-wt=3): 35 [] A=A.
% 1.57/2.06  ** KEPT (pick-wt=3): 36 [] preboolean(finite_subsets(A)).
% 1.57/2.06  ** KEPT (pick-wt=4): 37 [] element($f2(A),A).
% 1.57/2.06  ** KEPT (pick-wt=3): 38 [] cup_closed(powerset(A)).
% 1.57/2.06  ** KEPT (pick-wt=3): 39 [] diff_closed(powerset(A)).
% 1.57/2.06  ** KEPT (pick-wt=3): 40 [] preboolean(powerset(A)).
% 1.57/2.06  ** KEPT (pick-wt=2): 41 [] empty(empty_set).
% 1.57/2.06  ** KEPT (pick-wt=3): 42 [] cup_closed(finite_subsets(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 43 [] diff_closed(finite_subsets(A)).
% 1.57/2.07    Following clause subsumed by 36 during input processing: 0 [] preboolean(finite_subsets(A)).
% 1.57/2.07  ** KEPT (pick-wt=2): 44 [] finite($c1).
% 1.57/2.07  ** KEPT (pick-wt=2): 45 [] cup_closed($c2).
% 1.57/2.07  ** KEPT (pick-wt=2): 46 [] cap_closed($c2).
% 1.57/2.07  ** KEPT (pick-wt=2): 47 [] diff_closed($c2).
% 1.57/2.07  ** KEPT (pick-wt=2): 48 [] preboolean($c2).
% 1.57/2.07  ** KEPT (pick-wt=7): 49 [] empty(A)|element($f3(A),powerset(A)).
% 1.57/2.07  ** KEPT (pick-wt=2): 50 [] empty($c3).
% 1.57/2.07  ** KEPT (pick-wt=5): 51 [] element($f4(A),powerset(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 52 [] empty($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 53 [] relation($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 54 [] function($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 55 [] one_to_one($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 56 [] epsilon_transitive($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 57 [] epsilon_connected($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 58 [] ordinal($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 59 [] natural($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 60 [] finite($f4(A)).
% 1.57/2.07  ** KEPT (pick-wt=5): 61 [] element($f5(A),powerset(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 62 [] empty($f5(A)).
% 1.57/2.07  ** KEPT (pick-wt=7): 63 [] empty(A)|element($f6(A),powerset(A)).
% 1.57/2.07  ** KEPT (pick-wt=5): 64 [] empty(A)|finite($f6(A)).
% 1.57/2.07  ** KEPT (pick-wt=7): 65 [] empty(A)|element($f7(A),powerset(A)).
% 1.57/2.07  ** KEPT (pick-wt=5): 66 [] empty(A)|finite($f7(A)).
% 1.57/2.07  ** KEPT (pick-wt=3): 67 [] subset(A,A).
% 1.57/2.07  ** KEPT (pick-wt=4): 68 [] element($c5,powerset($c6)).
% 1.57/2.07  ** KEPT (pick-wt=2): 69 [] finite($c6).
% 1.57/2.07    Following clause subsumed by 35 during input processing: 0 [copy,35,flip.1] A=A.
% 1.57/2.07  35 back subsumes 34.
% 1.57/2.07  
% 1.57/2.07  ======= end of input processing =======
% 1.57/2.07  
% 1.57/2.07  =========== start of search ===========
% 1.57/2.07  
% 1.57/2.07  -------- PROOF -------- 
% 1.57/2.07  
% 1.57/2.07  ----> UNIT CONFLICT at   0.01 sec ----> 419 [binary,418.1,25.1] $F.
% 1.57/2.07  
% 1.57/2.07  Length of proof is 5.  Level of proof is 3.
% 1.57/2.07  
% 1.57/2.07  ---------------- PROOF ----------------
% 1.57/2.07  % SZS status Theorem
% 1.57/2.07  % SZS output start Refutation
% See solution above
% 1.57/2.07  ------------ end of proof -------------
% 1.57/2.07  
% 1.57/2.07  
% 1.57/2.07  Search stopped by max_proofs option.
% 1.57/2.07  
% 1.57/2.07  
% 1.57/2.07  Search stopped by max_proofs option.
% 1.57/2.07  
% 1.57/2.07  ============ end of search ============
% 1.57/2.07  
% 1.57/2.07  -------------- statistics -------------
% 1.57/2.07  clauses given                 64
% 1.57/2.07  clauses generated            703
% 1.57/2.07  clauses kept                 415
% 1.57/2.07  clauses forward subsumed     389
% 1.57/2.07  clauses back subsumed          8
% 1.57/2.07  Kbytes malloced             1953
% 1.57/2.07  
% 1.57/2.07  ----------- times (seconds) -----------
% 1.57/2.07  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.57/2.07  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.57/2.07  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.57/2.07  
% 1.57/2.07  That finishes the proof of the theorem.
% 1.57/2.07  
% 1.57/2.07  Process 7180 finished Wed Jul 27 07:27:55 2022
% 1.57/2.07  Otter interrupted
% 1.57/2.07  PROOF FOUND
%------------------------------------------------------------------------------