TSTP Solution File: GRA008+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GRA008+1 : TPTP v5.0.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 09:56:35 EST 2010

% Result   : Theorem 7.25s
% Output   : CNFRefutation 7.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   89
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  336 (  24 unt;   0 def)
%            Number of atoms       : 1568 ( 662 equ)
%            Maximal formula atoms :   37 (   4 avg)
%            Number of connectives : 1946 ( 714   ~;1041   |; 161   &)
%                                         (   7 <=>;  20  =>;   1  <=;   2 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   4 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-5 aty)
%            Number of variables   :  508 (  41 sgn 190   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( edge(X1)
     => ( vertex(head_of(X1))
        & vertex(tail_of(X1)) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',edge_ends_are_vertices) ).

fof(2,axiom,
    ! [X2,X3] :
      ( sequential(X2,X3)
    <=> ( edge(X2)
        & edge(X3)
        & X2 != X3
        & head_of(X2) = tail_of(X3) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',sequential_defn) ).

fof(3,axiom,
    ! [X1] :
      ( edge(X1)
     => head_of(X1) != tail_of(X1) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',no_loops) ).

fof(4,axiom,
    ! [X4,X5,X6] :
      ( shortest_path(X4,X5,X6)
    <=> ( path(X4,X5,X6)
        & X4 != X5
        & ! [X7] :
            ( path(X4,X5,X7)
           => less_or_equal(length_of(X6),length_of(X7)) ) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',shortest_path_defn) ).

fof(5,axiom,
    ( complete
   => ! [X4,X5] :
        ( ( vertex(X4)
          & vertex(X5)
          & X4 != X5 )
       => ? [X1] :
            ( edge(X1)
            & ( ( X4 = head_of(X1)
                & X5 = tail_of(X1) )
            <~> ( X5 = head_of(X1)
                & X4 = tail_of(X1) ) ) ) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',complete_properties) ).

fof(6,axiom,
    ! [X7,X4,X5] :
      ( path(X4,X5,X7)
     => ! [X2,X3] :
          ( precedes(X2,X3,X7)
         => ( on_path(X2,X7)
            & on_path(X3,X7)
            & ( sequential(X2,X3)
            <~> ? [X8] :
                  ( sequential(X2,X8)
                  & precedes(X8,X3,X7) ) ) ) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',precedes_properties) ).

fof(7,axiom,
    ! [X4,X5,X2,X3,X7] :
      ( ( shortest_path(X4,X5,X7)
        & precedes(X2,X3,X7) )
     => ( ~ ? [X8] :
              ( tail_of(X8) = tail_of(X2)
              & head_of(X8) = head_of(X3) )
        & ~ precedes(X3,X2,X7) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',shortest_path_properties) ).

fof(8,axiom,
    ! [X7,X4,X5] :
      ( path(X4,X5,X7)
     => ! [X2,X3] :
          ( precedes(X2,X3,X7)
         <= ( on_path(X2,X7)
            & on_path(X3,X7)
            & ( sequential(X2,X3)
              | ? [X8] :
                  ( sequential(X2,X8)
                  & precedes(X8,X3,X7) ) ) ) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',precedes_defn) ).

fof(13,conjecture,
    ( complete
   => ! [X4,X5,X2,X3,X7] :
        ( ( shortest_path(X4,X5,X7)
          & precedes(X2,X3,X7)
          & sequential(X2,X3) )
       => ? [X8] : triangle(X2,X3,X8) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',sequential_is_triangle) ).

fof(14,axiom,
    ! [X2,X3,X8] :
      ( triangle(X2,X3,X8)
    <=> ( edge(X2)
        & edge(X3)
        & edge(X8)
        & sequential(X2,X3)
        & sequential(X3,X8)
        & sequential(X8,X2) ) ),
    file('/tmp/tmp2znHc3/sel_GRA008+1.p_1',triangle_defn) ).

fof(15,negated_conjecture,
    ~ ( complete
     => ! [X4,X5,X2,X3,X7] :
          ( ( shortest_path(X4,X5,X7)
            & precedes(X2,X3,X7)
            & sequential(X2,X3) )
         => ? [X8] : triangle(X2,X3,X8) ) ),
    inference(assume_negation,[status(cth)],[13]) ).

fof(16,plain,
    ( complete
   => ! [X4,X5] :
        ( ( vertex(X4)
          & vertex(X5)
          & X4 != X5 )
       => ? [X1] :
            ( edge(X1)
            & ~ ( ( X4 = head_of(X1)
                  & X5 = tail_of(X1) )
              <=> ( X5 = head_of(X1)
                  & X4 = tail_of(X1) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).

fof(17,plain,
    ! [X7,X4,X5] :
      ( path(X4,X5,X7)
     => ! [X2,X3] :
          ( precedes(X2,X3,X7)
         => ( on_path(X2,X7)
            & on_path(X3,X7)
            & ~ ( sequential(X2,X3)
              <=> ? [X8] :
                    ( sequential(X2,X8)
                    & precedes(X8,X3,X7) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(18,plain,
    ! [X4,X5,X2,X3,X7] :
      ( ( shortest_path(X4,X5,X7)
        & precedes(X2,X3,X7) )
     => ( ~ ? [X8] :
              ( tail_of(X8) = tail_of(X2)
              & head_of(X8) = head_of(X3) )
        & ~ precedes(X3,X2,X7) ) ),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(19,plain,
    ! [X7,X4,X5] :
      ( path(X4,X5,X7)
     => ! [X2,X3] :
          ( ( on_path(X2,X7)
            & on_path(X3,X7)
            & ( sequential(X2,X3)
              | ? [X8] :
                  ( sequential(X2,X8)
                  & precedes(X8,X3,X7) ) ) )
         => precedes(X2,X3,X7) ) ),
    inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).

fof(20,plain,
    ! [X1] :
      ( ~ edge(X1)
      | ( vertex(head_of(X1))
        & vertex(tail_of(X1)) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(21,plain,
    ! [X2] :
      ( ~ edge(X2)
      | ( vertex(head_of(X2))
        & vertex(tail_of(X2)) ) ),
    inference(variable_rename,[status(thm)],[20]) ).

fof(22,plain,
    ! [X2] :
      ( ( vertex(head_of(X2))
        | ~ edge(X2) )
      & ( vertex(tail_of(X2))
        | ~ edge(X2) ) ),
    inference(distribute,[status(thm)],[21]) ).

cnf(23,plain,
    ( vertex(tail_of(X1))
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(24,plain,
    ( vertex(head_of(X1))
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(25,plain,
    ! [X2,X3] :
      ( ( ~ sequential(X2,X3)
        | ( edge(X2)
          & edge(X3)
          & X2 != X3
          & head_of(X2) = tail_of(X3) ) )
      & ( ~ edge(X2)
        | ~ edge(X3)
        | X2 = X3
        | head_of(X2) != tail_of(X3)
        | sequential(X2,X3) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(26,plain,
    ! [X4,X5] :
      ( ( ~ sequential(X4,X5)
        | ( edge(X4)
          & edge(X5)
          & X4 != X5
          & head_of(X4) = tail_of(X5) ) )
      & ( ~ edge(X4)
        | ~ edge(X5)
        | X4 = X5
        | head_of(X4) != tail_of(X5)
        | sequential(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[25]) ).

fof(27,plain,
    ! [X4,X5] :
      ( ( edge(X4)
        | ~ sequential(X4,X5) )
      & ( edge(X5)
        | ~ sequential(X4,X5) )
      & ( X4 != X5
        | ~ sequential(X4,X5) )
      & ( head_of(X4) = tail_of(X5)
        | ~ sequential(X4,X5) )
      & ( ~ edge(X4)
        | ~ edge(X5)
        | X4 = X5
        | head_of(X4) != tail_of(X5)
        | sequential(X4,X5) ) ),
    inference(distribute,[status(thm)],[26]) ).

cnf(28,plain,
    ( sequential(X1,X2)
    | X1 = X2
    | head_of(X1) != tail_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(29,plain,
    ( head_of(X1) = tail_of(X2)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(30,plain,
    ( ~ sequential(X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(31,plain,
    ( edge(X2)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(32,plain,
    ( edge(X1)
    | ~ sequential(X1,X2) ),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(33,plain,
    ! [X1] :
      ( ~ edge(X1)
      | head_of(X1) != tail_of(X1) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(34,plain,
    ! [X2] :
      ( ~ edge(X2)
      | head_of(X2) != tail_of(X2) ),
    inference(variable_rename,[status(thm)],[33]) ).

cnf(35,plain,
    ( head_of(X1) != tail_of(X1)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(36,plain,
    ! [X4,X5,X6] :
      ( ( ~ shortest_path(X4,X5,X6)
        | ( path(X4,X5,X6)
          & X4 != X5
          & ! [X7] :
              ( ~ path(X4,X5,X7)
              | less_or_equal(length_of(X6),length_of(X7)) ) ) )
      & ( ~ path(X4,X5,X6)
        | X4 = X5
        | ? [X7] :
            ( path(X4,X5,X7)
            & ~ less_or_equal(length_of(X6),length_of(X7)) )
        | shortest_path(X4,X5,X6) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(37,plain,
    ! [X8,X9,X10] :
      ( ( ~ shortest_path(X8,X9,X10)
        | ( path(X8,X9,X10)
          & X8 != X9
          & ! [X11] :
              ( ~ path(X8,X9,X11)
              | less_or_equal(length_of(X10),length_of(X11)) ) ) )
      & ( ~ path(X8,X9,X10)
        | X8 = X9
        | ? [X12] :
            ( path(X8,X9,X12)
            & ~ less_or_equal(length_of(X10),length_of(X12)) )
        | shortest_path(X8,X9,X10) ) ),
    inference(variable_rename,[status(thm)],[36]) ).

fof(38,plain,
    ! [X8,X9,X10] :
      ( ( ~ shortest_path(X8,X9,X10)
        | ( path(X8,X9,X10)
          & X8 != X9
          & ! [X11] :
              ( ~ path(X8,X9,X11)
              | less_or_equal(length_of(X10),length_of(X11)) ) ) )
      & ( ~ path(X8,X9,X10)
        | X8 = X9
        | ( path(X8,X9,esk1_3(X8,X9,X10))
          & ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10))) )
        | shortest_path(X8,X9,X10) ) ),
    inference(skolemize,[status(esa)],[37]) ).

fof(39,plain,
    ! [X8,X9,X10,X11] :
      ( ( ( ( ~ path(X8,X9,X11)
            | less_or_equal(length_of(X10),length_of(X11)) )
          & path(X8,X9,X10)
          & X8 != X9 )
        | ~ shortest_path(X8,X9,X10) )
      & ( ~ path(X8,X9,X10)
        | X8 = X9
        | ( path(X8,X9,esk1_3(X8,X9,X10))
          & ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10))) )
        | shortest_path(X8,X9,X10) ) ),
    inference(shift_quantors,[status(thm)],[38]) ).

fof(40,plain,
    ! [X8,X9,X10,X11] :
      ( ( ~ path(X8,X9,X11)
        | less_or_equal(length_of(X10),length_of(X11))
        | ~ shortest_path(X8,X9,X10) )
      & ( path(X8,X9,X10)
        | ~ shortest_path(X8,X9,X10) )
      & ( X8 != X9
        | ~ shortest_path(X8,X9,X10) )
      & ( path(X8,X9,esk1_3(X8,X9,X10))
        | ~ path(X8,X9,X10)
        | X8 = X9
        | shortest_path(X8,X9,X10) )
      & ( ~ less_or_equal(length_of(X10),length_of(esk1_3(X8,X9,X10)))
        | ~ path(X8,X9,X10)
        | X8 = X9
        | shortest_path(X8,X9,X10) ) ),
    inference(distribute,[status(thm)],[39]) ).

cnf(44,plain,
    ( path(X1,X2,X3)
    | ~ shortest_path(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(46,plain,
    ( ~ complete
    | ! [X4,X5] :
        ( ~ vertex(X4)
        | ~ vertex(X5)
        | X4 = X5
        | ? [X1] :
            ( edge(X1)
            & ( X4 != head_of(X1)
              | X5 != tail_of(X1)
              | X5 != head_of(X1)
              | X4 != tail_of(X1) )
            & ( ( X4 = head_of(X1)
                & X5 = tail_of(X1) )
              | ( X5 = head_of(X1)
                & X4 = tail_of(X1) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(47,plain,
    ( ~ complete
    | ! [X6,X7] :
        ( ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ? [X8] :
            ( edge(X8)
            & ( X6 != head_of(X8)
              | X7 != tail_of(X8)
              | X7 != head_of(X8)
              | X6 != tail_of(X8) )
            & ( ( X6 = head_of(X8)
                & X7 = tail_of(X8) )
              | ( X7 = head_of(X8)
                & X6 = tail_of(X8) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,plain,
    ( ~ complete
    | ! [X6,X7] :
        ( ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ( edge(esk2_2(X6,X7))
          & ( X6 != head_of(esk2_2(X6,X7))
            | X7 != tail_of(esk2_2(X6,X7))
            | X7 != head_of(esk2_2(X6,X7))
            | X6 != tail_of(esk2_2(X6,X7)) )
          & ( ( X6 = head_of(esk2_2(X6,X7))
              & X7 = tail_of(esk2_2(X6,X7)) )
            | ( X7 = head_of(esk2_2(X6,X7))
              & X6 = tail_of(esk2_2(X6,X7)) ) ) ) ) ),
    inference(skolemize,[status(esa)],[47]) ).

fof(49,plain,
    ! [X6,X7] :
      ( ~ vertex(X6)
      | ~ vertex(X7)
      | X6 = X7
      | ( edge(esk2_2(X6,X7))
        & ( X6 != head_of(esk2_2(X6,X7))
          | X7 != tail_of(esk2_2(X6,X7))
          | X7 != head_of(esk2_2(X6,X7))
          | X6 != tail_of(esk2_2(X6,X7)) )
        & ( ( X6 = head_of(esk2_2(X6,X7))
            & X7 = tail_of(esk2_2(X6,X7)) )
          | ( X7 = head_of(esk2_2(X6,X7))
            & X6 = tail_of(esk2_2(X6,X7)) ) ) )
      | ~ complete ),
    inference(shift_quantors,[status(thm)],[48]) ).

fof(50,plain,
    ! [X6,X7] :
      ( ( edge(esk2_2(X6,X7))
        | ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ~ complete )
      & ( X6 != head_of(esk2_2(X6,X7))
        | X7 != tail_of(esk2_2(X6,X7))
        | X7 != head_of(esk2_2(X6,X7))
        | X6 != tail_of(esk2_2(X6,X7))
        | ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ~ complete )
      & ( X7 = head_of(esk2_2(X6,X7))
        | X6 = head_of(esk2_2(X6,X7))
        | ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ~ complete )
      & ( X6 = tail_of(esk2_2(X6,X7))
        | X6 = head_of(esk2_2(X6,X7))
        | ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ~ complete )
      & ( X7 = head_of(esk2_2(X6,X7))
        | X7 = tail_of(esk2_2(X6,X7))
        | ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ~ complete )
      & ( X6 = tail_of(esk2_2(X6,X7))
        | X7 = tail_of(esk2_2(X6,X7))
        | ~ vertex(X6)
        | ~ vertex(X7)
        | X6 = X7
        | ~ complete ) ),
    inference(distribute,[status(thm)],[49]) ).

cnf(51,plain,
    ( X1 = X2
    | X2 = tail_of(esk2_2(X1,X2))
    | X1 = tail_of(esk2_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(52,plain,
    ( X1 = X2
    | X2 = tail_of(esk2_2(X1,X2))
    | X2 = head_of(esk2_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(53,plain,
    ( X1 = X2
    | X1 = head_of(esk2_2(X1,X2))
    | X1 = tail_of(esk2_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(54,plain,
    ( X1 = X2
    | X1 = head_of(esk2_2(X1,X2))
    | X2 = head_of(esk2_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(56,plain,
    ( X1 = X2
    | edge(esk2_2(X1,X2))
    | ~ complete
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(57,plain,
    ! [X7,X4,X5] :
      ( ~ path(X4,X5,X7)
      | ! [X2,X3] :
          ( ~ precedes(X2,X3,X7)
          | ( on_path(X2,X7)
            & on_path(X3,X7)
            & ( ~ sequential(X2,X3)
              | ! [X8] :
                  ( ~ sequential(X2,X8)
                  | ~ precedes(X8,X3,X7) ) )
            & ( sequential(X2,X3)
              | ? [X8] :
                  ( sequential(X2,X8)
                  & precedes(X8,X3,X7) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(58,plain,
    ! [X9,X10,X11] :
      ( ~ path(X10,X11,X9)
      | ! [X12,X13] :
          ( ~ precedes(X12,X13,X9)
          | ( on_path(X12,X9)
            & on_path(X13,X9)
            & ( ~ sequential(X12,X13)
              | ! [X14] :
                  ( ~ sequential(X12,X14)
                  | ~ precedes(X14,X13,X9) ) )
            & ( sequential(X12,X13)
              | ? [X15] :
                  ( sequential(X12,X15)
                  & precedes(X15,X13,X9) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[57]) ).

fof(59,plain,
    ! [X9,X10,X11] :
      ( ~ path(X10,X11,X9)
      | ! [X12,X13] :
          ( ~ precedes(X12,X13,X9)
          | ( on_path(X12,X9)
            & on_path(X13,X9)
            & ( ~ sequential(X12,X13)
              | ! [X14] :
                  ( ~ sequential(X12,X14)
                  | ~ precedes(X14,X13,X9) ) )
            & ( sequential(X12,X13)
              | ( sequential(X12,esk3_5(X9,X10,X11,X12,X13))
                & precedes(esk3_5(X9,X10,X11,X12,X13),X13,X9) ) ) ) ) ),
    inference(skolemize,[status(esa)],[58]) ).

fof(60,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ( ~ sequential(X12,X14)
          | ~ precedes(X14,X13,X9)
          | ~ sequential(X12,X13) )
        & ( sequential(X12,X13)
          | ( sequential(X12,esk3_5(X9,X10,X11,X12,X13))
            & precedes(esk3_5(X9,X10,X11,X12,X13),X13,X9) ) )
        & on_path(X12,X9)
        & on_path(X13,X9) )
      | ~ precedes(X12,X13,X9)
      | ~ path(X10,X11,X9) ),
    inference(shift_quantors,[status(thm)],[59]) ).

fof(61,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ~ sequential(X12,X14)
        | ~ precedes(X14,X13,X9)
        | ~ sequential(X12,X13)
        | ~ precedes(X12,X13,X9)
        | ~ path(X10,X11,X9) )
      & ( sequential(X12,esk3_5(X9,X10,X11,X12,X13))
        | sequential(X12,X13)
        | ~ precedes(X12,X13,X9)
        | ~ path(X10,X11,X9) )
      & ( precedes(esk3_5(X9,X10,X11,X12,X13),X13,X9)
        | sequential(X12,X13)
        | ~ precedes(X12,X13,X9)
        | ~ path(X10,X11,X9) )
      & ( on_path(X12,X9)
        | ~ precedes(X12,X13,X9)
        | ~ path(X10,X11,X9) )
      & ( on_path(X13,X9)
        | ~ precedes(X12,X13,X9)
        | ~ path(X10,X11,X9) ) ),
    inference(distribute,[status(thm)],[60]) ).

cnf(62,plain,
    ( on_path(X5,X3)
    | ~ path(X1,X2,X3)
    | ~ precedes(X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(63,plain,
    ( on_path(X4,X3)
    | ~ path(X1,X2,X3)
    | ~ precedes(X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(64,plain,
    ( sequential(X4,X5)
    | precedes(esk3_5(X3,X1,X2,X4,X5),X5,X3)
    | ~ path(X1,X2,X3)
    | ~ precedes(X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(65,plain,
    ( sequential(X4,X5)
    | sequential(X4,esk3_5(X3,X1,X2,X4,X5))
    | ~ path(X1,X2,X3)
    | ~ precedes(X4,X5,X3) ),
    inference(split_conjunct,[status(thm)],[61]) ).

fof(67,plain,
    ! [X4,X5,X2,X3,X7] :
      ( ~ shortest_path(X4,X5,X7)
      | ~ precedes(X2,X3,X7)
      | ( ! [X8] :
            ( tail_of(X8) != tail_of(X2)
            | head_of(X8) != head_of(X3) )
        & ~ precedes(X3,X2,X7) ) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(68,plain,
    ! [X9,X10,X11,X12,X13] :
      ( ~ shortest_path(X9,X10,X13)
      | ~ precedes(X11,X12,X13)
      | ( ! [X14] :
            ( tail_of(X14) != tail_of(X11)
            | head_of(X14) != head_of(X12) )
        & ~ precedes(X12,X11,X13) ) ),
    inference(variable_rename,[status(thm)],[67]) ).

fof(69,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ( tail_of(X14) != tail_of(X11)
          | head_of(X14) != head_of(X12) )
        & ~ precedes(X12,X11,X13) )
      | ~ shortest_path(X9,X10,X13)
      | ~ precedes(X11,X12,X13) ),
    inference(shift_quantors,[status(thm)],[68]) ).

fof(70,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( tail_of(X14) != tail_of(X11)
        | head_of(X14) != head_of(X12)
        | ~ shortest_path(X9,X10,X13)
        | ~ precedes(X11,X12,X13) )
      & ( ~ precedes(X12,X11,X13)
        | ~ shortest_path(X9,X10,X13)
        | ~ precedes(X11,X12,X13) ) ),
    inference(distribute,[status(thm)],[69]) ).

cnf(71,plain,
    ( ~ precedes(X1,X2,X3)
    | ~ shortest_path(X4,X5,X3)
    | ~ precedes(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[70]) ).

cnf(72,plain,
    ( ~ precedes(X1,X2,X3)
    | ~ shortest_path(X4,X5,X3)
    | head_of(X6) != head_of(X2)
    | tail_of(X6) != tail_of(X1) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(73,plain,
    ! [X7,X4,X5] :
      ( ~ path(X4,X5,X7)
      | ! [X2,X3] :
          ( ~ on_path(X2,X7)
          | ~ on_path(X3,X7)
          | ( ~ sequential(X2,X3)
            & ! [X8] :
                ( ~ sequential(X2,X8)
                | ~ precedes(X8,X3,X7) ) )
          | precedes(X2,X3,X7) ) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(74,plain,
    ! [X9,X10,X11] :
      ( ~ path(X10,X11,X9)
      | ! [X12,X13] :
          ( ~ on_path(X12,X9)
          | ~ on_path(X13,X9)
          | ( ~ sequential(X12,X13)
            & ! [X14] :
                ( ~ sequential(X12,X14)
                | ~ precedes(X14,X13,X9) ) )
          | precedes(X12,X13,X9) ) ),
    inference(variable_rename,[status(thm)],[73]) ).

fof(75,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ( ~ sequential(X12,X14)
          | ~ precedes(X14,X13,X9) )
        & ~ sequential(X12,X13) )
      | ~ on_path(X12,X9)
      | ~ on_path(X13,X9)
      | precedes(X12,X13,X9)
      | ~ path(X10,X11,X9) ),
    inference(shift_quantors,[status(thm)],[74]) ).

fof(76,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ~ sequential(X12,X14)
        | ~ precedes(X14,X13,X9)
        | ~ on_path(X12,X9)
        | ~ on_path(X13,X9)
        | precedes(X12,X13,X9)
        | ~ path(X10,X11,X9) )
      & ( ~ sequential(X12,X13)
        | ~ on_path(X12,X9)
        | ~ on_path(X13,X9)
        | precedes(X12,X13,X9)
        | ~ path(X10,X11,X9) ) ),
    inference(distribute,[status(thm)],[75]) ).

cnf(77,plain,
    ( precedes(X4,X5,X3)
    | ~ path(X1,X2,X3)
    | ~ on_path(X5,X3)
    | ~ on_path(X4,X3)
    | ~ sequential(X4,X5) ),
    inference(split_conjunct,[status(thm)],[76]) ).

cnf(78,plain,
    ( precedes(X4,X5,X3)
    | ~ path(X1,X2,X3)
    | ~ on_path(X5,X3)
    | ~ on_path(X4,X3)
    | ~ precedes(X6,X5,X3)
    | ~ sequential(X4,X6) ),
    inference(split_conjunct,[status(thm)],[76]) ).

fof(96,negated_conjecture,
    ( complete
    & ? [X4,X5,X2,X3,X7] :
        ( shortest_path(X4,X5,X7)
        & precedes(X2,X3,X7)
        & sequential(X2,X3)
        & ! [X8] : ~ triangle(X2,X3,X8) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(97,negated_conjecture,
    ( complete
    & ? [X9,X10,X11,X12,X13] :
        ( shortest_path(X9,X10,X13)
        & precedes(X11,X12,X13)
        & sequential(X11,X12)
        & ! [X14] : ~ triangle(X11,X12,X14) ) ),
    inference(variable_rename,[status(thm)],[96]) ).

fof(98,negated_conjecture,
    ( complete
    & shortest_path(esk6_0,esk7_0,esk10_0)
    & precedes(esk8_0,esk9_0,esk10_0)
    & sequential(esk8_0,esk9_0)
    & ! [X14] : ~ triangle(esk8_0,esk9_0,X14) ),
    inference(skolemize,[status(esa)],[97]) ).

fof(99,negated_conjecture,
    ! [X14] :
      ( ~ triangle(esk8_0,esk9_0,X14)
      & shortest_path(esk6_0,esk7_0,esk10_0)
      & precedes(esk8_0,esk9_0,esk10_0)
      & sequential(esk8_0,esk9_0)
      & complete ),
    inference(shift_quantors,[status(thm)],[98]) ).

cnf(100,negated_conjecture,
    complete,
    inference(split_conjunct,[status(thm)],[99]) ).

cnf(101,negated_conjecture,
    sequential(esk8_0,esk9_0),
    inference(split_conjunct,[status(thm)],[99]) ).

cnf(102,negated_conjecture,
    precedes(esk8_0,esk9_0,esk10_0),
    inference(split_conjunct,[status(thm)],[99]) ).

cnf(103,negated_conjecture,
    shortest_path(esk6_0,esk7_0,esk10_0),
    inference(split_conjunct,[status(thm)],[99]) ).

cnf(104,negated_conjecture,
    ~ triangle(esk8_0,esk9_0,X1),
    inference(split_conjunct,[status(thm)],[99]) ).

fof(105,plain,
    ! [X2,X3,X8] :
      ( ( ~ triangle(X2,X3,X8)
        | ( edge(X2)
          & edge(X3)
          & edge(X8)
          & sequential(X2,X3)
          & sequential(X3,X8)
          & sequential(X8,X2) ) )
      & ( ~ edge(X2)
        | ~ edge(X3)
        | ~ edge(X8)
        | ~ sequential(X2,X3)
        | ~ sequential(X3,X8)
        | ~ sequential(X8,X2)
        | triangle(X2,X3,X8) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(106,plain,
    ! [X9,X10,X11] :
      ( ( ~ triangle(X9,X10,X11)
        | ( edge(X9)
          & edge(X10)
          & edge(X11)
          & sequential(X9,X10)
          & sequential(X10,X11)
          & sequential(X11,X9) ) )
      & ( ~ edge(X9)
        | ~ edge(X10)
        | ~ edge(X11)
        | ~ sequential(X9,X10)
        | ~ sequential(X10,X11)
        | ~ sequential(X11,X9)
        | triangle(X9,X10,X11) ) ),
    inference(variable_rename,[status(thm)],[105]) ).

fof(107,plain,
    ! [X9,X10,X11] :
      ( ( edge(X9)
        | ~ triangle(X9,X10,X11) )
      & ( edge(X10)
        | ~ triangle(X9,X10,X11) )
      & ( edge(X11)
        | ~ triangle(X9,X10,X11) )
      & ( sequential(X9,X10)
        | ~ triangle(X9,X10,X11) )
      & ( sequential(X10,X11)
        | ~ triangle(X9,X10,X11) )
      & ( sequential(X11,X9)
        | ~ triangle(X9,X10,X11) )
      & ( ~ edge(X9)
        | ~ edge(X10)
        | ~ edge(X11)
        | ~ sequential(X9,X10)
        | ~ sequential(X10,X11)
        | ~ sequential(X11,X9)
        | triangle(X9,X10,X11) ) ),
    inference(distribute,[status(thm)],[106]) ).

cnf(108,plain,
    ( triangle(X1,X2,X3)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2)
    | ~ edge(X3)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(split_conjunct,[status(thm)],[107]) ).

cnf(115,negated_conjecture,
    edge(esk9_0),
    inference(spm,[status(thm)],[31,101,theory(equality)]) ).

cnf(116,negated_conjecture,
    edge(esk8_0),
    inference(spm,[status(thm)],[32,101,theory(equality)]) ).

cnf(117,plain,
    ~ sequential(X1,X1),
    inference(er,[status(thm)],[30,theory(equality)]) ).

cnf(119,negated_conjecture,
    tail_of(esk9_0) = head_of(esk8_0),
    inference(spm,[status(thm)],[29,101,theory(equality)]) ).

cnf(120,negated_conjecture,
    path(esk6_0,esk7_0,esk10_0),
    inference(spm,[status(thm)],[44,103,theory(equality)]) ).

cnf(122,negated_conjecture,
    ( on_path(esk9_0,esk10_0)
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[62,102,theory(equality)]) ).

cnf(124,plain,
    ( X1 = X2
    | edge(esk2_2(X1,X2))
    | $false
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(rw,[status(thm)],[56,100,theory(equality)]) ).

cnf(125,plain,
    ( X1 = X2
    | edge(esk2_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[124,theory(equality)]) ).

cnf(127,negated_conjecture,
    ( head_of(esk9_0) != head_of(X1)
    | tail_of(esk8_0) != tail_of(X1)
    | ~ shortest_path(X2,X3,esk10_0) ),
    inference(spm,[status(thm)],[72,102,theory(equality)]) ).

cnf(128,plain,
    ( edge(esk3_5(X1,X2,X3,X4,X5))
    | sequential(X4,X5)
    | ~ precedes(X4,X5,X1)
    | ~ path(X2,X3,X1) ),
    inference(spm,[status(thm)],[31,65,theory(equality)]) ).

cnf(130,plain,
    ( tail_of(esk3_5(X1,X2,X3,X4,X5)) = head_of(X4)
    | sequential(X4,X5)
    | ~ precedes(X4,X5,X1)
    | ~ path(X2,X3,X1) ),
    inference(spm,[status(thm)],[29,65,theory(equality)]) ).

cnf(131,plain,
    ( triangle(X1,X2,X3)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2)
    | ~ edge(X3)
    | ~ edge(X2) ),
    inference(csr,[status(thm)],[108,32]) ).

cnf(132,plain,
    ( triangle(X1,X2,X3)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2)
    | ~ edge(X3) ),
    inference(csr,[status(thm)],[131,32]) ).

cnf(133,plain,
    ( triangle(X1,X2,X3)
    | ~ sequential(X3,X1)
    | ~ sequential(X2,X3)
    | ~ sequential(X1,X2) ),
    inference(csr,[status(thm)],[132,32]) ).

cnf(134,negated_conjecture,
    ( ~ sequential(X1,esk8_0)
    | ~ sequential(esk9_0,X1)
    | ~ sequential(esk8_0,esk9_0) ),
    inference(spm,[status(thm)],[104,133,theory(equality)]) ).

cnf(141,negated_conjecture,
    ( ~ sequential(X1,esk8_0)
    | ~ sequential(esk9_0,X1)
    | $false ),
    inference(rw,[status(thm)],[134,101,theory(equality)]) ).

cnf(142,negated_conjecture,
    ( ~ sequential(X1,esk8_0)
    | ~ sequential(esk9_0,X1) ),
    inference(cn,[status(thm)],[141,theory(equality)]) ).

cnf(143,plain,
    ( X1 = X2
    | head_of(esk2_2(X1,X2)) = X2
    | head_of(esk2_2(X1,X2)) = X1
    | $false
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(rw,[status(thm)],[54,100,theory(equality)]) ).

cnf(144,plain,
    ( X1 = X2
    | head_of(esk2_2(X1,X2)) = X2
    | head_of(esk2_2(X1,X2)) = X1
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[143,theory(equality)]) ).

cnf(145,plain,
    ( head_of(esk2_2(X1,head_of(X2))) = X1
    | head_of(esk2_2(X1,head_of(X2))) = head_of(X2)
    | X1 = head_of(X2)
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(spm,[status(thm)],[144,24,theory(equality)]) ).

cnf(146,plain,
    ( head_of(esk2_2(X1,tail_of(X2))) = X1
    | head_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
    | X1 = tail_of(X2)
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(spm,[status(thm)],[144,23,theory(equality)]) ).

cnf(151,plain,
    ( sequential(X4,X5)
    | ~ precedes(X5,esk3_5(X1,X2,X3,X4,X5),X1)
    | ~ shortest_path(X6,X7,X1)
    | ~ precedes(X4,X5,X1)
    | ~ path(X2,X3,X1) ),
    inference(spm,[status(thm)],[71,64,theory(equality)]) ).

cnf(153,plain,
    ( on_path(esk3_5(X1,X2,X3,X4,X5),X1)
    | sequential(X4,X5)
    | ~ path(X6,X7,X1)
    | ~ precedes(X4,X5,X1)
    | ~ path(X2,X3,X1) ),
    inference(spm,[status(thm)],[63,64,theory(equality)]) ).

cnf(156,plain,
    ( X1 = X2
    | head_of(esk2_2(X1,X2)) = X2
    | tail_of(esk2_2(X1,X2)) = X2
    | $false
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(rw,[status(thm)],[52,100,theory(equality)]) ).

cnf(157,plain,
    ( X1 = X2
    | head_of(esk2_2(X1,X2)) = X2
    | tail_of(esk2_2(X1,X2)) = X2
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[156,theory(equality)]) ).

cnf(160,plain,
    ( esk2_2(X1,X2) = X3
    | sequential(esk2_2(X1,X2),X3)
    | tail_of(esk2_2(X1,X2)) = X2
    | X1 = X2
    | tail_of(X3) != X2
    | ~ edge(X3)
    | ~ edge(esk2_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[28,157,theory(equality)]) ).

cnf(161,plain,
    ( X1 = X2
    | head_of(esk2_2(X1,X2)) = X1
    | tail_of(esk2_2(X1,X2)) = X1
    | $false
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(rw,[status(thm)],[53,100,theory(equality)]) ).

cnf(162,plain,
    ( X1 = X2
    | head_of(esk2_2(X1,X2)) = X1
    | tail_of(esk2_2(X1,X2)) = X1
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[161,theory(equality)]) ).

cnf(165,plain,
    ( esk2_2(X1,X2) = X3
    | sequential(esk2_2(X1,X2),X3)
    | tail_of(esk2_2(X1,X2)) = X1
    | X1 = X2
    | tail_of(X3) != X1
    | ~ edge(X3)
    | ~ edge(esk2_2(X1,X2))
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[28,162,theory(equality)]) ).

cnf(167,plain,
    ( precedes(X4,X5,X3)
    | ~ on_path(X4,X3)
    | ~ precedes(X6,X5,X3)
    | ~ path(X1,X2,X3)
    | ~ sequential(X4,X6) ),
    inference(csr,[status(thm)],[78,62]) ).

cnf(169,plain,
    ( X1 = X2
    | tail_of(esk2_2(X1,X2)) = X2
    | tail_of(esk2_2(X1,X2)) = X1
    | $false
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(rw,[status(thm)],[51,100,theory(equality)]) ).

cnf(170,plain,
    ( X1 = X2
    | tail_of(esk2_2(X1,X2)) = X2
    | tail_of(esk2_2(X1,X2)) = X1
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(cn,[status(thm)],[169,theory(equality)]) ).

cnf(171,plain,
    ( tail_of(esk2_2(X1,head_of(X2))) = X1
    | tail_of(esk2_2(X1,head_of(X2))) = head_of(X2)
    | X1 = head_of(X2)
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(spm,[status(thm)],[170,24,theory(equality)]) ).

cnf(172,plain,
    ( tail_of(esk2_2(X1,tail_of(X2))) = X1
    | tail_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
    | X1 = tail_of(X2)
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(spm,[status(thm)],[170,23,theory(equality)]) ).

cnf(180,negated_conjecture,
    ( precedes(X1,X2,esk10_0)
    | ~ on_path(X2,esk10_0)
    | ~ on_path(X1,esk10_0)
    | ~ sequential(X1,X2) ),
    inference(spm,[status(thm)],[77,120,theory(equality)]) ).

cnf(181,negated_conjecture,
    ( precedes(X1,X2,esk10_0)
    | ~ on_path(X1,esk10_0)
    | ~ precedes(X3,X2,esk10_0)
    | ~ sequential(X1,X3) ),
    inference(spm,[status(thm)],[167,120,theory(equality)]) ).

cnf(182,negated_conjecture,
    ( vertex(tail_of(esk9_0))
    | ~ edge(esk8_0) ),
    inference(spm,[status(thm)],[24,119,theory(equality)]) ).

cnf(183,negated_conjecture,
    ( tail_of(esk9_0) != tail_of(esk8_0)
    | ~ edge(esk8_0) ),
    inference(spm,[status(thm)],[35,119,theory(equality)]) ).

cnf(184,negated_conjecture,
    ( esk8_0 = X1
    | sequential(esk8_0,X1)
    | tail_of(X1) != tail_of(esk9_0)
    | ~ edge(X1)
    | ~ edge(esk8_0) ),
    inference(spm,[status(thm)],[28,119,theory(equality)]) ).

cnf(185,negated_conjecture,
    ( vertex(tail_of(esk9_0))
    | $false ),
    inference(rw,[status(thm)],[182,116,theory(equality)]) ).

cnf(186,negated_conjecture,
    vertex(tail_of(esk9_0)),
    inference(cn,[status(thm)],[185,theory(equality)]) ).

cnf(187,negated_conjecture,
    ( tail_of(esk9_0) != tail_of(esk8_0)
    | $false ),
    inference(rw,[status(thm)],[183,116,theory(equality)]) ).

cnf(188,negated_conjecture,
    tail_of(esk9_0) != tail_of(esk8_0),
    inference(cn,[status(thm)],[187,theory(equality)]) ).

cnf(189,negated_conjecture,
    ( esk8_0 = X1
    | sequential(esk8_0,X1)
    | tail_of(X1) != tail_of(esk9_0)
    | ~ edge(X1)
    | $false ),
    inference(rw,[status(thm)],[184,116,theory(equality)]) ).

cnf(190,negated_conjecture,
    ( esk8_0 = X1
    | sequential(esk8_0,X1)
    | tail_of(X1) != tail_of(esk9_0)
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[189,theory(equality)]) ).

cnf(198,negated_conjecture,
    ( head_of(esk2_2(X1,tail_of(esk9_0))) = X1
    | head_of(esk2_2(X1,tail_of(esk9_0))) = tail_of(esk9_0)
    | X1 = tail_of(esk9_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[144,186,theory(equality)]) ).

cnf(199,negated_conjecture,
    ( tail_of(esk2_2(X1,tail_of(esk9_0))) = X1
    | tail_of(esk2_2(X1,tail_of(esk9_0))) = tail_of(esk9_0)
    | X1 = tail_of(esk9_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[170,186,theory(equality)]) ).

cnf(202,negated_conjecture,
    on_path(esk9_0,esk10_0),
    inference(spm,[status(thm)],[122,120,theory(equality)]) ).

fof(218,plain,
    ( ~ epred3_0
  <=> ! [X1] :
        ( tail_of(esk8_0) != tail_of(X1)
        | head_of(esk9_0) != head_of(X1) ) ),
    introduced(definition),
    [split] ).

cnf(219,plain,
    ( epred3_0
    | tail_of(esk8_0) != tail_of(X1)
    | head_of(esk9_0) != head_of(X1) ),
    inference(split_equiv,[status(thm)],[218]) ).

fof(220,plain,
    ( ~ epred4_0
  <=> ! [X3,X2] : ~ shortest_path(X2,X3,esk10_0) ),
    introduced(definition),
    [split] ).

cnf(221,plain,
    ( epred4_0
    | ~ shortest_path(X2,X3,esk10_0) ),
    inference(split_equiv,[status(thm)],[220]) ).

cnf(222,negated_conjecture,
    ( ~ epred4_0
    | ~ epred3_0 ),
    inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[127,218,theory(equality)]),220,theory(equality)]),
    [split] ).

cnf(223,negated_conjecture,
    epred4_0,
    inference(spm,[status(thm)],[221,103,theory(equality)]) ).

cnf(225,negated_conjecture,
    ( $false
    | ~ epred3_0 ),
    inference(rw,[status(thm)],[222,223,theory(equality)]) ).

cnf(226,negated_conjecture,
    ~ epred3_0,
    inference(cn,[status(thm)],[225,theory(equality)]) ).

cnf(233,negated_conjecture,
    ( tail_of(esk8_0) != tail_of(X1)
    | head_of(esk9_0) != head_of(X1) ),
    inference(sr,[status(thm)],[219,226,theory(equality)]) ).

cnf(236,negated_conjecture,
    ( tail_of(esk2_2(X1,X2)) = X1
    | X1 = X2
    | tail_of(esk8_0) != tail_of(esk2_2(X1,X2))
    | head_of(esk9_0) != X1
    | ~ vertex(X2)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[233,162,theory(equality)]) ).

cnf(241,negated_conjecture,
    ( precedes(X1,esk9_0,esk10_0)
    | ~ on_path(X1,esk10_0)
    | ~ sequential(X1,esk8_0) ),
    inference(spm,[status(thm)],[181,102,theory(equality)]) ).

cnf(243,negated_conjecture,
    ( precedes(esk9_0,esk9_0,esk10_0)
    | ~ sequential(esk9_0,esk8_0) ),
    inference(spm,[status(thm)],[241,202,theory(equality)]) ).

cnf(248,negated_conjecture,
    ( ~ precedes(esk9_0,esk9_0,esk10_0)
    | ~ shortest_path(X1,X2,esk10_0)
    | ~ sequential(esk9_0,esk8_0) ),
    inference(spm,[status(thm)],[71,243,theory(equality)]) ).

cnf(263,negated_conjecture,
    ( ~ shortest_path(X1,X2,esk10_0)
    | ~ sequential(esk9_0,esk8_0) ),
    inference(csr,[status(thm)],[248,243]) ).

cnf(264,negated_conjecture,
    ~ sequential(esk9_0,esk8_0),
    inference(spm,[status(thm)],[263,103,theory(equality)]) ).

cnf(278,negated_conjecture,
    ( esk8_0 = esk3_5(X1,X2,X3,X4,X5)
    | sequential(esk8_0,esk3_5(X1,X2,X3,X4,X5))
    | sequential(X4,X5)
    | head_of(X4) != tail_of(esk9_0)
    | ~ edge(esk3_5(X1,X2,X3,X4,X5))
    | ~ precedes(X4,X5,X1)
    | ~ path(X2,X3,X1) ),
    inference(spm,[status(thm)],[190,130,theory(equality)]) ).

cnf(289,plain,
    ( head_of(esk2_2(tail_of(X1),head_of(X2))) = head_of(X2)
    | head_of(esk2_2(tail_of(X1),head_of(X2))) = tail_of(X1)
    | tail_of(X1) = head_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[145,23,theory(equality)]) ).

cnf(314,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(X1)
    | head_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(esk9_0)
    | tail_of(esk9_0) = tail_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[146,186,theory(equality)]) ).

cnf(315,plain,
    ( head_of(esk2_2(head_of(X1),tail_of(X2))) = tail_of(X2)
    | head_of(esk2_2(head_of(X1),tail_of(X2))) = head_of(X1)
    | head_of(X1) = tail_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[146,24,theory(equality)]) ).

cnf(406,negated_conjecture,
    ( head_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(esk9_0)
    | head_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(X1)
    | tail_of(X1) = tail_of(esk9_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[198,23,theory(equality)]) ).

cnf(439,negated_conjecture,
    ( tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(X1)
    | tail_of(X1) = tail_of(esk9_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[199,23,theory(equality)]) ).

cnf(440,negated_conjecture,
    ( on_path(esk3_5(esk10_0,X1,X2,X3,X4),esk10_0)
    | sequential(X3,X4)
    | ~ precedes(X3,X4,esk10_0)
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[153,120,theory(equality)]) ).

cnf(452,negated_conjecture,
    ( precedes(X1,esk3_5(esk10_0,X2,X3,X4,X5),esk10_0)
    | sequential(X4,X5)
    | ~ on_path(X1,esk10_0)
    | ~ sequential(X1,esk3_5(esk10_0,X2,X3,X4,X5))
    | ~ precedes(X4,X5,esk10_0)
    | ~ path(X2,X3,esk10_0) ),
    inference(spm,[status(thm)],[180,440,theory(equality)]) ).

cnf(471,plain,
    ( tail_of(esk2_2(X1,X2)) = X2
    | esk2_2(X1,X2) = X3
    | X1 = X2
    | sequential(esk2_2(X1,X2),X3)
    | tail_of(X3) != X2
    | ~ vertex(X2)
    | ~ vertex(X1)
    | ~ edge(X3) ),
    inference(csr,[status(thm)],[160,125]) ).

cnf(472,plain,
    ( tail_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
    | esk2_2(X1,tail_of(X2)) = X2
    | X1 = tail_of(X2)
    | sequential(esk2_2(X1,tail_of(X2)),X2)
    | ~ vertex(tail_of(X2))
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(er,[status(thm)],[471,theory(equality)]) ).

cnf(500,plain,
    ( tail_of(esk2_2(X1,X2)) = X1
    | esk2_2(X1,X2) = X3
    | X1 = X2
    | sequential(esk2_2(X1,X2),X3)
    | tail_of(X3) != X1
    | ~ vertex(X2)
    | ~ vertex(X1)
    | ~ edge(X3) ),
    inference(csr,[status(thm)],[165,125]) ).

cnf(501,plain,
    ( tail_of(esk2_2(tail_of(X1),X2)) = tail_of(X1)
    | esk2_2(tail_of(X1),X2) = X1
    | tail_of(X1) = X2
    | sequential(esk2_2(tail_of(X1),X2),X1)
    | ~ vertex(X2)
    | ~ vertex(tail_of(X1))
    | ~ edge(X1) ),
    inference(er,[status(thm)],[500,theory(equality)]) ).

cnf(535,plain,
    ( tail_of(esk2_2(tail_of(X1),head_of(X2))) = head_of(X2)
    | tail_of(esk2_2(tail_of(X1),head_of(X2))) = tail_of(X1)
    | tail_of(X1) = head_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[171,23,theory(equality)]) ).

cnf(542,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(X1)
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(esk9_0)
    | tail_of(esk9_0) = tail_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[172,186,theory(equality)]) ).

cnf(543,plain,
    ( tail_of(esk2_2(head_of(X1),tail_of(X2))) = tail_of(X2)
    | tail_of(esk2_2(head_of(X1),tail_of(X2))) = head_of(X1)
    | head_of(X1) = tail_of(X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[172,24,theory(equality)]) ).

cnf(627,negated_conjecture,
    ( esk3_5(X1,X2,X3,X4,X5) = esk8_0
    | sequential(esk8_0,esk3_5(X1,X2,X3,X4,X5))
    | sequential(X4,X5)
    | head_of(X4) != tail_of(esk9_0)
    | ~ precedes(X4,X5,X1)
    | ~ path(X2,X3,X1) ),
    inference(csr,[status(thm)],[278,128]) ).

cnf(750,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk9_0) = tail_of(esk8_0) ),
    inference(spm,[status(thm)],[314,116,theory(equality)]) ).

cnf(755,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0) ),
    inference(sr,[status(thm)],[750,188,theory(equality)]) ).

cnf(756,negated_conjecture,
    ( head_of(esk2_2(tail_of(X1),head_of(esk9_0))) = tail_of(X1)
    | head_of(esk2_2(tail_of(X1),head_of(esk9_0))) = head_of(esk9_0)
    | tail_of(X1) = head_of(esk9_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[289,115,theory(equality)]) ).

cnf(768,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk9_0) != tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) ),
    inference(spm,[status(thm)],[35,755,theory(equality)]) ).

cnf(770,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(tail_of(esk9_0)) ),
    inference(spm,[status(thm)],[157,755,theory(equality)]) ).

cnf(771,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != tail_of(esk9_0) ),
    inference(spm,[status(thm)],[233,755,theory(equality)]) ).

cnf(775,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[770,186,theory(equality)]) ).

cnf(776,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(cn,[status(thm)],[775,theory(equality)]) ).

cnf(777,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(sr,[status(thm)],[776,188,theory(equality)]) ).

cnf(804,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk8_0) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(tail_of(esk9_0)) ),
    inference(spm,[status(thm)],[162,777,theory(equality)]) ).

cnf(810,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk8_0) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[804,186,theory(equality)]) ).

cnf(811,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk8_0) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(cn,[status(thm)],[810,theory(equality)]) ).

cnf(812,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(sr,[status(thm)],[811,188,theory(equality)]) ).

cnf(825,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk8_0) = tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(tail_of(esk9_0))
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0) ),
    inference(spm,[status(thm)],[162,771,theory(equality)]) ).

cnf(832,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk8_0) = tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | $false
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0) ),
    inference(rw,[status(thm)],[825,186,theory(equality)]) ).

cnf(833,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk8_0) = tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0) ),
    inference(cn,[status(thm)],[832,theory(equality)]) ).

cnf(834,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0) ),
    inference(sr,[status(thm)],[833,188,theory(equality)]) ).

cnf(946,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) != tail_of(esk9_0) ),
    inference(spm,[status(thm)],[24,768,theory(equality)]) ).

cnf(1035,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(csr,[status(thm)],[834,812]) ).

cnf(1037,negated_conjecture,
    ( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | tail_of(esk9_0) != head_of(X1)
    | ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(X1)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(spm,[status(thm)],[28,1035,theory(equality)]) ).

cnf(1082,negated_conjecture,
    ( head_of(esk2_2(head_of(X1),tail_of(esk8_0))) = head_of(X1)
    | head_of(esk2_2(head_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[315,116,theory(equality)]) ).

cnf(1266,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
    | head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) = tail_of(esk9_0) ),
    inference(spm,[status(thm)],[406,116,theory(equality)]) ).

cnf(1271,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
    | head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0) ),
    inference(sr,[status(thm)],[1266,188,theory(equality)]) ).

cnf(1276,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
    | tail_of(esk9_0) != tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0)))
    | ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
    inference(spm,[status(thm)],[35,1271,theory(equality)]) ).

cnf(1477,negated_conjecture,
    ( sequential(X1,X2)
    | ~ precedes(X1,X2,esk10_0)
    | ~ path(X3,X4,esk10_0)
    | ~ shortest_path(X5,X6,esk10_0)
    | ~ on_path(X2,esk10_0)
    | ~ sequential(X2,esk3_5(esk10_0,X3,X4,X1,X2)) ),
    inference(spm,[status(thm)],[151,452,theory(equality)]) ).

cnf(1504,negated_conjecture,
    ( sequential(X1,X2)
    | ~ precedes(X1,X2,esk10_0)
    | ~ path(X3,X4,esk10_0)
    | ~ shortest_path(X5,X6,esk10_0)
    | ~ sequential(X2,esk3_5(esk10_0,X3,X4,X1,X2)) ),
    inference(csr,[status(thm)],[1477,62]) ).

cnf(1508,negated_conjecture,
    ( sequential(X1,esk8_0)
    | esk3_5(esk10_0,X2,X3,X1,esk8_0) = esk8_0
    | ~ precedes(X1,esk8_0,esk10_0)
    | ~ path(X2,X3,esk10_0)
    | ~ shortest_path(X4,X5,esk10_0)
    | head_of(X1) != tail_of(esk9_0) ),
    inference(spm,[status(thm)],[1504,627,theory(equality)]) ).

cnf(1570,negated_conjecture,
    ( esk3_5(esk10_0,X1,X2,X3,esk8_0) = esk8_0
    | sequential(X3,esk8_0)
    | head_of(X3) != tail_of(esk9_0)
    | ~ precedes(X3,esk8_0,esk10_0)
    | ~ path(X1,X2,esk10_0) ),
    inference(spm,[status(thm)],[1508,103,theory(equality)]) ).

cnf(1571,negated_conjecture,
    ( sequential(X1,esk8_0)
    | ~ precedes(X1,esk8_0,esk10_0)
    | ~ path(X2,X3,esk10_0)
    | head_of(X1) != tail_of(esk9_0) ),
    inference(spm,[status(thm)],[65,1570,theory(equality)]) ).

cnf(1620,negated_conjecture,
    ( sequential(X1,esk8_0)
    | head_of(X1) != tail_of(esk9_0)
    | ~ precedes(X1,esk8_0,esk10_0) ),
    inference(spm,[status(thm)],[1571,120,theory(equality)]) ).

cnf(1621,negated_conjecture,
    ( sequential(esk8_0,esk8_0)
    | ~ precedes(esk8_0,esk8_0,esk10_0) ),
    inference(spm,[status(thm)],[1620,119,theory(equality)]) ).

cnf(1636,negated_conjecture,
    ~ precedes(esk8_0,esk8_0,esk10_0),
    inference(sr,[status(thm)],[1621,117,theory(equality)]) ).

cnf(1732,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0)))
    | tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) != tail_of(esk9_0) ),
    inference(spm,[status(thm)],[24,1276,theory(equality)]) ).

cnf(2376,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) = tail_of(esk9_0) ),
    inference(spm,[status(thm)],[439,116,theory(equality)]) ).

cnf(2381,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0) ),
    inference(sr,[status(thm)],[2376,188,theory(equality)]) ).

cnf(2406,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
    | ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
    inference(spm,[status(thm)],[1732,2381,theory(equality)]) ).

cnf(2421,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | ~ edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
    inference(spm,[status(thm)],[23,2406,theory(equality)]) ).

cnf(2522,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | tail_of(esk9_0) = tail_of(esk8_0) ),
    inference(spm,[status(thm)],[542,116,theory(equality)]) ).

cnf(2527,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0) ),
    inference(sr,[status(thm)],[2522,188,theory(equality)]) ).

cnf(2546,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) ),
    inference(spm,[status(thm)],[946,2527,theory(equality)]) ).

cnf(2565,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) ),
    inference(spm,[status(thm)],[23,2546,theory(equality)]) ).

cnf(3000,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = head_of(esk9_0)
    | head_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) = head_of(esk9_0) ),
    inference(spm,[status(thm)],[756,116,theory(equality)]) ).

cnf(3043,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
    inference(spm,[status(thm)],[233,3000,theory(equality)]) ).

cnf(3058,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0)))
    | ~ edge(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
    inference(spm,[status(thm)],[35,3043,theory(equality)]) ).

cnf(3627,plain,
    ( tail_of(esk2_2(X1,tail_of(X2))) = tail_of(X2)
    | esk2_2(X1,tail_of(X2)) = X2
    | X1 = tail_of(X2)
    | sequential(esk2_2(X1,tail_of(X2)),X2)
    | ~ vertex(X1)
    | ~ edge(X2) ),
    inference(csr,[status(thm)],[472,23]) ).

cnf(3628,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(X1))) = tail_of(X1)
    | esk2_2(tail_of(esk9_0),tail_of(X1)) = X1
    | tail_of(esk9_0) = tail_of(X1)
    | sequential(esk2_2(tail_of(esk9_0),tail_of(X1)),X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[3627,186,theory(equality)]) ).

cnf(3629,plain,
    ( tail_of(esk2_2(head_of(X1),tail_of(X2))) = tail_of(X2)
    | esk2_2(head_of(X1),tail_of(X2)) = X2
    | head_of(X1) = tail_of(X2)
    | sequential(esk2_2(head_of(X1),tail_of(X2)),X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[3627,24,theory(equality)]) ).

cnf(3630,plain,
    ( tail_of(esk2_2(tail_of(X1),tail_of(X2))) = tail_of(X2)
    | esk2_2(tail_of(X1),tail_of(X2)) = X2
    | tail_of(X1) = tail_of(X2)
    | sequential(esk2_2(tail_of(X1),tail_of(X2)),X2)
    | ~ edge(X2)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[3627,23,theory(equality)]) ).

cnf(4045,negated_conjecture,
    ( tail_of(esk2_2(tail_of(X1),head_of(esk9_0))) = tail_of(X1)
    | tail_of(esk2_2(tail_of(X1),head_of(esk9_0))) = head_of(esk9_0)
    | tail_of(X1) = head_of(esk9_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[535,115,theory(equality)]) ).

cnf(4178,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = head_of(esk9_0)
    | tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
    | tail_of(esk8_0) = head_of(esk9_0) ),
    inference(spm,[status(thm)],[4045,116,theory(equality)]) ).

cnf(4204,negated_conjecture,
    ( vertex(head_of(esk9_0))
    | tail_of(esk2_2(tail_of(esk8_0),head_of(esk9_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | ~ edge(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
    inference(spm,[status(thm)],[23,4178,theory(equality)]) ).

cnf(4231,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0))
    | ~ edge(esk2_2(tail_of(esk8_0),head_of(esk9_0))) ),
    inference(csr,[status(thm)],[4204,3058]) ).

cnf(4295,plain,
    ( tail_of(esk2_2(tail_of(X1),X2)) = tail_of(X1)
    | esk2_2(tail_of(X1),X2) = X1
    | tail_of(X1) = X2
    | sequential(esk2_2(tail_of(X1),X2),X1)
    | ~ vertex(X2)
    | ~ edge(X1) ),
    inference(csr,[status(thm)],[501,23]) ).

cnf(4296,negated_conjecture,
    ( tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(X1)
    | esk2_2(tail_of(X1),tail_of(esk9_0)) = X1
    | tail_of(X1) = tail_of(esk9_0)
    | sequential(esk2_2(tail_of(X1),tail_of(esk9_0)),X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[4295,186,theory(equality)]) ).

cnf(4297,plain,
    ( tail_of(esk2_2(tail_of(X1),head_of(X2))) = tail_of(X1)
    | esk2_2(tail_of(X1),head_of(X2)) = X1
    | tail_of(X1) = head_of(X2)
    | sequential(esk2_2(tail_of(X1),head_of(X2)),X1)
    | ~ edge(X1)
    | ~ edge(X2) ),
    inference(spm,[status(thm)],[4295,24,theory(equality)]) ).

cnf(4350,negated_conjecture,
    ( tail_of(esk2_2(head_of(X1),tail_of(esk8_0))) = head_of(X1)
    | tail_of(esk2_2(head_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[543,116,theory(equality)]) ).

cnf(6043,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | tail_of(esk9_0) = tail_of(esk8_0)
    | sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0) ),
    inference(spm,[status(thm)],[3628,116,theory(equality)]) ).

cnf(6050,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0) ),
    inference(sr,[status(thm)],[6043,188,theory(equality)]) ).

cnf(6060,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(tail_of(esk9_0)) ),
    inference(spm,[status(thm)],[236,6050,theory(equality)]) ).

cnf(6094,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[6060,186,theory(equality)]) ).

cnf(6095,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(cn,[status(thm)],[6094,theory(equality)]) ).

cnf(6096,negated_conjecture,
    ( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk9_0),tail_of(esk8_0)),esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(sr,[status(thm)],[6095,188,theory(equality)]) ).

cnf(6122,negated_conjecture,
    ( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | ~ sequential(esk9_0,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(spm,[status(thm)],[142,6096,theory(equality)]) ).

cnf(6610,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | tail_of(esk8_0) = tail_of(esk9_0)
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0) ),
    inference(spm,[status(thm)],[4296,116,theory(equality)]) ).

cnf(6618,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) = tail_of(esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0) ),
    inference(sr,[status(thm)],[6610,188,theory(equality)]) ).

cnf(16962,negated_conjecture,
    ( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != tail_of(esk9_0)
    | head_of(X1) != tail_of(esk9_0)
    | ~ edge(esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(X1) ),
    inference(csr,[status(thm)],[1037,2565]) ).

cnf(16963,negated_conjecture,
    ( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | head_of(X1) != tail_of(esk9_0)
    | ~ edge(X1)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(tail_of(esk9_0)) ),
    inference(spm,[status(thm)],[16962,125,theory(equality)]) ).

cnf(16966,negated_conjecture,
    ( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | head_of(X1) != tail_of(esk9_0)
    | ~ edge(X1)
    | ~ vertex(tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[16963,186,theory(equality)]) ).

cnf(16967,negated_conjecture,
    ( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | head_of(X1) != tail_of(esk9_0)
    | ~ edge(X1)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(cn,[status(thm)],[16966,theory(equality)]) ).

cnf(16968,negated_conjecture,
    ( X1 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | sequential(X1,esk2_2(tail_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != tail_of(esk9_0)
    | head_of(X1) != tail_of(esk9_0)
    | ~ edge(X1)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(sr,[status(thm)],[16967,188,theory(equality)]) ).

cnf(17284,negated_conjecture,
    ( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | esk9_0 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ edge(esk9_0) ),
    inference(spm,[status(thm)],[6122,16968,theory(equality)]) ).

cnf(17292,negated_conjecture,
    ( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | esk9_0 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[17284,115,theory(equality)]) ).

cnf(17293,negated_conjecture,
    ( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | esk9_0 = esk2_2(tail_of(esk9_0),tail_of(esk8_0))
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(cn,[status(thm)],[17292,theory(equality)]) ).

cnf(17296,negated_conjecture,
    ( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | esk9_0 != esk8_0
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(ef,[status(thm)],[17293,theory(equality)]) ).

cnf(17328,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | esk9_0 = esk8_0
    | sequential(esk9_0,esk8_0)
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(spm,[status(thm)],[6050,17293,theory(equality)]) ).

cnf(17444,negated_conjecture,
    ( esk9_0 = esk8_0
    | sequential(esk9_0,esk8_0)
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(sr,[status(thm)],[17328,188,theory(equality)]) ).

cnf(17445,negated_conjecture,
    ( esk9_0 = esk8_0
    | esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(sr,[status(thm)],[17444,264,theory(equality)]) ).

cnf(17572,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(tail_of(esk9_0))
    | esk9_0 != esk8_0 ),
    inference(spm,[status(thm)],[236,17296,theory(equality)]) ).

cnf(17647,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | $false
    | esk9_0 != esk8_0 ),
    inference(rw,[status(thm)],[17572,186,theory(equality)]) ).

cnf(17648,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | esk9_0 != esk8_0 ),
    inference(cn,[status(thm)],[17647,theory(equality)]) ).

cnf(17649,negated_conjecture,
    ( head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | esk9_0 != esk8_0 ),
    inference(sr,[status(thm)],[17648,188,theory(equality)]) ).

cnf(17840,negated_conjecture,
    ( head_of(esk9_0) != tail_of(esk9_0)
    | esk9_0 != esk8_0
    | ~ edge(esk8_0) ),
    inference(spm,[status(thm)],[17649,23,theory(equality)]) ).

cnf(17843,negated_conjecture,
    ( head_of(esk9_0) != tail_of(esk9_0)
    | esk9_0 != esk8_0
    | $false ),
    inference(rw,[status(thm)],[17840,116,theory(equality)]) ).

cnf(17844,negated_conjecture,
    ( head_of(esk9_0) != tail_of(esk9_0)
    | esk9_0 != esk8_0 ),
    inference(cn,[status(thm)],[17843,theory(equality)]) ).

cnf(17848,negated_conjecture,
    ( esk2_2(tail_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(csr,[status(thm)],[17445,17844]) ).

cnf(17851,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(tail_of(esk9_0)) ),
    inference(spm,[status(thm)],[236,17848,theory(equality)]) ).

cnf(17926,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[17851,186,theory(equality)]) ).

cnf(17927,negated_conjecture,
    ( tail_of(esk8_0) = tail_of(esk9_0)
    | head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(cn,[status(thm)],[17926,theory(equality)]) ).

cnf(17928,negated_conjecture,
    ( head_of(esk9_0) != tail_of(esk9_0)
    | ~ vertex(tail_of(esk8_0)) ),
    inference(sr,[status(thm)],[17927,188,theory(equality)]) ).

cnf(18127,negated_conjecture,
    ( head_of(esk9_0) != tail_of(esk9_0)
    | ~ edge(esk8_0) ),
    inference(spm,[status(thm)],[17928,23,theory(equality)]) ).

cnf(18130,negated_conjecture,
    ( head_of(esk9_0) != tail_of(esk9_0)
    | $false ),
    inference(rw,[status(thm)],[18127,116,theory(equality)]) ).

cnf(18131,negated_conjecture,
    head_of(esk9_0) != tail_of(esk9_0),
    inference(cn,[status(thm)],[18130,theory(equality)]) ).

cnf(27976,negated_conjecture,
    ( tail_of(esk2_2(head_of(X1),tail_of(esk8_0))) = tail_of(esk8_0)
    | esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
    | head_of(X1) = tail_of(esk8_0)
    | sequential(esk2_2(head_of(X1),tail_of(esk8_0)),esk8_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[3629,116,theory(equality)]) ).

cnf(28400,negated_conjecture,
    ( tail_of(esk8_0) = head_of(X1)
    | esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
    | sequential(esk2_2(head_of(X1),tail_of(esk8_0)),esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(head_of(X1))
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[236,27976,theory(equality)]) ).

cnf(28784,negated_conjecture,
    ( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
    | head_of(X1) = tail_of(esk8_0)
    | sequential(esk2_2(head_of(X1),tail_of(esk8_0)),esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ vertex(tail_of(esk8_0))
    | ~ edge(X1) ),
    inference(csr,[status(thm)],[28400,24]) ).

cnf(28791,negated_conjecture,
    ( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
    | head_of(X1) = tail_of(esk8_0)
    | ~ sequential(esk9_0,esk2_2(head_of(X1),tail_of(esk8_0)))
    | head_of(esk9_0) != head_of(X1)
    | ~ vertex(tail_of(esk8_0))
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[142,28784,theory(equality)]) ).

cnf(29928,negated_conjecture,
    ( tail_of(esk2_2(tail_of(X1),tail_of(esk9_0))) = tail_of(esk9_0)
    | esk2_2(tail_of(X1),tail_of(esk9_0)) = esk9_0
    | tail_of(X1) = tail_of(esk9_0)
    | sequential(esk2_2(tail_of(X1),tail_of(esk9_0)),esk9_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[3630,115,theory(equality)]) ).

cnf(30054,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0)
    | ~ edge(esk8_0) ),
    inference(spm,[status(thm)],[6618,29928,theory(equality)]) ).

cnf(30114,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0)
    | $false ),
    inference(rw,[status(thm)],[30054,116,theory(equality)]) ).

cnf(30115,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0) ),
    inference(cn,[status(thm)],[30114,theory(equality)]) ).

cnf(30116,negated_conjecture,
    ( esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0)
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk9_0) ),
    inference(sr,[status(thm)],[30115,188,theory(equality)]) ).

cnf(30161,negated_conjecture,
    ( edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0)))
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | sequential(esk2_2(tail_of(esk8_0),tail_of(esk9_0)),esk8_0) ),
    inference(spm,[status(thm)],[32,30116,theory(equality)]) ).

cnf(30167,negated_conjecture,
    ( esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | edge(esk2_2(tail_of(esk8_0),tail_of(esk9_0))) ),
    inference(csr,[status(thm)],[30161,32]) ).

cnf(30175,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk9_0 ),
    inference(spm,[status(thm)],[2421,30167,theory(equality)]) ).

cnf(30212,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | ~ edge(esk9_0) ),
    inference(spm,[status(thm)],[2421,30175,theory(equality)]) ).

cnf(30303,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0
    | $false ),
    inference(rw,[status(thm)],[30212,115,theory(equality)]) ).

cnf(30304,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | esk2_2(tail_of(esk8_0),tail_of(esk9_0)) = esk8_0 ),
    inference(cn,[status(thm)],[30303,theory(equality)]) ).

cnf(30463,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | ~ edge(esk8_0) ),
    inference(spm,[status(thm)],[2421,30304,theory(equality)]) ).

cnf(30552,negated_conjecture,
    ( vertex(tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[30463,116,theory(equality)]) ).

cnf(30553,negated_conjecture,
    vertex(tail_of(esk8_0)),
    inference(cn,[status(thm)],[30552,theory(equality)]) ).

cnf(30707,negated_conjecture,
    ( head_of(esk2_2(X1,tail_of(esk8_0))) = X1
    | head_of(esk2_2(X1,tail_of(esk8_0))) = tail_of(esk8_0)
    | X1 = tail_of(esk8_0)
    | ~ vertex(X1) ),
    inference(spm,[status(thm)],[144,30553,theory(equality)]) ).

cnf(30709,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
    | head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | tail_of(esk8_0) = head_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[145,30553,theory(equality)]) ).

cnf(30733,negated_conjecture,
    ( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ sequential(esk9_0,esk2_2(head_of(X1),tail_of(esk8_0)))
    | $false
    | ~ edge(X1) ),
    inference(rw,[status(thm)],[28791,30553,theory(equality)]) ).

cnf(30734,negated_conjecture,
    ( esk2_2(head_of(X1),tail_of(esk8_0)) = esk8_0
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ sequential(esk9_0,esk2_2(head_of(X1),tail_of(esk8_0)))
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[30733,theory(equality)]) ).

cnf(32282,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | ~ vertex(head_of(X1))
    | ~ vertex(tail_of(esk8_0))
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[162,30709,theory(equality)]) ).

cnf(32284,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | tail_of(esk8_0) != tail_of(esk2_2(tail_of(esk8_0),head_of(X1)))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[233,30709,theory(equality)]) ).

cnf(32417,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | ~ vertex(head_of(X1))
    | $false
    | ~ edge(X1) ),
    inference(rw,[status(thm)],[32282,30553,theory(equality)]) ).

cnf(32418,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | ~ vertex(head_of(X1))
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[32417,theory(equality)]) ).

cnf(32995,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | ~ edge(X1) ),
    inference(csr,[status(thm)],[32418,24]) ).

cnf(33260,negated_conjecture,
    ( head_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(csr,[status(thm)],[32284,32995]) ).

cnf(33265,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
    | tail_of(esk8_0) = head_of(X1)
    | ~ vertex(head_of(X1))
    | ~ vertex(tail_of(esk8_0))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[157,33260,theory(equality)]) ).

cnf(33391,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
    | tail_of(esk8_0) = head_of(X1)
    | ~ vertex(head_of(X1))
    | $false
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(rw,[status(thm)],[33265,30553,theory(equality)]) ).

cnf(33392,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
    | tail_of(esk8_0) = head_of(X1)
    | ~ vertex(head_of(X1))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[33391,theory(equality)]) ).

cnf(33590,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = head_of(X1)
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(csr,[status(thm)],[33392,24]) ).

cnf(42262,negated_conjecture,
    ( tail_of(esk2_2(tail_of(esk8_0),head_of(X1))) = tail_of(esk8_0)
    | esk2_2(tail_of(esk8_0),head_of(X1)) = esk8_0
    | tail_of(esk8_0) = head_of(X1)
    | sequential(esk2_2(tail_of(esk8_0),head_of(X1)),esk8_0)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[4297,116,theory(equality)]) ).

cnf(42767,negated_conjecture,
    ( tail_of(esk8_0) = head_of(X1)
    | esk2_2(tail_of(esk8_0),head_of(X1)) = esk8_0
    | sequential(esk2_2(tail_of(esk8_0),head_of(X1)),esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[33590,42262,theory(equality)]) ).

cnf(43083,negated_conjecture,
    ( edge(esk2_2(tail_of(esk8_0),head_of(X1)))
    | esk2_2(tail_of(esk8_0),head_of(X1)) = esk8_0
    | head_of(X1) = tail_of(esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[32,42767,theory(equality)]) ).

cnf(43265,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0))
    | esk2_2(tail_of(esk8_0),head_of(esk9_0)) = esk8_0
    | ~ edge(esk9_0) ),
    inference(spm,[status(thm)],[4231,43083,theory(equality)]) ).

cnf(43323,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0))
    | esk2_2(tail_of(esk8_0),head_of(esk9_0)) = esk8_0
    | $false ),
    inference(rw,[status(thm)],[43265,115,theory(equality)]) ).

cnf(43324,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0))
    | esk2_2(tail_of(esk8_0),head_of(esk9_0)) = esk8_0 ),
    inference(cn,[status(thm)],[43323,theory(equality)]) ).

cnf(43355,negated_conjecture,
    ( head_of(esk8_0) = tail_of(esk8_0)
    | head_of(esk8_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0)) ),
    inference(spm,[status(thm)],[3000,43324,theory(equality)]) ).

cnf(43429,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk8_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0)) ),
    inference(rw,[status(thm)],[43355,119,theory(equality)]) ).

cnf(43430,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk9_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0)) ),
    inference(rw,[status(thm)],[43429,119,theory(equality)]) ).

cnf(43431,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0)) ),
    inference(sr,[status(thm)],[43430,188,theory(equality)]) ).

cnf(43432,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk8_0)
    | vertex(head_of(esk9_0)) ),
    inference(sr,[status(thm)],[43431,18131,theory(equality)]) ).

cnf(43616,negated_conjecture,
    ( head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0) ),
    inference(spm,[status(thm)],[30707,43432,theory(equality)]) ).

cnf(44292,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(head_of(esk9_0)) ),
    inference(spm,[status(thm)],[157,43616,theory(equality)]) ).

cnf(44293,negated_conjecture,
    ( head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk8_0) != tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) ),
    inference(spm,[status(thm)],[233,43616,theory(equality)]) ).

cnf(44421,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | $false
    | ~ vertex(head_of(esk9_0)) ),
    inference(rw,[status(thm)],[44292,30553,theory(equality)]) ).

cnf(44422,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | ~ vertex(head_of(esk9_0)) ),
    inference(cn,[status(thm)],[44421,theory(equality)]) ).

cnf(45726,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0) ),
    inference(csr,[status(thm)],[44422,43432]) ).

cnf(45727,negated_conjecture,
    ( head_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = tail_of(esk8_0)
    | head_of(esk9_0) = tail_of(esk8_0) ),
    inference(csr,[status(thm)],[45726,44293]) ).

cnf(45731,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
    | tail_of(esk8_0) = head_of(esk9_0)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(head_of(esk9_0)) ),
    inference(spm,[status(thm)],[162,45727,theory(equality)]) ).

cnf(45834,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
    | tail_of(esk8_0) = head_of(esk9_0)
    | $false
    | ~ vertex(head_of(esk9_0)) ),
    inference(rw,[status(thm)],[45731,30553,theory(equality)]) ).

cnf(45835,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
    | tail_of(esk8_0) = head_of(esk9_0)
    | ~ vertex(head_of(esk9_0)) ),
    inference(cn,[status(thm)],[45834,theory(equality)]) ).

cnf(45883,negated_conjecture,
    ( tail_of(esk2_2(head_of(esk9_0),tail_of(esk8_0))) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0) ),
    inference(csr,[status(thm)],[45835,43432]) ).

cnf(45885,negated_conjecture,
    ( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
    | sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(esk2_2(head_of(esk9_0),tail_of(esk8_0)))
    | ~ edge(X1) ),
    inference(spm,[status(thm)],[28,45883,theory(equality)]) ).

cnf(56712,negated_conjecture,
    ( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
    | head_of(esk9_0) = tail_of(esk8_0)
    | sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1)
    | ~ vertex(tail_of(esk8_0))
    | ~ vertex(head_of(esk9_0)) ),
    inference(spm,[status(thm)],[45885,125,theory(equality)]) ).

cnf(56715,negated_conjecture,
    ( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
    | head_of(esk9_0) = tail_of(esk8_0)
    | sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1)
    | $false
    | ~ vertex(head_of(esk9_0)) ),
    inference(rw,[status(thm)],[56712,30553,theory(equality)]) ).

cnf(56716,negated_conjecture,
    ( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
    | head_of(esk9_0) = tail_of(esk8_0)
    | sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1)
    | ~ vertex(head_of(esk9_0)) ),
    inference(cn,[status(thm)],[56715,theory(equality)]) ).

cnf(56892,negated_conjecture,
    ( X1 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
    | head_of(esk9_0) = tail_of(esk8_0)
    | sequential(X1,esk2_2(head_of(esk9_0),tail_of(esk8_0)))
    | head_of(esk9_0) != head_of(X1)
    | ~ edge(X1) ),
    inference(csr,[status(thm)],[56716,43432]) ).

cnf(56903,negated_conjecture,
    ( esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | head_of(esk9_0) = tail_of(esk8_0)
    | esk9_0 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
    | ~ edge(esk9_0) ),
    inference(spm,[status(thm)],[30734,56892,theory(equality)]) ).

cnf(56908,negated_conjecture,
    ( esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | head_of(esk9_0) = tail_of(esk8_0)
    | esk9_0 = esk2_2(head_of(esk9_0),tail_of(esk8_0))
    | $false ),
    inference(rw,[status(thm)],[56903,115,theory(equality)]) ).

cnf(56909,negated_conjecture,
    ( esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | head_of(esk9_0) = tail_of(esk8_0)
    | esk9_0 = esk2_2(head_of(esk9_0),tail_of(esk8_0)) ),
    inference(cn,[status(thm)],[56908,theory(equality)]) ).

cnf(56925,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk9_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | ~ edge(esk9_0) ),
    inference(spm,[status(thm)],[4350,56909,theory(equality)]) ).

cnf(57038,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk9_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0
    | $false ),
    inference(rw,[status(thm)],[56925,115,theory(equality)]) ).

cnf(57039,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk9_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0 ),
    inference(cn,[status(thm)],[57038,theory(equality)]) ).

cnf(57040,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0 ),
    inference(sr,[status(thm)],[57039,188,theory(equality)]) ).

cnf(57041,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk8_0)
    | esk2_2(head_of(esk9_0),tail_of(esk8_0)) = esk8_0 ),
    inference(sr,[status(thm)],[57040,18131,theory(equality)]) ).

cnf(57236,negated_conjecture,
    ( head_of(esk8_0) = tail_of(esk8_0)
    | head_of(esk8_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | ~ edge(esk9_0) ),
    inference(spm,[status(thm)],[1082,57041,theory(equality)]) ).

cnf(57311,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | head_of(esk8_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | ~ edge(esk9_0) ),
    inference(rw,[status(thm)],[57236,119,theory(equality)]) ).

cnf(57312,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk9_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | ~ edge(esk9_0) ),
    inference(rw,[status(thm)],[57311,119,theory(equality)]) ).

cnf(57313,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk9_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0)
    | $false ),
    inference(rw,[status(thm)],[57312,115,theory(equality)]) ).

cnf(57314,negated_conjecture,
    ( tail_of(esk9_0) = tail_of(esk8_0)
    | tail_of(esk9_0) = head_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0) ),
    inference(cn,[status(thm)],[57313,theory(equality)]) ).

cnf(57315,negated_conjecture,
    ( head_of(esk9_0) = tail_of(esk9_0)
    | head_of(esk9_0) = tail_of(esk8_0) ),
    inference(sr,[status(thm)],[57314,188,theory(equality)]) ).

cnf(57316,negated_conjecture,
    head_of(esk9_0) = tail_of(esk8_0),
    inference(sr,[status(thm)],[57315,18131,theory(equality)]) ).

cnf(57494,negated_conjecture,
    ( esk9_0 = X1
    | sequential(esk9_0,X1)
    | tail_of(X1) != tail_of(esk8_0)
    | ~ edge(X1)
    | ~ edge(esk9_0) ),
    inference(spm,[status(thm)],[28,57316,theory(equality)]) ).

cnf(58242,negated_conjecture,
    ( esk9_0 = X1
    | sequential(esk9_0,X1)
    | tail_of(X1) != tail_of(esk8_0)
    | ~ edge(X1)
    | $false ),
    inference(rw,[status(thm)],[57494,115,theory(equality)]) ).

cnf(58243,negated_conjecture,
    ( esk9_0 = X1
    | sequential(esk9_0,X1)
    | tail_of(X1) != tail_of(esk8_0)
    | ~ edge(X1) ),
    inference(cn,[status(thm)],[58242,theory(equality)]) ).

cnf(58565,negated_conjecture,
    ( esk9_0 = esk8_0
    | sequential(esk9_0,esk8_0)
    | ~ edge(esk8_0) ),
    inference(er,[status(thm)],[58243,theory(equality)]) ).

cnf(58610,negated_conjecture,
    ( esk9_0 = esk8_0
    | sequential(esk9_0,esk8_0)
    | $false ),
    inference(rw,[status(thm)],[58565,116,theory(equality)]) ).

cnf(58611,negated_conjecture,
    ( esk9_0 = esk8_0
    | sequential(esk9_0,esk8_0) ),
    inference(cn,[status(thm)],[58610,theory(equality)]) ).

cnf(58612,negated_conjecture,
    esk9_0 = esk8_0,
    inference(sr,[status(thm)],[58611,264,theory(equality)]) ).

cnf(58623,negated_conjecture,
    precedes(esk8_0,esk8_0,esk10_0),
    inference(rw,[status(thm)],[102,58612,theory(equality)]) ).

cnf(58624,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[58623,1636,theory(equality)]) ).

cnf(58625,negated_conjecture,
    $false,
    58624,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRA/GRA008+1.p
% --creating new selector for [GRA001+0.ax]
% -running prover on /tmp/tmp2znHc3/sel_GRA008+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRA008+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRA/GRA008+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRA/GRA008+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------