TSTP Solution File: GRA008+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : GRA008+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fiKLKVqwEa true

% Computer : n025.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 129.44s 19.27s
% Output   : Refutation 129.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  191 (  47 unt;  20 typ;   0 def)
%            Number of atoms       :  602 ( 226 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives : 1959 ( 249   ~; 375   |;  35   &;1279   @)
%                                         (   3 <=>;  16  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;   7 con; 0-3 aty)
%            Number of variables   :  273 (   0   ^; 266   !;   7   ?; 273   :)

% Comments : 
%------------------------------------------------------------------------------
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__9_type,type,
    sk__9: $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(sk__type,type,
    sk_: $i > $i > $i ).

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

thf(sk__8_type,type,
    sk__8: $i ).

thf(triangle_type,type,
    triangle: $i > $i > $i > $o ).

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

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

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

thf(sk__10_type,type,
    sk__10: $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(sequential_is_triangle,conjecture,
    ( complete
   => ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
        ( ( ( shortest_path @ V1 @ V2 @ P )
          & ( precedes @ E1 @ E2 @ P )
          & ( sequential @ E1 @ E2 ) )
       => ? [E3: $i] : ( triangle @ E1 @ E2 @ 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 )
            & ( sequential @ E1 @ E2 ) )
         => ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ),
    inference('cnf.neg',[status(esa)],[sequential_is_triangle]) ).

thf(zip_derived_cl61,plain,
    sequential @ sk__10 @ sk__11,
    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_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_cl59,plain,
    complete,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl94,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ ( sk_ @ X0 @ X1 ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl59]) ).

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_cl59_001,plain,
    complete,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl103,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X0
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl59]) ).

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_cl317,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0
       != ( tail_of @ X1 ) )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X2 )
      | ( X0 = X2 )
      | ( X2
        = ( head_of @ ( sk_ @ X2 @ X0 ) ) )
      | ~ ( edge @ ( sk_ @ X2 @ X0 ) )
      | ~ ( edge @ X1 )
      | ( ( sk_ @ X2 @ X0 )
        = X1 )
      | ( sequential @ ( sk_ @ X2 @ X0 ) @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl103,zip_derived_cl30]) ).

thf(zip_derived_cl20464,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0 = X1 )
      | ( sequential @ ( sk_ @ X1 @ X0 ) @ X2 )
      | ( ( sk_ @ X1 @ X0 )
        = X2 )
      | ~ ( edge @ X2 )
      | ( X1
        = ( head_of @ ( sk_ @ X1 @ X0 ) ) )
      | ( X0 = X1 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( X0
       != ( tail_of @ X2 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl94,zip_derived_cl317]) ).

thf(zip_derived_cl20465,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0
       != ( tail_of @ X2 ) )
      | ( X1
        = ( head_of @ ( sk_ @ X1 @ X0 ) ) )
      | ~ ( edge @ X2 )
      | ( ( sk_ @ X1 @ X0 )
        = X2 )
      | ( sequential @ ( sk_ @ X1 @ X0 ) @ X2 )
      | ( X0 = X1 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl20464]) ).

thf(zip_derived_cl21424,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ ( tail_of @ X0 ) )
      | ~ ( vertex @ X1 )
      | ( ( tail_of @ X0 )
        = X1 )
      | ( sequential @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) @ X0 )
      | ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
        = X0 )
      | ~ ( edge @ X0 )
      | ( X1
        = ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl20465]) ).

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

thf(zip_derived_cl2,plain,
    ! [X0: $i] :
      ( ( vertex @ ( tail_of @ X0 ) )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[edge_ends_are_vertices]) ).

thf(zip_derived_cl41085,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) )
      | ~ ( edge @ X0 )
      | ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
        = X0 )
      | ( sequential @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) @ X0 )
      | ( ( tail_of @ X0 )
        = X1 )
      | ~ ( vertex @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl21424,zip_derived_cl2]) ).

thf(zip_derived_cl26,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ X0 )
      | ~ ( sequential @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl41496,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X1 )
      | ( ( tail_of @ X0 )
        = X1 )
      | ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
        = X0 )
      | ~ ( edge @ X0 )
      | ( X1
        = ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) )
      | ( edge @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41085,zip_derived_cl26]) ).

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

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

thf(zip_derived_cl62_002,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_cl89,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(zip_derived_cl63_003,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_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_cl127,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( path @ X1 @ X0 @ sk__12 )
      | ( on_path @ sk__10 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl37]) ).

thf(zip_derived_cl128,plain,
    on_path @ sk__10 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl127]) ).

thf(zip_derived_cl89_004,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('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_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_cl151,plain,
    ! [X0: $i] :
      ( ( in_path @ ( tail_of @ X0 ) @ sk__12 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl20]) ).

thf(zip_derived_cl152,plain,
    in_path @ ( tail_of @ sk__10 ) @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl128,zip_derived_cl151]) ).

thf(zip_derived_cl89_005,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('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_cl93,plain,
    ! [X0: $i] :
      ( ( vertex @ X0 )
      | ~ ( in_path @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl25]) ).

thf(zip_derived_cl154,plain,
    vertex @ ( tail_of @ sk__10 ),
    inference('sup-',[status(thm)],[zip_derived_cl152,zip_derived_cl93]) ).

thf(zip_derived_cl5,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
        = ( tail_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_cl59_006,plain,
    complete,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl98,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X0
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl59]) ).

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_cl59_007,plain,
    complete,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl73,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl59]) ).

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_cl433,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0
       != ( tail_of @ X1 ) )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X2 )
      | ( X0 = X2 )
      | ( X2
        = ( tail_of @ ( sk_ @ X2 @ X0 ) ) )
      | ~ ( shortest_path @ X5 @ X4 @ X3 )
      | ~ ( precedes @ X1 @ X6 @ X3 )
      | ( ( head_of @ ( sk_ @ X2 @ X0 ) )
       != ( head_of @ X6 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl43]) ).

thf(zip_derived_cl19372,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X0
       != ( head_of @ X1 ) )
      | ~ ( vertex @ X2 )
      | ~ ( vertex @ X0 )
      | ( X2 = X0 )
      | ( X0
        = ( tail_of @ ( sk_ @ X0 @ X2 ) ) )
      | ~ ( precedes @ X4 @ X1 @ X3 )
      | ~ ( shortest_path @ X6 @ X5 @ X3 )
      | ( X0
        = ( tail_of @ ( sk_ @ X0 @ X2 ) ) )
      | ( X2 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X2 )
      | ( X2
       != ( tail_of @ X4 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl98,zip_derived_cl433]) ).

thf(zip_derived_cl19394,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
      ( ( X2
       != ( tail_of @ X4 ) )
      | ~ ( shortest_path @ X6 @ X5 @ X3 )
      | ~ ( precedes @ X4 @ X1 @ X3 )
      | ( X0
        = ( tail_of @ ( sk_ @ X0 @ X2 ) ) )
      | ( X2 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X2 )
      | ( X0
       != ( head_of @ X1 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl19372]) ).

thf(zip_derived_cl19576,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( X0
       != ( head_of @ X1 ) )
      | ~ ( vertex @ ( tail_of @ X2 ) )
      | ~ ( vertex @ X0 )
      | ( ( tail_of @ X2 )
        = X0 )
      | ( X0
        = ( tail_of @ ( sk_ @ X0 @ ( tail_of @ X2 ) ) ) )
      | ~ ( precedes @ X2 @ X1 @ X3 )
      | ~ ( shortest_path @ X5 @ X4 @ X3 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl19394]) ).

thf(zip_derived_cl19648,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ~ ( shortest_path @ X2 @ X1 @ X0 )
      | ~ ( precedes @ sk__10 @ X3 @ X0 )
      | ( X4
        = ( tail_of @ ( sk_ @ X4 @ ( tail_of @ sk__10 ) ) ) )
      | ( ( tail_of @ sk__10 )
        = X4 )
      | ~ ( vertex @ X4 )
      | ( X4
       != ( head_of @ X3 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl154,zip_derived_cl19576]) ).

thf(zip_derived_cl19677,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X0
       != ( head_of @ sk__11 ) )
      | ~ ( vertex @ X0 )
      | ( ( tail_of @ sk__10 )
        = X0 )
      | ( X0
        = ( tail_of @ ( sk_ @ X0 @ ( tail_of @ sk__10 ) ) ) )
      | ~ ( shortest_path @ X2 @ X1 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl19648]) ).

thf(zip_derived_cl19678,plain,
    ! [X0: $i] :
      ( ( X0
        = ( tail_of @ ( sk_ @ X0 @ ( tail_of @ sk__10 ) ) ) )
      | ( ( tail_of @ sk__10 )
        = X0 )
      | ~ ( vertex @ X0 )
      | ( X0
       != ( head_of @ sk__11 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl19677]) ).

thf(zip_derived_cl19679,plain,
    ( ~ ( vertex @ ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl19678]) ).

thf(zip_derived_cl89_008,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

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

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_cl124,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( path @ X1 @ X0 @ sk__12 )
      | ( on_path @ sk__11 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl36]) ).

thf(zip_derived_cl125,plain,
    on_path @ sk__11 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl124]) ).

thf(zip_derived_cl89_010,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

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_cl158,plain,
    ! [X0: $i] :
      ( ( in_path @ ( head_of @ X0 ) @ sk__12 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl21]) ).

thf(zip_derived_cl160,plain,
    in_path @ ( head_of @ sk__11 ) @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl125,zip_derived_cl158]) ).

thf(zip_derived_cl93_011,plain,
    ! [X0: $i] :
      ( ( vertex @ X0 )
      | ~ ( in_path @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl25]) ).

thf(zip_derived_cl162,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('sup-',[status(thm)],[zip_derived_cl160,zip_derived_cl93]) ).

thf(zip_derived_cl19680,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl19679,zip_derived_cl162]) ).

thf(zip_derived_cl103_012,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X0
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl59]) ).

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_cl108,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
       != ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( X1 = X0 )
      | ( X1
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ~ ( edge @ ( sk_ @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl103,zip_derived_cl0]) ).

thf(zip_derived_cl94_013,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ ( sk_ @ X0 @ X1 ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl59]) ).

thf(zip_derived_cl2094,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( head_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0
       != ( tail_of @ ( sk_ @ X0 @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl108,zip_derived_cl94]) ).

thf(zip_derived_cl19952,plain,
    ( ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ~ ( vertex @ ( tail_of @ sk__10 ) )
    | ~ ( vertex @ ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl19680,zip_derived_cl2094]) ).

thf(zip_derived_cl154_014,plain,
    vertex @ ( tail_of @ sk__10 ),
    inference('sup-',[status(thm)],[zip_derived_cl152,zip_derived_cl93]) ).

thf(zip_derived_cl162_015,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('sup-',[status(thm)],[zip_derived_cl160,zip_derived_cl93]) ).

thf(zip_derived_cl20011,plain,
    ( ( ( head_of @ sk__11 )
     != ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl19952,zip_derived_cl154,zip_derived_cl162]) ).

thf(zip_derived_cl20012,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl20011]) ).

thf(zip_derived_cl42000,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( edge @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ~ ( edge @ sk__10 )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ~ ( vertex @ ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl41496,zip_derived_cl20012]) ).

thf(zip_derived_cl61_016,plain,
    sequential @ sk__10 @ sk__11,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl26_017,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ X0 )
      | ~ ( sequential @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl66,plain,
    edge @ sk__10,
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl26]) ).

thf(zip_derived_cl162_018,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('sup-',[status(thm)],[zip_derived_cl160,zip_derived_cl93]) ).

thf(zip_derived_cl42085,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( edge @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl42000,zip_derived_cl66,zip_derived_cl162]) ).

thf(zip_derived_cl42086,plain,
    ( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( edge @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl42085]) ).

thf(zip_derived_cl41085_019,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
        = ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) )
      | ~ ( edge @ X0 )
      | ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
        = X0 )
      | ( sequential @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) @ X0 )
      | ( ( tail_of @ X0 )
        = X1 )
      | ~ ( vertex @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl21424,zip_derived_cl2]) ).

thf(zip_derived_cl0_020,plain,
    ! [X0: $i] :
      ( ( ( head_of @ X0 )
       != ( tail_of @ X0 ) )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[no_loops]) ).

thf(zip_derived_cl41086,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
       != ( tail_of @ ( sk_ @ X0 @ ( tail_of @ X1 ) ) ) )
      | ~ ( vertex @ X0 )
      | ( ( tail_of @ X1 )
        = X0 )
      | ( sequential @ ( sk_ @ X0 @ ( tail_of @ X1 ) ) @ X1 )
      | ( ( sk_ @ X0 @ ( tail_of @ X1 ) )
        = X1 )
      | ~ ( edge @ X1 )
      | ~ ( edge @ ( sk_ @ X0 @ ( tail_of @ X1 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl41085,zip_derived_cl0]) ).

thf(zip_derived_cl54112,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ~ ( edge @ sk__10 )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ~ ( vertex @ ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
     != ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl42086,zip_derived_cl41086]) ).

thf(zip_derived_cl66_021,plain,
    edge @ sk__10,
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl26]) ).

thf(zip_derived_cl162_022,plain,
    vertex @ ( head_of @ sk__11 ),
    inference('sup-',[status(thm)],[zip_derived_cl160,zip_derived_cl93]) ).

thf(zip_derived_cl54147,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
     != ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl54112,zip_derived_cl66,zip_derived_cl162]) ).

thf(zip_derived_cl54148,plain,
    ( ( ( head_of @ sk__11 )
     != ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
    | ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl54147]) ).

thf(zip_derived_cl19680_023,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl19679,zip_derived_cl162]) ).

thf(zip_derived_cl55187,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 ) ),
    inference(clc,[status(thm)],[zip_derived_cl54148,zip_derived_cl19680]) ).

thf(zip_derived_cl94_024,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ ( sk_ @ X0 @ X1 ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl59]) ).

thf(zip_derived_cl73_025,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ( X1 = X0 )
      | ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl59]) ).

thf(zip_derived_cl30_026,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_cl320,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( head_of @ X2 )
       != X0 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( X1 = X0 )
      | ( X1
        = ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
      | ~ ( edge @ X2 )
      | ~ ( edge @ ( sk_ @ X0 @ X1 ) )
      | ( X2
        = ( sk_ @ X0 @ X1 ) )
      | ( sequential @ X2 @ ( sk_ @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl30]) ).

thf(zip_derived_cl20847,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( vertex @ X0 )
      | ~ ( vertex @ X1 )
      | ( X0 = X1 )
      | ( sequential @ X2 @ ( sk_ @ X1 @ X0 ) )
      | ( X2
        = ( sk_ @ X1 @ X0 ) )
      | ~ ( edge @ X2 )
      | ( X0
        = ( tail_of @ ( sk_ @ X1 @ X0 ) ) )
      | ( X0 = X1 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 )
      | ( ( head_of @ X2 )
       != X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl94,zip_derived_cl320]) ).

thf(zip_derived_cl20848,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( head_of @ X2 )
       != X1 )
      | ( X0
        = ( tail_of @ ( sk_ @ X1 @ X0 ) ) )
      | ~ ( edge @ X2 )
      | ( X2
        = ( sk_ @ X1 @ X0 ) )
      | ( sequential @ X2 @ ( sk_ @ X1 @ X0 ) )
      | ( X0 = X1 )
      | ~ ( vertex @ X1 )
      | ~ ( vertex @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl20847]) ).

thf(zip_derived_cl21803,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( vertex @ X0 )
      | ~ ( vertex @ ( head_of @ X1 ) )
      | ( X0
        = ( head_of @ X1 ) )
      | ( sequential @ X1 @ ( sk_ @ ( head_of @ X1 ) @ X0 ) )
      | ( X1
        = ( sk_ @ ( head_of @ X1 ) @ X0 ) )
      | ~ ( edge @ X1 )
      | ( X0
        = ( tail_of @ ( sk_ @ ( head_of @ X1 ) @ X0 ) ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl20848]) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i] :
      ( ( vertex @ ( head_of @ X0 ) )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[edge_ends_are_vertices]) ).

thf(zip_derived_cl52493,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
        = ( tail_of @ ( sk_ @ ( head_of @ X1 ) @ X0 ) ) )
      | ~ ( edge @ X1 )
      | ( X1
        = ( sk_ @ ( head_of @ X1 ) @ X0 ) )
      | ( sequential @ X1 @ ( sk_ @ ( head_of @ X1 ) @ X0 ) )
      | ( X0
        = ( head_of @ X1 ) )
      | ~ ( vertex @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl21803,zip_derived_cl1]) ).

thf(zip_derived_cl61_027,plain,
    sequential @ sk__10 @ sk__11,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(triangle_defn,axiom,
    ! [E1: $i,E2: $i,E3: $i] :
      ( ( triangle @ E1 @ E2 @ E3 )
    <=> ( ( edge @ E1 )
        & ( edge @ E2 )
        & ( edge @ E3 )
        & ( sequential @ E1 @ E2 )
        & ( sequential @ E2 @ E3 )
        & ( sequential @ E3 @ E1 ) ) ) ).

thf(zip_derived_cl51,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( triangle @ X0 @ X1 @ X2 )
      | ~ ( sequential @ X2 @ X0 )
      | ~ ( sequential @ X1 @ X2 )
      | ~ ( sequential @ X0 @ X1 )
      | ~ ( edge @ X2 )
      | ~ ( edge @ X1 )
      | ~ ( edge @ X0 ) ),
    inference(cnf,[status(esa)],[triangle_defn]) ).

thf(zip_derived_cl26_028,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ X0 )
      | ~ ( sequential @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl780,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( edge @ X0 )
      | ~ ( edge @ X1 )
      | ~ ( sequential @ X0 @ X1 )
      | ~ ( sequential @ X1 @ X2 )
      | ~ ( sequential @ X2 @ X0 )
      | ( triangle @ X0 @ X1 @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl51,zip_derived_cl26]) ).

thf(zip_derived_cl26_029,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ X0 )
      | ~ ( sequential @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl781,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( triangle @ X0 @ X1 @ X2 )
      | ~ ( sequential @ X2 @ X0 )
      | ~ ( sequential @ X1 @ X2 )
      | ~ ( sequential @ X0 @ X1 )
      | ~ ( edge @ X1 ) ),
    inference(clc,[status(thm)],[zip_derived_cl780,zip_derived_cl26]) ).

thf(zip_derived_cl26_030,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ X0 )
      | ~ ( sequential @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl782,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( sequential @ X0 @ X1 )
      | ~ ( sequential @ X1 @ X2 )
      | ~ ( sequential @ X2 @ X0 )
      | ( triangle @ X0 @ X1 @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl781,zip_derived_cl26]) ).

thf(zip_derived_cl783,plain,
    ! [X0: $i] :
      ( ( triangle @ sk__10 @ sk__11 @ X0 )
      | ~ ( sequential @ X0 @ sk__10 )
      | ~ ( sequential @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl782]) ).

thf(zip_derived_cl60,plain,
    ! [X0: $i] :
      ~ ( triangle @ sk__10 @ sk__11 @ X0 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl788,plain,
    ! [X0: $i] :
      ( ~ ( sequential @ sk__11 @ X0 )
      | ~ ( sequential @ X0 @ sk__10 ) ),
    inference(clc,[status(thm)],[zip_derived_cl783,zip_derived_cl60]) ).

thf(zip_derived_cl52571,plain,
    ! [X0: $i] :
      ( ~ ( vertex @ X0 )
      | ( X0
        = ( head_of @ sk__11 ) )
      | ( sk__11
        = ( sk_ @ ( head_of @ sk__11 ) @ X0 ) )
      | ~ ( edge @ sk__11 )
      | ( X0
        = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) ) )
      | ~ ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) @ sk__10 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl52493,zip_derived_cl788]) ).

thf(zip_derived_cl61_031,plain,
    sequential @ sk__10 @ sk__11,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl27,plain,
    ! [X0: $i,X1: $i] :
      ( ( edge @ X0 )
      | ~ ( sequential @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl67,plain,
    edge @ sk__11,
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl27]) ).

thf(zip_derived_cl52642,plain,
    ! [X0: $i] :
      ( ~ ( vertex @ X0 )
      | ( X0
        = ( head_of @ sk__11 ) )
      | ( sk__11
        = ( sk_ @ ( head_of @ sk__11 ) @ X0 ) )
      | ( X0
        = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) ) )
      | ~ ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) @ sk__10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl52571,zip_derived_cl67]) ).

thf(zip_derived_cl55192,plain,
    ( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
    | ( sk__11
      = ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ~ ( vertex @ ( tail_of @ sk__10 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl55187,zip_derived_cl52642]) ).

thf(zip_derived_cl154_032,plain,
    vertex @ ( tail_of @ sk__10 ),
    inference('sup-',[status(thm)],[zip_derived_cl152,zip_derived_cl93]) ).

thf(zip_derived_cl55194,plain,
    ( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
    | ( sk__11
      = ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl55192,zip_derived_cl154]) ).

thf(zip_derived_cl55195,plain,
    ( ( sk__11
      = ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ( ( tail_of @ sk__10 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl55194]) ).

thf(zip_derived_cl19680_033,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl19679,zip_derived_cl162]) ).

thf(zip_derived_cl55820,plain,
    ( ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( sk__11
      = ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl55195,zip_derived_cl19680]) ).

thf(zip_derived_cl56053,plain,
    ( ( sk__11
      = ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl55820]) ).

thf(zip_derived_cl20012_034,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl20011]) ).

thf(zip_derived_cl56401,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) )
    | ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl56053,zip_derived_cl20012]) ).

thf(zip_derived_cl57099,plain,
    ( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
      = sk__10 )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl56401]) ).

thf(zip_derived_cl19680_035,plain,
    ( ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( head_of @ sk__11 )
      = ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl19679,zip_derived_cl162]) ).

thf(zip_derived_cl57451,plain,
    ( ( ( head_of @ sk__11 )
      = ( tail_of @ sk__10 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) )
    | ( ( tail_of @ sk__10 )
      = ( head_of @ sk__11 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl57099,zip_derived_cl19680]) ).

thf(zip_derived_cl58144,plain,
    ( ( head_of @ sk__11 )
    = ( tail_of @ sk__10 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl57451]) ).

thf(zip_derived_cl30_036,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_cl58305,plain,
    ! [X0: $i] :
      ( ( ( tail_of @ sk__10 )
       != ( tail_of @ X0 ) )
      | ~ ( edge @ sk__11 )
      | ~ ( edge @ X0 )
      | ( sk__11 = X0 )
      | ( sequential @ sk__11 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl58144,zip_derived_cl30]) ).

thf(zip_derived_cl67_037,plain,
    edge @ sk__11,
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl27]) ).

thf(zip_derived_cl58716,plain,
    ! [X0: $i] :
      ( ( ( tail_of @ sk__10 )
       != ( tail_of @ X0 ) )
      | ~ ( edge @ X0 )
      | ( sk__11 = X0 )
      | ( sequential @ sk__11 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl58305,zip_derived_cl67]) ).

thf(zip_derived_cl62948,plain,
    ( ( sequential @ sk__11 @ sk__10 )
    | ( sk__11 = sk__10 )
    | ~ ( edge @ sk__10 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl58716]) ).

thf(zip_derived_cl66_038,plain,
    edge @ sk__10,
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl26]) ).

thf(zip_derived_cl62949,plain,
    ( ( sequential @ sk__11 @ sk__10 )
    | ( sk__11 = sk__10 ) ),
    inference(demod,[status(thm)],[zip_derived_cl62948,zip_derived_cl66]) ).

thf(zip_derived_cl125_039,plain,
    on_path @ sk__11 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl124]) ).

thf(zip_derived_cl89_040,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('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_cl526,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( on_path @ X0 @ sk__12 )
      | ~ ( on_path @ X1 @ sk__12 )
      | ~ ( sequential @ X0 @ X1 )
      | ( precedes @ X0 @ X1 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl32]) ).

thf(zip_derived_cl605,plain,
    ! [X0: $i] :
      ( ( precedes @ sk__11 @ X0 @ sk__12 )
      | ~ ( sequential @ sk__11 @ X0 )
      | ~ ( on_path @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl125,zip_derived_cl526]) ).

thf(zip_derived_cl62958,plain,
    ( ( sk__11 = sk__10 )
    | ~ ( on_path @ sk__10 @ sk__12 )
    | ( precedes @ sk__11 @ sk__10 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62949,zip_derived_cl605]) ).

thf(zip_derived_cl128_041,plain,
    on_path @ sk__10 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl127]) ).

thf(zip_derived_cl62961,plain,
    ( ( sk__11 = sk__10 )
    | ( precedes @ sk__11 @ sk__10 @ sk__12 ) ),
    inference(demod,[status(thm)],[zip_derived_cl62958,zip_derived_cl128]) ).

thf(zip_derived_cl61_042,plain,
    sequential @ sk__10 @ sk__11,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl128_043,plain,
    on_path @ sk__10 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl127]) ).

thf(zip_derived_cl89_044,plain,
    path @ sk__8 @ sk__9 @ sk__12,
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl38]) ).

thf(zip_derived_cl31,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ( precedes @ X0 @ X1 @ X2 )
      | ~ ( sequential @ X0 @ X3 )
      | ~ ( precedes @ X3 @ X1 @ X2 )
      | ~ ( on_path @ X1 @ X2 )
      | ~ ( on_path @ X0 @ X2 )
      | ~ ( path @ X4 @ X5 @ X2 ) ),
    inference(cnf,[status(esa)],[precedes_defn]) ).

thf(zip_derived_cl36_045,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_cl935,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
      ( ~ ( path @ X4 @ X5 @ X2 )
      | ~ ( on_path @ X0 @ X2 )
      | ~ ( precedes @ X3 @ X1 @ X2 )
      | ~ ( sequential @ X0 @ X3 )
      | ( precedes @ X0 @ X1 @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl31,zip_derived_cl36]) ).

thf(zip_derived_cl939,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( precedes @ X1 @ X0 @ sk__12 )
      | ~ ( sequential @ X1 @ X2 )
      | ~ ( precedes @ X2 @ X0 @ sk__12 )
      | ~ ( on_path @ X1 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl935]) ).

thf(zip_derived_cl1027,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( precedes @ X1 @ X0 @ sk__12 )
      | ~ ( sequential @ sk__10 @ X1 )
      | ( precedes @ sk__10 @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl128,zip_derived_cl939]) ).

thf(zip_derived_cl1029,plain,
    ! [X0: $i] :
      ( ( precedes @ sk__10 @ X0 @ sk__12 )
      | ~ ( precedes @ sk__11 @ X0 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl1027]) ).

thf(zip_derived_cl62980,plain,
    ( ( sk__11 = sk__10 )
    | ( precedes @ sk__10 @ sk__10 @ sk__12 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl62961,zip_derived_cl1029]) ).

thf(zip_derived_cl62_046,plain,
    shortest_path @ sk__8 @ sk__9 @ 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_cl87,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ~ ( shortest_path @ X3 @ X2 @ X0 )
      | ~ ( precedes @ X1 @ X1 @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl88,plain,
    ! [X0: $i] :
      ~ ( precedes @ X0 @ X0 @ sk__12 ),
    inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl87]) ).

thf(zip_derived_cl62993,plain,
    sk__11 = sk__10,
    inference(clc,[status(thm)],[zip_derived_cl62980,zip_derived_cl88]) ).

thf(zip_derived_cl28,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1 != X0 )
      | ~ ( sequential @ X1 @ X0 ) ),
    inference(cnf,[status(esa)],[sequential_defn]) ).

thf(zip_derived_cl64,plain,
    ! [X0: $i] :
      ~ ( sequential @ X0 @ X0 ),
    inference(eq_res,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl62995,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl61,zip_derived_cl62993,zip_derived_cl64]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRA008+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.fiKLKVqwEa true
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 04:01:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.36  % Running in FO mode
% 0.21/0.63  % Total configuration time : 435
% 0.21/0.63  % Estimated wc time : 1092
% 0.21/0.63  % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.70  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.71  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.79  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 129.44/19.27  % Solved by fo/fo5.sh.
% 129.44/19.27  % done 2781 iterations in 18.471s
% 129.44/19.27  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 129.44/19.27  % SZS output start Refutation
% See solution above
% 129.44/19.27  
% 129.44/19.27  
% 129.44/19.27  % Terminating...
% 130.36/19.39  % Runner terminated.
% 130.36/19.41  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------