TSTP Solution File: KRS076+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : KRS076+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 13:01:05 EDT 2022

% Result   : Unsatisfiable 2.02s 2.21s
% Output   : Refutation 2.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   22 (  12 unt;   0 nHn;  22 RR)
%            Number of literals    :   35 (   4 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(21,axiom,
    ( ~ cUnsatisfiable(A)
    | rf(A,dollar_f1(A)) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ cUnsatisfiable(A)
    | cp(dollar_f1(A)) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ cUnsatisfiable(A)
    | rf1(A,dollar_f3(A)) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ cUnsatisfiable(A)
    | ~ cp(dollar_f3(A)) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ cUnsatisfiable(A)
    | ~ rinvF1(dollar_f3(A),B)
    | rs(B,dollar_f2(A,B)) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ rf(A,B)
    | ~ rf(A,C)
    | B = C ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ rf1(A,B)
    | ~ rf1(A,C)
    | B = C ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(34,axiom,
    ( rinvF1(A,B)
    | ~ rf1(B,A) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ rs(A,B)
    | rf1(A,B) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ rs(A,B)
    | rf(A,B) ),
    file('KRS076+1.p',unknown),
    [] ).

cnf(46,axiom,
    cUnsatisfiable(i2003_11_14_17_19_06193),
    file('KRS076+1.p',unknown),
    [] ).

cnf(47,plain,
    rf1(i2003_11_14_17_19_06193,dollar_f3(i2003_11_14_17_19_06193)),
    inference(hyper,[status(thm)],[46,23]),
    [iquote('hyper,46,23')] ).

cnf(48,plain,
    cp(dollar_f1(i2003_11_14_17_19_06193)),
    inference(hyper,[status(thm)],[46,22]),
    [iquote('hyper,46,22')] ).

cnf(49,plain,
    rf(i2003_11_14_17_19_06193,dollar_f1(i2003_11_14_17_19_06193)),
    inference(hyper,[status(thm)],[46,21]),
    [iquote('hyper,46,21')] ).

cnf(59,plain,
    rinvF1(dollar_f3(i2003_11_14_17_19_06193),i2003_11_14_17_19_06193),
    inference(hyper,[status(thm)],[47,34]),
    [iquote('hyper,47,34')] ).

cnf(79,plain,
    rs(i2003_11_14_17_19_06193,dollar_f2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193)),
    inference(hyper,[status(thm)],[59,25,46]),
    [iquote('hyper,59,25,46')] ).

cnf(98,plain,
    rf(i2003_11_14_17_19_06193,dollar_f2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193)),
    inference(hyper,[status(thm)],[79,39]),
    [iquote('hyper,79,39')] ).

cnf(99,plain,
    rf1(i2003_11_14_17_19_06193,dollar_f2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193)),
    inference(hyper,[status(thm)],[79,38]),
    [iquote('hyper,79,38')] ).

cnf(118,plain,
    dollar_f1(i2003_11_14_17_19_06193) = dollar_f2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193),
    inference(hyper,[status(thm)],[98,29,49]),
    [iquote('hyper,98,29,49')] ).

cnf(134,plain,
    cp(dollar_f2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),118]),
    [iquote('back_demod,48,demod,118')] ).

cnf(148,plain,
    dollar_f3(i2003_11_14_17_19_06193) = dollar_f2(i2003_11_14_17_19_06193,i2003_11_14_17_19_06193),
    inference(hyper,[status(thm)],[99,30,47]),
    [iquote('hyper,99,30,47')] ).

cnf(202,plain,
    $false,
    inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[148,24]),46,134]),
    [iquote('para_from,148.1.1,24.2.1,unit_del,46,134')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : KRS076+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 03:50:18 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 2.02/2.21  ----- Otter 3.3f, August 2004 -----
% 2.02/2.21  The process was started by sandbox2 on n023.cluster.edu,
% 2.02/2.21  Wed Jul 27 03:50:18 2022
% 2.02/2.21  The command was "./otter".  The process ID is 12714.
% 2.02/2.21  
% 2.02/2.21  set(prolog_style_variables).
% 2.02/2.21  set(auto).
% 2.02/2.21     dependent: set(auto1).
% 2.02/2.21     dependent: set(process_input).
% 2.02/2.21     dependent: clear(print_kept).
% 2.02/2.21     dependent: clear(print_new_demod).
% 2.02/2.21     dependent: clear(print_back_demod).
% 2.02/2.21     dependent: clear(print_back_sub).
% 2.02/2.21     dependent: set(control_memory).
% 2.02/2.21     dependent: assign(max_mem, 12000).
% 2.02/2.21     dependent: assign(pick_given_ratio, 4).
% 2.02/2.21     dependent: assign(stats_level, 1).
% 2.02/2.21     dependent: assign(max_seconds, 10800).
% 2.02/2.21  clear(print_given).
% 2.02/2.21  
% 2.02/2.21  formula_list(usable).
% 2.02/2.21  all A (A=A).
% 2.02/2.21  all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 2.02/2.21  all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 2.02/2.21  all A B (A=B&cowlThing(A)->cowlThing(B)).
% 2.02/2.21  all A B (A=B&cp(A)->cp(B)).
% 2.02/2.21  all A B C (A=B&rf(A,C)->rf(B,C)).
% 2.02/2.21  all A B C (A=B&rf(C,A)->rf(C,B)).
% 2.02/2.21  all A B C (A=B&rf1(A,C)->rf1(B,C)).
% 2.02/2.21  all A B C (A=B&rf1(C,A)->rf1(C,B)).
% 2.02/2.21  all A B C (A=B&rinvF(A,C)->rinvF(B,C)).
% 2.02/2.21  all A B C (A=B&rinvF(C,A)->rinvF(C,B)).
% 2.02/2.21  all A B C (A=B&rinvF1(A,C)->rinvF1(B,C)).
% 2.02/2.21  all A B C (A=B&rinvF1(C,A)->rinvF1(C,B)).
% 2.02/2.21  all A B C (A=B&rinvS(A,C)->rinvS(B,C)).
% 2.02/2.21  all A B C (A=B&rinvS(C,A)->rinvS(C,B)).
% 2.02/2.21  all A B C (A=B&rs(A,C)->rs(B,C)).
% 2.02/2.21  all A B C (A=B&rs(C,A)->rs(C,B)).
% 2.02/2.21  all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 2.02/2.21  all A B (A=B&xsd_string(A)->xsd_string(B)).
% 2.02/2.21  all X (cowlThing(X)& -cowlNothing(X)).
% 2.02/2.21  all X (xsd_string(X)<-> -xsd_integer(X)).
% 2.02/2.21  all X (cUnsatisfiable(X)<-> (exists Y (rf(X,Y)&cp(Y)))& (exists Y (rf1(X,Y)& -cp(Y)& (all Z (rinvF1(Y,Z)-> (exists W (rs(Z,W)&cowlThing(W)))))))).
% 2.02/2.21  all X Y Z (rf(X,Y)&rf(X,Z)->Y=Z).
% 2.02/2.21  all X Y Z (rf1(X,Y)&rf1(X,Z)->Y=Z).
% 2.02/2.21  all X Y (rinvF(X,Y)<->rf(Y,X)).
% 2.02/2.21  all X Y (rinvF1(X,Y)<->rf1(Y,X)).
% 2.02/2.21  all X Y (rinvS(X,Y)<->rs(Y,X)).
% 2.02/2.21  all X Y Z (rs(X,Y)&rs(X,Z)->Y=Z).
% 2.02/2.21  cUnsatisfiable(i2003_11_14_17_19_06193).
% 2.02/2.21  all X Y (rs(X,Y)->rf1(X,Y)).
% 2.02/2.21  all X Y (rs(X,Y)->rf(X,Y)).
% 2.02/2.21  end_of_list.
% 2.02/2.21  
% 2.02/2.21  -------> usable clausifies to:
% 2.02/2.21  
% 2.02/2.21  list(usable).
% 2.02/2.21  0 [] A=A.
% 2.02/2.21  0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 2.02/2.21  0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 2.02/2.21  0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 2.02/2.21  0 [] A!=B| -cp(A)|cp(B).
% 2.02/2.21  0 [] A!=B| -rf(A,C)|rf(B,C).
% 2.02/2.21  0 [] A!=B| -rf(C,A)|rf(C,B).
% 2.02/2.21  0 [] A!=B| -rf1(A,C)|rf1(B,C).
% 2.02/2.21  0 [] A!=B| -rf1(C,A)|rf1(C,B).
% 2.02/2.21  0 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 2.02/2.21  0 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 2.02/2.21  0 [] A!=B| -rinvF1(A,C)|rinvF1(B,C).
% 2.02/2.21  0 [] A!=B| -rinvF1(C,A)|rinvF1(C,B).
% 2.02/2.21  0 [] A!=B| -rinvS(A,C)|rinvS(B,C).
% 2.02/2.21  0 [] A!=B| -rinvS(C,A)|rinvS(C,B).
% 2.02/2.21  0 [] A!=B| -rs(A,C)|rs(B,C).
% 2.02/2.21  0 [] A!=B| -rs(C,A)|rs(C,B).
% 2.02/2.21  0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 2.02/2.21  0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 2.02/2.21  0 [] cowlThing(X).
% 2.02/2.21  0 [] -cowlNothing(X).
% 2.02/2.21  0 [] -xsd_string(X)| -xsd_integer(X).
% 2.02/2.21  0 [] xsd_string(X)|xsd_integer(X).
% 2.02/2.21  0 [] -cUnsatisfiable(X)|rf(X,$f1(X)).
% 2.02/2.21  0 [] -cUnsatisfiable(X)|cp($f1(X)).
% 2.02/2.21  0 [] -cUnsatisfiable(X)|rf1(X,$f3(X)).
% 2.02/2.21  0 [] -cUnsatisfiable(X)| -cp($f3(X)).
% 2.02/2.21  0 [] -cUnsatisfiable(X)| -rinvF1($f3(X),Z)|rs(Z,$f2(X,Z)).
% 2.02/2.21  0 [] -cUnsatisfiable(X)| -rinvF1($f3(X),Z)|cowlThing($f2(X,Z)).
% 2.02/2.21  0 [] cUnsatisfiable(X)| -rf(X,Y)| -cp(Y)| -rf1(X,X1)|cp(X1)|rinvF1(X1,$f4(X,X1)).
% 2.02/2.21  0 [] cUnsatisfiable(X)| -rf(X,Y)| -cp(Y)| -rf1(X,X1)|cp(X1)| -rs($f4(X,X1),W)| -cowlThing(W).
% 2.02/2.21  0 [] -rf(X,Y)| -rf(X,Z)|Y=Z.
% 2.02/2.21  0 [] -rf1(X,Y)| -rf1(X,Z)|Y=Z.
% 2.02/2.21  0 [] -rinvF(X,Y)|rf(Y,X).
% 2.02/2.21  0 [] rinvF(X,Y)| -rf(Y,X).
% 2.02/2.21  0 [] -rinvF1(X,Y)|rf1(Y,X).
% 2.02/2.21  0 [] rinvF1(X,Y)| -rf1(Y,X).
% 2.02/2.21  0 [] -rinvS(X,Y)|rs(Y,X).
% 2.02/2.21  0 [] rinvS(X,Y)| -rs(Y,X).
% 2.02/2.21  0 [] -rs(X,Y)| -rs(X,Z)|Y=Z.
% 2.02/2.21  0 [] cUnsatisfiable(i2003_11_14_17_19_06193).
% 2.02/2.21  0 [] -rs(X,Y)|rf1(X,Y).
% 2.02/2.21  0 [] -rs(X,Y)|rf(X,Y).
% 2.02/2.21  end_of_list.
% 2.02/2.21  
% 2.02/2.21  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 2.02/2.21  
% 2.02/2.21  This ia a non-Horn set with equality.  The strategy will be
% 2.02/2.21  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.02/2.21  deletion, with positive clauses in sos and nonpositive
% 2.02/2.21  clauses in usable.
% 2.02/2.21  
% 2.02/2.21     dependent: set(knuth_bendix).
% 2.02/2.21     dependent: set(anl_eq).
% 2.02/2.21     dependent: set(para_from).
% 2.02/2.21     dependent: set(para_into).
% 2.02/2.21     dependent: clear(para_from_right).
% 2.02/2.21     dependent: clear(para_into_right).
% 2.02/2.21     dependent: set(para_from_vars).
% 2.02/2.21     dependent: set(eq_units_both_ways).
% 2.02/2.21     dependent: set(dynamic_demod_all).
% 2.02/2.21     dependent: set(dynamic_demod).
% 2.02/2.21     dependent: set(order_eq).
% 2.02/2.21     dependent: set(back_demod).
% 2.02/2.21     dependent: set(lrpo).
% 2.02/2.21     dependent: set(hyper_res).
% 2.02/2.21     dependent: set(unit_deletion).
% 2.02/2.21     dependent: set(factor).
% 2.02/2.21  
% 2.02/2.21  ------------> process usable:
% 2.02/2.21  ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 2.02/2.21  ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 2.02/2.21  ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 2.02/2.21  ** KEPT (pick-wt=7): 4 [] A!=B| -cp(A)|cp(B).
% 2.02/2.21  ** KEPT (pick-wt=9): 5 [] A!=B| -rf(A,C)|rf(B,C).
% 2.02/2.21  ** KEPT (pick-wt=9): 6 [] A!=B| -rf(C,A)|rf(C,B).
% 2.02/2.21  ** KEPT (pick-wt=9): 7 [] A!=B| -rf1(A,C)|rf1(B,C).
% 2.02/2.21  ** KEPT (pick-wt=9): 8 [] A!=B| -rf1(C,A)|rf1(C,B).
% 2.02/2.21  ** KEPT (pick-wt=9): 9 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 2.02/2.21  ** KEPT (pick-wt=9): 10 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 2.02/2.21  ** KEPT (pick-wt=9): 11 [] A!=B| -rinvF1(A,C)|rinvF1(B,C).
% 2.02/2.21  ** KEPT (pick-wt=9): 12 [] A!=B| -rinvF1(C,A)|rinvF1(C,B).
% 2.02/2.21  ** KEPT (pick-wt=9): 13 [] A!=B| -rinvS(A,C)|rinvS(B,C).
% 2.02/2.21  ** KEPT (pick-wt=9): 14 [] A!=B| -rinvS(C,A)|rinvS(C,B).
% 2.02/2.21  ** KEPT (pick-wt=9): 15 [] A!=B| -rs(A,C)|rs(B,C).
% 2.02/2.21  ** KEPT (pick-wt=9): 16 [] A!=B| -rs(C,A)|rs(C,B).
% 2.02/2.21  ** KEPT (pick-wt=7): 17 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 2.02/2.21  ** KEPT (pick-wt=7): 18 [] A!=B| -xsd_string(A)|xsd_string(B).
% 2.02/2.21  ** KEPT (pick-wt=2): 19 [] -cowlNothing(A).
% 2.02/2.21  ** KEPT (pick-wt=4): 20 [] -xsd_string(A)| -xsd_integer(A).
% 2.02/2.21  ** KEPT (pick-wt=6): 21 [] -cUnsatisfiable(A)|rf(A,$f1(A)).
% 2.02/2.21  ** KEPT (pick-wt=5): 22 [] -cUnsatisfiable(A)|cp($f1(A)).
% 2.02/2.21  ** KEPT (pick-wt=6): 23 [] -cUnsatisfiable(A)|rf1(A,$f3(A)).
% 2.02/2.21  ** KEPT (pick-wt=5): 24 [] -cUnsatisfiable(A)| -cp($f3(A)).
% 2.02/2.21  ** KEPT (pick-wt=11): 25 [] -cUnsatisfiable(A)| -rinvF1($f3(A),B)|rs(B,$f2(A,B)).
% 2.02/2.21  ** KEPT (pick-wt=10): 26 [] -cUnsatisfiable(A)| -rinvF1($f3(A),B)|cowlThing($f2(A,B)).
% 2.02/2.21  ** KEPT (pick-wt=17): 27 [] cUnsatisfiable(A)| -rf(A,B)| -cp(B)| -rf1(A,C)|cp(C)|rinvF1(C,$f4(A,C)).
% 2.02/2.21  ** KEPT (pick-wt=19): 28 [] cUnsatisfiable(A)| -rf(A,B)| -cp(B)| -rf1(A,C)|cp(C)| -rs($f4(A,C),D)| -cowlThing(D).
% 2.02/2.21  ** KEPT (pick-wt=9): 29 [] -rf(A,B)| -rf(A,C)|B=C.
% 2.02/2.21  ** KEPT (pick-wt=9): 30 [] -rf1(A,B)| -rf1(A,C)|B=C.
% 2.02/2.21  ** KEPT (pick-wt=6): 31 [] -rinvF(A,B)|rf(B,A).
% 2.02/2.21  ** KEPT (pick-wt=6): 32 [] rinvF(A,B)| -rf(B,A).
% 2.02/2.21  ** KEPT (pick-wt=6): 33 [] -rinvF1(A,B)|rf1(B,A).
% 2.02/2.21  ** KEPT (pick-wt=6): 34 [] rinvF1(A,B)| -rf1(B,A).
% 2.02/2.21  ** KEPT (pick-wt=6): 35 [] -rinvS(A,B)|rs(B,A).
% 2.02/2.21  ** KEPT (pick-wt=6): 36 [] rinvS(A,B)| -rs(B,A).
% 2.02/2.21  ** KEPT (pick-wt=9): 37 [] -rs(A,B)| -rs(A,C)|B=C.
% 2.02/2.21  ** KEPT (pick-wt=6): 38 [] -rs(A,B)|rf1(A,B).
% 2.02/2.21  ** KEPT (pick-wt=6): 39 [] -rs(A,B)|rf(A,B).
% 2.02/2.21  19 back subsumes 2.
% 2.02/2.21  
% 2.02/2.21  ------------> process sos:
% 2.02/2.21  ** KEPT (pick-wt=3): 43 [] A=A.
% 2.02/2.21  ** KEPT (pick-wt=2): 44 [] cowlThing(A).
% 2.02/2.21  ** KEPT (pick-wt=4): 45 [] xsd_string(A)|xsd_integer(A).
% 2.02/2.21  ** KEPT (pick-wt=2): 46 [] cUnsatisfiable(i2003_11_14_17_19_06193).
% 2.02/2.21    Following clause subsumed by 43 during input processing: 0 [copy,43,flip.1] A=A.
% 2.02/2.21  43 back subsumes 42.
% 2.02/2.21  43 back subsumes 41.
% 2.02/2.21  43 back subsumes 40.
% 2.02/2.21  44 back subsumes 26.
% 2.02/2.21  44 back subsumes 3.
% 2.02/2.21  
% 2.02/2.21  ======= end of input processing =======
% 2.02/2.21  
% 2.02/2.21  =========== start of search ===========
% 2.02/2.21  
% 2.02/2.21  -------- PROOF -------- 
% 2.02/2.21  
% 2.02/2.21  -----> EMPTY CLAUSE at   0.01 sec ----> 202 [para_from,148.1.1,24.2.1,unit_del,46,134] $F.
% 2.02/2.21  
% 2.02/2.21  Length of proof is 10.  Level of proof is 6.
% 2.02/2.21  
% 2.02/2.21  ---------------- PROOF ----------------
% 2.02/2.21  % SZS status Theorem
% 2.02/2.21  % SZS output start Refutation
% See solution above
% 2.02/2.21  ------------ end of proof -------------
% 2.02/2.21  
% 2.02/2.21  
% 2.02/2.21  Search stopped by max_proofs option.
% 2.02/2.21  
% 2.02/2.21  
% 2.02/2.21  Search stopped by max_proofs option.
% 2.02/2.21  
% 2.02/2.21  ============ end of search ============
% 2.02/2.21  
% 2.02/2.21  -------------- statistics -------------
% 2.02/2.21  clauses given                 20
% 2.02/2.21  clauses generated            366
% 2.02/2.21  clauses kept                 199
% 2.02/2.21  clauses forward subsumed     242
% 2.02/2.21  clauses back subsumed          6
% 2.02/2.21  Kbytes malloced              976
% 2.02/2.21  
% 2.02/2.21  ----------- times (seconds) -----------
% 2.02/2.21  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 2.02/2.21  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.02/2.21  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.02/2.21  
% 2.02/2.21  That finishes the proof of the theorem.
% 2.02/2.21  
% 2.02/2.21  Process 12714 finished Wed Jul 27 03:50:20 2022
% 2.02/2.21  Otter interrupted
% 2.02/2.21  PROOF FOUND
%------------------------------------------------------------------------------