TSTP Solution File: GRA007+2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : GRA007+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rHorJPj8pv true

% Computer : n032.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 : Thu Aug 31 00:10:10 EDT 2023

% Result   : Theorem 6.93s 1.52s
% Output   : Refutation 6.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  131 (  36 unt;  19 typ;   0 def)
%            Number of atoms       :  363 ( 135 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives : 1146 ( 182   ~; 201   |;  31   &; 713   @)
%                                         (   2 <=>;  15  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;   7 con; 0-3 aty)
%            Number of variables   :  180 (   0   ^; 173   !;   7   ?; 180   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk__8_type,type,
    sk__8: $i ).

thf(edge_type,type,
    edge: $i > $o ).

thf(sequential_type,type,
    sequential: $i > $i > $o ).

thf(length_of_type,type,
    length_of: $i > $i ).

thf(sk__10_type,type,
    sk__10: $i ).

thf(sk__11_type,type,
    sk__11: $i ).

thf(in_path_type,type,
    in_path: $i > $i > $o ).

thf(vertex_type,type,
    vertex: $i > $o ).

thf(precedes_type,type,
    precedes: $i > $i > $i > $o ).

thf(head_of_type,type,
    head_of: $i > $i ).

thf(on_path_type,type,
    on_path: $i > $i > $o ).

thf(shortest_path_type,type,
    shortest_path: $i > $i > $i > $o ).

thf(sk__type,type,
    sk_: $i > $i > $i ).

thf(less_or_equal_type,type,
    less_or_equal: $i > $i > $o ).

thf(sk__9_type,type,
    sk__9: $i ).

thf(tail_of_type,type,
    tail_of: $i > $i ).

thf(path_type,type,
    path: $i > $i > $i > $o ).

thf(sk__12_type,type,
    sk__12: $i ).

thf(complete_type,type,
    complete: $o ).

thf(back_edge,conjecture,
    ( complete
   => ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
        ( ( ( shortest_path @ V1 @ V2 @ P )
          & ( precedes @ E1 @ E2 @ P ) )
       => ? [E3: $i] :
            ( ( ( head_of @ E3 )
              = ( tail_of @ E1 ) )
            & ( ( tail_of @ E3 )
              = ( head_of @ E2 ) )
            & ( edge @ E3 ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( complete
     => ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
          ( ( ( shortest_path @ V1 @ V2 @ P )
            & ( precedes @ E1 @ E2 @ P ) )
         => ? [E3: $i] :
              ( ( ( head_of @ E3 )
                = ( tail_of @ E1 ) )
              & ( ( tail_of @ E3 )
                = ( head_of @ E2 ) )
              & ( edge @ E3 ) ) ) ),
    inference('cnf.neg',[status(esa)],[back_edge]) ).

thf(zip_derived_cl60,plain,
    complete,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(complete_properties,axiom,
    ( complete
   => ! [V1: $i,V2: $i] :
        ( ( ( vertex @ V1 )
          & ( vertex @ V2 )
          & ( V1 != V2 ) )
       => ? [E: $i] :
            ( ( ( ( V1
                  = ( head_of @ E ) )
                & ( V2
                  = ( tail_of @ E ) ) )
            <~> ( ( V2
                  = ( head_of @ E ) )
                & ( V1
                  = ( tail_of @ E ) ) ) )
            & ( edge @ E ) ) ) ) ).

thf(zip_derived_cl6,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X0
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ~ complete ),
    inference(cnf,[status(esa)],[complete_properties]) ).

thf(zip_derived_cl409,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0 = X1 )
      | ( X1
        = ( head_of @ ( sk_ @ X1 @ X0 ) ) )
      | ( X0
        = ( head_of @ ( sk_ @ X1 @ X0 ) ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl60,zip_derived_cl6]) ).

thf(zip_derived_cl60_001,plain,
    complete,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ ( sk_ @ X0 @ X1 ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ~ complete ),
    inference(cnf,[status(esa)],[complete_properties]) ).

thf(zip_derived_cl410,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0 = X1 )
      | ( edge @ ( sk_ @ X1 @ X0 ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl60,zip_derived_cl8]) ).

thf(zip_derived_cl60_002,plain,
    complete,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ~ complete ),
    inference(cnf,[status(esa)],[complete_properties]) ).

thf(zip_derived_cl406,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( X1 = X0 )
      | ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X0
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl60,zip_derived_cl3]) ).

thf(no_loops,axiom,
    ! [E: $i] :
      ( ( edge @ E )
     => ( ( head_of @ E )
       != ( tail_of @ E ) ) ) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i] :
      ( ( ( head_of @ X0 )
       != ( tail_of @ X0 ) )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[no_loops]) ).

thf(zip_derived_cl621,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( ( head_of @ ( sk_ @ X0 @ X1 ) )
       != X0 )
      | ~ ( edge @ ( sk_ @ X0 @ X1 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl406,zip_derived_cl0]) ).

thf(zip_derived_cl410_003,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0 = X1 )
      | ( edge @ ( sk_ @ X1 @ X0 ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl60,zip_derived_cl8]) ).

thf(zip_derived_cl757,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( head_of @ ( sk_ @ X0 @ X1 ) )
       != X0 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( X1 = X0 )
      | ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl621,zip_derived_cl410]) ).

thf(zip_derived_cl61,plain,
    ! [X0: $i] :
      ( ( ( head_of @ X0 )
       != ( tail_of @ sk__10 ) )
      | ( ( tail_of @ X0 )
       != ( head_of @ sk__11 ) )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl761,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = X1 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ ( sk_ @ X1 @ X0 ) )
       != X1 )
      | ( ( head_of @ ( sk_ @ X1 @ X0 ) )
       != ( tail_of @ sk__10 ) )
      | ( X0
       != ( head_of @ sk__11 ) )
      | ~ ( edge @ ( sk_ @ X1 @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl757,zip_derived_cl61]) ).

thf(zip_derived_cl814,plain,
    ! [X0: $i] :
      ( ~ ( edge @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != ( tail_of @ sk__10 ) )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != X0 )
      | ~ ( vertex @ ( head_of @ sk__11 ) )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl761]) ).

thf(zip_derived_cl62,plain,
    shortest_path @ sk__8 @ sk__9 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(shortest_path_defn,axiom,
    ! [V1: $i,V2: $i,SP: $i] :
      ( ( shortest_path @ V1 @ V2 @ SP )
    <=> ( ( path @ V1 @ V2 @ SP )
        & ( V1 != V2 )
        & ! [P: $i] :
            ( ( path @ V1 @ V2 @ P )
           => ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ) ).

thf(zip_derived_cl38,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( path @ X0 @ X1 @ X2 )
      | ~ ( shortest_path @ X0 @ X1 @ X2 ) ),
    inference(cnf,[status(esa)],[shortest_path_defn]) ).

thf(zip_derived_cl421,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(zip_derived_cl63,plain,
    precedes @ sk__10 @ sk__11 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(precedes_properties,axiom,
    ! [P: $i,V1: $i,V2: $i] :
      ( ( path @ V1 @ V2 @ P )
     => ! [E1: $i,E2: $i] :
          ( ( precedes @ E1 @ E2 @ P )
         => ( ( on_path @ E1 @ P )
            & ( on_path @ E2 @ P )
            & ( ( sequential @ E1 @ E2 )
            <~> ? [E3: $i] :
                  ( ( precedes @ E3 @ E2 @ P )
                  & ( sequential @ E1 @ E3 ) ) ) ) ) ) ).

thf(zip_derived_cl36,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( precedes @ X0 @ X1 @ X2 )
      | ( on_path @ X1 @ X2 )
      | ~ ( path @ X3 @ X4 @ X2 ) ),
    inference(cnf,[status(esa)],[precedes_properties]) ).

thf(zip_derived_cl456,plain,
    ! [X0: $i,X1: $i] :
      ( ( on_path @ sk__11 @ sk__12 )
      | ~ ( path @ X1 @ X0 @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl36]) ).

thf(zip_derived_cl461,plain,
    on_path @ sk__11 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl456]) ).

thf(zip_derived_cl421_004,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(on_path_properties,axiom,
    ! [V1: $i,V2: $i,P: $i,E: $i] :
      ( ( ( path @ V1 @ V2 @ P )
        & ( on_path @ E @ P ) )
     => ( ( edge @ E )
        & ( in_path @ ( head_of @ E ) @ P )
        & ( in_path @ ( tail_of @ E ) @ P ) ) ) ).

thf(zip_derived_cl21,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( path @ X0 @ X1 @ X2 )
      | ~ ( on_path @ X3 @ X2 )
      | ( in_path @ ( head_of @ X3 ) @ X2 ) ),
    inference(cnf,[status(esa)],[on_path_properties]) ).

thf(zip_derived_cl476,plain,
    ! [X0: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ( in_path @ ( head_of @ X0 ) @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl21]) ).

thf(zip_derived_cl421_005,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(in_path_properties,axiom,
    ! [V1: $i,V2: $i,P: $i,V: $i] :
      ( ( ( path @ V1 @ V2 @ P )
        & ( in_path @ V @ P ) )
     => ( ( vertex @ V )
        & ? [E: $i] :
            ( ( ( V
                = ( tail_of @ E ) )
              | ( V
                = ( head_of @ E ) ) )
            & ( on_path @ E @ P ) ) ) ) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( path @ X0 @ X1 @ X2 )
      | ~ ( in_path @ X3 @ X2 )
      | ( vertex @ X3 ) ),
    inference(cnf,[status(esa)],[in_path_properties]) ).

thf(zip_derived_cl444,plain,
    ! [X0: $i] :
      ( ~ ( in_path @ X0 @ sk__12 )
      | ( vertex @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl25]) ).

thf(zip_derived_cl478,plain,
    ! [X0: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ( vertex @ ( head_of @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl476,zip_derived_cl444]) ).

thf(zip_derived_cl479,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl461,zip_derived_cl478]) ).

thf(zip_derived_cl815,plain,
    ! [X0: $i] :
      ( ~ ( edge @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != ( tail_of @ sk__10 ) )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != X0 )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl814,zip_derived_cl479]) ).

thf(zip_derived_cl1017,plain,
    ! [X0: $i] :
      ( ( ( head_of @ sk__11 )
        = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ ( head_of @ sk__11 ) )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != ( tail_of @ sk__10 ) )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != X0 )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl410,zip_derived_cl815]) ).

thf(zip_derived_cl479_006,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl461,zip_derived_cl478]) ).

thf(zip_derived_cl1018,plain,
    ! [X0: $i] :
      ( ( ( head_of @ sk__11 )
        = X0 )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != ( tail_of @ sk__10 ) )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != X0 )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1017,zip_derived_cl479]) ).

thf(zip_derived_cl1019,plain,
    ! [X0: $i] :
      ( ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != X0 )
      | ( ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) )
       != ( tail_of @ sk__10 ) )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1018]) ).

thf(zip_derived_cl1041,plain,
    ! [X0: $i] :
      ( ( ( head_of @ sk__11 )
        = ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) ) )
      | ( ( head_of @ sk__11 )
        = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ ( head_of @ sk__11 ) )
      | ( X0 != X0 )
      | ( X0
       != ( tail_of @ sk__10 ) )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl409,zip_derived_cl1019]) ).

thf(zip_derived_cl479_007,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl461,zip_derived_cl478]) ).

thf(zip_derived_cl1044,plain,
    ! [X0: $i] :
      ( ( ( head_of @ sk__11 )
        = ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) ) )
      | ( ( head_of @ sk__11 )
        = X0 )
      | ~ ( vertex @ X0 )
      | ( X0 != X0 )
      | ( X0
       != ( tail_of @ sk__10 ) )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl1041,zip_derived_cl479]) ).

thf(zip_derived_cl1045,plain,
    ! [X0: $i] :
      ( ( X0
       != ( tail_of @ sk__10 ) )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ sk__11 )
        = X0 )
      | ( ( head_of @ sk__11 )
        = ( head_of @ ( sk_ @ X0 @ ( head_of @ sk__11 ) ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1044]) ).

thf(zip_derived_cl62_008,plain,
    shortest_path @ sk__8 @ sk__9 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl63_009,plain,
    precedes @ sk__10 @ sk__11 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl421_010,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(zip_derived_cl63_011,plain,
    precedes @ sk__10 @ sk__11 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl37,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( precedes @ X0 @ X1 @ X2 )
      | ( on_path @ X0 @ X2 )
      | ~ ( path @ X3 @ X4 @ X2 ) ),
    inference(cnf,[status(esa)],[precedes_properties]) ).

thf(zip_derived_cl464,plain,
    ! [X0: $i,X1: $i] :
      ( ( on_path @ sk__10 @ sk__12 )
      | ~ ( path @ X1 @ X0 @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl37]) ).

thf(zip_derived_cl487,plain,
    on_path @ sk__10 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl464]) ).

thf(zip_derived_cl421_012,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( path @ X0 @ X1 @ X2 )
      | ~ ( on_path @ X3 @ X2 )
      | ( in_path @ ( tail_of @ X3 ) @ X2 ) ),
    inference(cnf,[status(esa)],[on_path_properties]) ).

thf(zip_derived_cl468,plain,
    ! [X0: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ( in_path @ ( tail_of @ X0 ) @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl20]) ).

thf(zip_derived_cl444_013,plain,
    ! [X0: $i] :
      ( ~ ( in_path @ X0 @ sk__12 )
      | ( vertex @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl25]) ).

thf(zip_derived_cl472,plain,
    ! [X0: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ( vertex @ ( tail_of @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl468,zip_derived_cl444]) ).

thf(zip_derived_cl489,plain,
    vertex @ ( tail_of @ sk__10 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl472]) ).

thf(zip_derived_cl406_014,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( X1 = X0 )
      | ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X0
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl60,zip_derived_cl3]) ).

thf(zip_derived_cl0_015,plain,
    ! [X0: $i] :
      ( ( ( head_of @ X0 )
       != ( tail_of @ X0 ) )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[no_loops]) ).

thf(zip_derived_cl608,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( tail_of @ ( sk_ @ X1 @ X0 ) ) )
      | ( X0 = X1 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ ( sk_ @ X1 @ X0 ) )
       != X0 )
      | ~ ( edge @ ( sk_ @ X1 @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl406,zip_derived_cl0]) ).

thf(zip_derived_cl410_016,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0 = X1 )
      | ( edge @ ( sk_ @ X1 @ X0 ) ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl60,zip_derived_cl8]) ).

thf(zip_derived_cl666,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( head_of @ ( sk_ @ X1 @ X0 ) )
       != X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0 = X1 )
      | ( X1
        = ( tail_of @ ( sk_ @ X1 @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl608,zip_derived_cl410]) ).

thf(shortest_path_properties,axiom,
    ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
      ( ( ( shortest_path @ V1 @ V2 @ P )
        & ( precedes @ E1 @ E2 @ P ) )
     => ( ~ ? [E3: $i] :
              ( ( ( head_of @ E3 )
                = ( head_of @ E2 ) )
              & ( ( tail_of @ E3 )
                = ( tail_of @ E1 ) ) )
        & ~ ( precedes @ E2 @ E1 @ P ) ) ) ).

thf(zip_derived_cl43,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( ( tail_of @ X1 )
       != ( tail_of @ X0 ) )
      | ( ( head_of @ X1 )
       != ( head_of @ X2 ) )
      | ~ ( precedes @ X0 @ X2 @ X3 )
      | ~ ( shortest_path @ X4 @ X5 @ X3 ) ),
    inference(cnf,[status(esa)],[shortest_path_properties]) ).

thf(zip_derived_cl676,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X2 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X2 )
      | ( ( head_of @ ( sk_ @ X0 @ X2 ) )
       != X2 )
      | ( X0
       != ( tail_of @ X1 ) )
      | ( ( head_of @ ( sk_ @ X0 @ X2 ) )
       != ( head_of @ X3 ) )
      | ~ ( precedes @ X1 @ X3 @ X4 )
      | ~ ( shortest_path @ X6 @ X5 @ X4 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl666,zip_derived_cl43]) ).

thf(zip_derived_cl1010,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( shortest_path @ X2 @ X1 @ X0 )
      | ~ ( precedes @ X4 @ X3 @ X0 )
      | ( ( head_of @ ( sk_ @ ( tail_of @ X4 ) @ X5 ) )
       != ( head_of @ X3 ) )
      | ( ( head_of @ ( sk_ @ ( tail_of @ X4 ) @ X5 ) )
       != X5 )
      | ~ ( vertex @ X5 )
      | ~ ( vertex @ ( tail_of @ X4 ) )
      | ( X5
        = ( tail_of @ X4 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl676]) ).

thf(zip_derived_cl2536,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( shortest_path @ X2 @ X1 @ X0 )
      | ~ ( precedes @ sk__10 @ X3 @ X0 )
      | ( ( head_of @ ( sk_ @ ( tail_of @ sk__10 ) @ X4 ) )
       != ( head_of @ X3 ) )
      | ( ( head_of @ ( sk_ @ ( tail_of @ sk__10 ) @ X4 ) )
       != X4 )
      | ~ ( vertex @ X4 )
      | ( X4
        = ( tail_of @ sk__10 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl489,zip_derived_cl1010]) ).

thf(zip_derived_cl2573,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( shortest_path @ X1 @ X0 @ sk__12 )
      | ( ( head_of @ ( sk_ @ ( tail_of @ sk__10 ) @ X2 ) )
       != ( head_of @ sk__11 ) )
      | ( ( head_of @ ( sk_ @ ( tail_of @ sk__10 ) @ X2 ) )
       != X2 )
      | ~ ( vertex @ X2 )
      | ( X2
        = ( tail_of @ sk__10 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl2536]) ).

thf(zip_derived_cl2577,plain,
    ! [X0: $i] :
      ( ( ( head_of @ ( sk_ @ ( tail_of @ sk__10 ) @ X0 ) )
       != ( head_of @ sk__11 ) )
      | ( ( head_of @ ( sk_ @ ( tail_of @ sk__10 ) @ X0 ) )
       != X0 )
      | ~ ( vertex @ X0 )
      | ( X0
        = ( tail_of @ sk__10 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl2573]) ).

thf(zip_derived_cl2580,plain,
    ( ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) )
    | ~ ( vertex @ ( tail_of @ sk__10 ) )
    | ( ( tail_of @ sk__10 )
     != ( tail_of @ sk__10 ) )
    | ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ~ ( vertex @ ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl1045,zip_derived_cl2577]) ).

thf(zip_derived_cl489_017,plain,
    vertex @ ( tail_of @ sk__10 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl472]) ).

thf(zip_derived_cl479_018,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl461,zip_derived_cl478]) ).

thf(zip_derived_cl2585,plain,
    ( ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) )
    | ( ( tail_of @ sk__10 )
     != ( tail_of @ sk__10 ) )
    | ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2580,zip_derived_cl489,zip_derived_cl479]) ).

thf(zip_derived_cl2586,plain,
    ( ( head_of @ sk__11 )
    = ( tail_of @ sk__10 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2585]) ).

thf(zip_derived_cl0_019,plain,
    ! [X0: $i] :
      ( ( ( head_of @ X0 )
       != ( tail_of @ X0 ) )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[no_loops]) ).

thf(zip_derived_cl2653,plain,
    ( ( ( head_of @ sk__10 )
     != ( head_of @ sk__11 ) )
    | ~ ( edge @ sk__10 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2586,zip_derived_cl0]) ).

thf(zip_derived_cl487_020,plain,
    on_path @ sk__10 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl464]) ).

thf(zip_derived_cl421_021,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( path @ X0 @ X1 @ X2 )
      | ~ ( on_path @ X3 @ X2 )
      | ( edge @ X3 ) ),
    inference(cnf,[status(esa)],[on_path_properties]) ).

thf(zip_derived_cl434,plain,
    ! [X0: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ( edge @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl22]) ).

thf(zip_derived_cl488,plain,
    edge @ sk__10,
    inference('s_sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl434]) ).

thf(zip_derived_cl2695,plain,
    ( ( head_of @ sk__10 )
   != ( head_of @ sk__11 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2653,zip_derived_cl488]) ).

thf(zip_derived_cl62_022,plain,
    shortest_path @ sk__8 @ sk__9 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl461_023,plain,
    on_path @ sk__11 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl456]) ).

thf(sequential_defn,axiom,
    ! [E1: $i,E2: $i] :
      ( ( sequential @ E1 @ E2 )
    <=> ( ( edge @ E1 )
        & ( edge @ E2 )
        & ( E1 != E2 )
        & ( ( head_of @ E1 )
          = ( tail_of @ E2 ) ) ) ) ).

thf(zip_derived_cl30,plain,
    ! [X0: $i,X1: $i] :
      ( ( sequential @ X0 @ X1 )
      | ( ( head_of @ X0 )
       != ( tail_of @ X1 ) )
      | ( X0 = X1 )
      | ~ ( edge @ X1 )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl487_024,plain,
    on_path @ sk__10 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl464]) ).

thf(zip_derived_cl421_025,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(precedes_defn,axiom,
    ! [P: $i,V1: $i,V2: $i] :
      ( ( path @ V1 @ V2 @ P )
     => ! [E1: $i,E2: $i] :
          ( ( ( on_path @ E1 @ P )
            & ( on_path @ E2 @ P )
            & ( ( sequential @ E1 @ E2 )
              | ? [E3: $i] :
                  ( ( precedes @ E3 @ E2 @ P )
                  & ( sequential @ E1 @ E3 ) ) ) )
         => ( precedes @ E1 @ E2 @ P ) ) ) ).

thf(zip_derived_cl32,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( precedes @ X0 @ X1 @ X2 )
      | ~ ( sequential @ X0 @ X1 )
      | ~ ( on_path @ X1 @ X2 )
      | ~ ( on_path @ X0 @ X2 )
      | ~ ( path @ X3 @ X4 @ X2 ) ),
    inference(cnf,[status(esa)],[precedes_defn]) ).

thf(zip_derived_cl501,plain,
    ! [X0: $i,X1: $i] :
      ( ( precedes @ X1 @ X0 @ sk__12 )
      | ~ ( sequential @ X1 @ X0 )
      | ~ ( on_path @ X0 @ sk__12 )
      | ~ ( on_path @ X1 @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl32]) ).

thf(zip_derived_cl546,plain,
    ! [X0: $i] :
      ( ( precedes @ X0 @ sk__10 @ sk__12 )
      | ~ ( sequential @ X0 @ sk__10 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl501]) ).

thf(zip_derived_cl560,plain,
    ! [X0: $i] :
      ( ~ ( edge @ X0 )
      | ~ ( edge @ sk__10 )
      | ( X0 = sk__10 )
      | ( ( head_of @ X0 )
       != ( tail_of @ sk__10 ) )
      | ( precedes @ X0 @ sk__10 @ sk__12 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl546]) ).

thf(zip_derived_cl488_026,plain,
    edge @ sk__10,
    inference('s_sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl434]) ).

thf(zip_derived_cl561,plain,
    ! [X0: $i] :
      ( ~ ( edge @ X0 )
      | ( X0 = sk__10 )
      | ( ( head_of @ X0 )
       != ( tail_of @ sk__10 ) )
      | ( precedes @ X0 @ sk__10 @ sk__12 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl488]) ).

thf(zip_derived_cl434_027,plain,
    ! [X0: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ( edge @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl421,zip_derived_cl22]) ).

thf(zip_derived_cl751,plain,
    ! [X0: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ( precedes @ X0 @ sk__10 @ sk__12 )
      | ( ( head_of @ X0 )
       != ( tail_of @ sk__10 ) )
      | ( X0 = sk__10 ) ),
    inference(clc,[status(thm)],[zip_derived_cl561,zip_derived_cl434]) ).

thf(zip_derived_cl756,plain,
    ( ( precedes @ sk__11 @ sk__10 @ sk__12 )
    | ( ( head_of @ sk__11 )
     != ( tail_of @ sk__10 ) )
    | ( sk__11 = sk__10 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl461,zip_derived_cl751]) ).

thf(zip_derived_cl2586_028,plain,
    ( ( head_of @ sk__11 )
    = ( tail_of @ sk__10 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2585]) ).

thf(zip_derived_cl2602,plain,
    ( ( precedes @ sk__11 @ sk__10 @ sk__12 )
    | ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ( sk__11 = sk__10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl756,zip_derived_cl2586]) ).

thf(zip_derived_cl2603,plain,
    ( ( sk__11 = sk__10 )
    | ( precedes @ sk__11 @ sk__10 @ sk__12 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2602]) ).

thf(zip_derived_cl63_029,plain,
    precedes @ sk__10 @ sk__11 @ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl44,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( precedes @ X0 @ X1 @ X2 )
      | ~ ( precedes @ X1 @ X0 @ X2 )
      | ~ ( shortest_path @ X3 @ X4 @ X2 ) ),
    inference(cnf,[status(esa)],[shortest_path_properties]) ).

thf(zip_derived_cl424,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( precedes @ sk__11 @ sk__10 @ sk__12 )
      | ~ ( shortest_path @ X1 @ X0 @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl44]) ).

thf(zip_derived_cl2752,plain,
    ! [X0: $i,X1: $i] :
      ( ( sk__11 = sk__10 )
      | ~ ( shortest_path @ X1 @ X0 @ sk__12 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2603,zip_derived_cl424]) ).

thf(zip_derived_cl2754,plain,
    sk__11 = sk__10,
    inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl2752]) ).

thf(zip_derived_cl2795,plain,
    ( ( head_of @ sk__10 )
   != ( head_of @ sk__10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2695,zip_derived_cl2754]) ).

thf(zip_derived_cl2796,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl2795]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : GRA007+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.10  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rHorJPj8pv true
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Sun Aug 27 03:52:44 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.10/0.30  % Running portfolio for 300 s
% 0.10/0.30  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.30  % Number of cores: 8
% 0.10/0.30  % Python version: Python 3.6.8
% 0.10/0.30  % Running in FO mode
% 0.15/0.48  % Total configuration time : 435
% 0.15/0.48  % Estimated wc time : 1092
% 0.15/0.48  % Estimated cpu time (7 cpus) : 156.0
% 0.15/0.55  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.15/0.56  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.15/0.56  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.15/0.56  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.15/0.57  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.15/0.58  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.15/0.61  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 6.93/1.52  % Solved by fo/fo6_bce.sh.
% 6.93/1.52  % BCE start: 64
% 6.93/1.52  % BCE eliminated: 1
% 6.93/1.52  % PE start: 63
% 6.93/1.52  logic: eq
% 6.93/1.52  % PE eliminated: 9
% 6.93/1.52  % done 502 iterations in 0.949s
% 6.93/1.52  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.93/1.52  % SZS output start Refutation
% See solution above
% 6.93/1.52  
% 6.93/1.52  
% 6.93/1.52  % Terminating...
% 7.56/1.60  % Runner terminated.
% 7.56/1.61  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------