TSTP Solution File: GRA008+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 20:43:13 EDT 2024

% Result   : Theorem 0.21s 0.40s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  250 (  27 unt;   0 def)
%            Number of atoms       :  829 ( 149 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  893 ( 314   ~; 314   |; 189   &)
%                                         (  34 <=>;  34  =>;   0  <=;   8 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   42 (  40 usr;  27 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-3 aty)
%            Number of variables   :  421 ( 367   !;  54   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f801,plain,
    $false,
    inference(avatar_sat_refutation,[],[f218,f225,f227,f253,f264,f268,f275,f318,f321,f355,f365,f503,f560,f570,f627,f687,f690,f738,f740,f742,f746,f786,f788,f790,f793]) ).

fof(f793,plain,
    ~ spl19_11,
    inference(avatar_contradiction_clause,[],[f792]) ).

fof(f792,plain,
    ( $false
    | ~ spl19_11 ),
    inference(subsumption_resolution,[],[f791,f197]) ).

fof(f197,plain,
    head_of(sK7) != head_of(sK8),
    inference(subsumption_resolution,[],[f195,f193]) ).

fof(f193,plain,
    edge(sK8),
    inference(resolution,[],[f129,f112]) ).

fof(f112,plain,
    sequential(sK7,sK8),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ( ! [X5] : ~ triangle(sK7,sK8,X5)
    & sequential(sK7,sK8)
    & precedes(sK7,sK8,sK9)
    & shortest_path(sK5,sK6,sK9)
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f40,f75]) ).

fof(f75,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ! [X5] : ~ triangle(X2,X3,X5)
        & sequential(X2,X3)
        & precedes(X2,X3,X4)
        & shortest_path(X0,X1,X4) )
   => ( ! [X5] : ~ triangle(sK7,sK8,X5)
      & sequential(sK7,sK8)
      & precedes(sK7,sK8,sK9)
      & shortest_path(sK5,sK6,sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ! [X5] : ~ triangle(X2,X3,X5)
        & sequential(X2,X3)
        & precedes(X2,X3,X4)
        & shortest_path(X0,X1,X4) )
    & complete ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ! [X5] : ~ triangle(X2,X3,X5)
        & sequential(X2,X3)
        & precedes(X2,X3,X4)
        & shortest_path(X0,X1,X4) )
    & complete ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ( complete
     => ! [X0,X1,X2,X3,X4] :
          ( ( sequential(X2,X3)
            & precedes(X2,X3,X4)
            & shortest_path(X0,X1,X4) )
         => ? [X5] : triangle(X2,X3,X5) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ( complete
     => ! [X1,X2,X6,X7,X3] :
          ( ( sequential(X6,X7)
            & precedes(X6,X7,X3)
            & shortest_path(X1,X2,X3) )
         => ? [X8] : triangle(X6,X7,X8) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ( complete
   => ! [X1,X2,X6,X7,X3] :
        ( ( sequential(X6,X7)
          & precedes(X6,X7,X3)
          & shortest_path(X1,X2,X3) )
       => ? [X8] : triangle(X6,X7,X8) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ~ sequential(X0,X1)
      | edge(X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( sequential(X0,X1)
        | head_of(X0) != tail_of(X1)
        | X0 = X1
        | ~ edge(X1)
        | ~ edge(X0) )
      & ( ( head_of(X0) = tail_of(X1)
          & X0 != X1
          & edge(X1)
          & edge(X0) )
        | ~ sequential(X0,X1) ) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( sequential(X0,X1)
        | head_of(X0) != tail_of(X1)
        | X0 = X1
        | ~ edge(X1)
        | ~ edge(X0) )
      & ( ( head_of(X0) = tail_of(X1)
          & X0 != X1
          & edge(X1)
          & edge(X0) )
        | ~ sequential(X0,X1) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
    <=> ( head_of(X0) = tail_of(X1)
        & X0 != X1
        & edge(X1)
        & edge(X0) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X6,X7] :
      ( sequential(X6,X7)
    <=> ( head_of(X6) = tail_of(X7)
        & X6 != X7
        & edge(X7)
        & edge(X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).

fof(f195,plain,
    ( head_of(sK7) != head_of(sK8)
    | ~ edge(sK8) ),
    inference(superposition,[],[f124,f194]) ).

fof(f194,plain,
    head_of(sK7) = tail_of(sK8),
    inference(resolution,[],[f131,f112]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ~ sequential(X0,X1)
      | head_of(X0) = tail_of(X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f124,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( edge(X0)
     => head_of(X0) != tail_of(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).

fof(f791,plain,
    ( head_of(sK7) = head_of(sK8)
    | ~ spl19_11 ),
    inference(forward_demodulation,[],[f759,f194]) ).

fof(f759,plain,
    ( tail_of(sK8) = head_of(sK8)
    | ~ spl19_11 ),
    inference(superposition,[],[f324,f346]) ).

fof(f346,plain,
    ( sK8 = sK10(sK7,sK8)
    | ~ spl19_11 ),
    inference(avatar_component_clause,[],[f344]) ).

fof(f344,plain,
    ( spl19_11
  <=> sK8 = sK10(sK7,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).

fof(f324,plain,
    head_of(sK8) = tail_of(sK10(sK7,sK8)),
    inference(resolution,[],[f323,f111]) ).

fof(f111,plain,
    precedes(sK7,sK8,sK9),
    inference(cnf_transformation,[],[f76]) ).

fof(f323,plain,
    ! [X0,X1] :
      ( ~ precedes(X0,X1,sK9)
      | head_of(X1) = tail_of(sK10(X0,X1)) ),
    inference(resolution,[],[f188,f110]) ).

fof(f110,plain,
    shortest_path(sK5,sK6,sK9),
    inference(cnf_transformation,[],[f76]) ).

fof(f188,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ precedes(X2,X3,X4)
      | head_of(X3) = tail_of(sK10(X2,X3)) ),
    inference(global_subsumption,[],[f113,f112,f111,f110,f109,f116,f187,f115]) ).

fof(f115,plain,
    ! [X2,X3,X0,X1,X4] :
      ( head_of(X3) = tail_of(sK10(X2,X3))
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4)
      | ~ complete ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ( ! [X0,X1,X2,X3,X4] :
        ( ( tail_of(X2) = head_of(sK10(X2,X3))
          & head_of(X3) = tail_of(sK10(X2,X3))
          & edge(sK10(X2,X3)) )
        | ~ precedes(X2,X3,X4)
        | ~ shortest_path(X0,X1,X4) )
    | ~ complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f42,f77]) ).

fof(f77,plain,
    ! [X2,X3] :
      ( ? [X5] :
          ( tail_of(X2) = head_of(X5)
          & tail_of(X5) = head_of(X3)
          & edge(X5) )
     => ( tail_of(X2) = head_of(sK10(X2,X3))
        & head_of(X3) = tail_of(sK10(X2,X3))
        & edge(sK10(X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ( ! [X0,X1,X2,X3,X4] :
        ( ? [X5] :
            ( tail_of(X2) = head_of(X5)
            & tail_of(X5) = head_of(X3)
            & edge(X5) )
        | ~ precedes(X2,X3,X4)
        | ~ shortest_path(X0,X1,X4) )
    | ~ complete ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ( ! [X0,X1,X2,X3,X4] :
        ( ? [X5] :
            ( tail_of(X2) = head_of(X5)
            & tail_of(X5) = head_of(X3)
            & edge(X5) )
        | ~ precedes(X2,X3,X4)
        | ~ shortest_path(X0,X1,X4) )
    | ~ complete ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ( complete
   => ! [X0,X1,X2,X3,X4] :
        ( ( precedes(X2,X3,X4)
          & shortest_path(X0,X1,X4) )
       => ? [X5] :
            ( tail_of(X2) = head_of(X5)
            & tail_of(X5) = head_of(X3)
            & edge(X5) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ( complete
   => ! [X1,X2,X6,X7,X3] :
        ( ( precedes(X6,X7,X3)
          & shortest_path(X1,X2,X3) )
       => ? [X8] :
            ( tail_of(X6) = head_of(X8)
            & tail_of(X8) = head_of(X7)
            & edge(X8) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).

fof(f187,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ precedes(X2,X3,X4)
      | tail_of(X2) = head_of(sK10(X2,X3)) ),
    inference(global_subsumption,[],[f113,f112,f111,f110,f109,f116]) ).

fof(f116,plain,
    ! [X2,X3,X0,X1,X4] :
      ( tail_of(X2) = head_of(sK10(X2,X3))
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4)
      | ~ complete ),
    inference(cnf_transformation,[],[f78]) ).

fof(f109,plain,
    complete,
    inference(cnf_transformation,[],[f76]) ).

fof(f113,plain,
    ! [X5] : ~ triangle(sK7,sK8,X5),
    inference(cnf_transformation,[],[f76]) ).

fof(f790,plain,
    ( ~ spl19_3
    | spl19_9
    | ~ spl19_11 ),
    inference(avatar_contradiction_clause,[],[f789]) ).

fof(f789,plain,
    ( $false
    | ~ spl19_3
    | spl19_9
    | ~ spl19_11 ),
    inference(subsumption_resolution,[],[f758,f224]) ).

fof(f224,plain,
    ( on_path(sK8,sK9)
    | ~ spl19_3 ),
    inference(avatar_component_clause,[],[f222]) ).

fof(f222,plain,
    ( spl19_3
  <=> on_path(sK8,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).

fof(f758,plain,
    ( ~ on_path(sK8,sK9)
    | spl19_9
    | ~ spl19_11 ),
    inference(superposition,[],[f313,f346]) ).

fof(f313,plain,
    ( ~ on_path(sK10(sK7,sK8),sK9)
    | spl19_9 ),
    inference(avatar_component_clause,[],[f311]) ).

fof(f311,plain,
    ( spl19_9
  <=> on_path(sK10(sK7,sK8),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).

fof(f788,plain,
    ~ spl19_11,
    inference(avatar_contradiction_clause,[],[f787]) ).

fof(f787,plain,
    ( $false
    | ~ spl19_11 ),
    inference(subsumption_resolution,[],[f757,f330]) ).

fof(f330,plain,
    tail_of(sK7) != head_of(sK8),
    inference(superposition,[],[f329,f306]) ).

fof(f306,plain,
    tail_of(sK7) = head_of(sK10(sK7,sK8)),
    inference(resolution,[],[f305,f111]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( ~ precedes(X0,X1,sK9)
      | tail_of(X0) = head_of(sK10(X0,X1)) ),
    inference(resolution,[],[f187,f110]) ).

fof(f329,plain,
    head_of(sK10(sK7,sK8)) != head_of(sK8),
    inference(subsumption_resolution,[],[f327,f255]) ).

fof(f255,plain,
    edge(sK10(sK7,sK8)),
    inference(resolution,[],[f254,f111]) ).

fof(f254,plain,
    ! [X0,X1] :
      ( ~ precedes(X0,X1,sK9)
      | edge(sK10(X0,X1)) ),
    inference(resolution,[],[f189,f110]) ).

fof(f189,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ shortest_path(X0,X1,X4)
      | ~ precedes(X2,X3,X4)
      | edge(sK10(X2,X3)) ),
    inference(global_subsumption,[],[f113,f112,f111,f110,f109,f116,f187,f115,f188,f114]) ).

fof(f114,plain,
    ! [X2,X3,X0,X1,X4] :
      ( edge(sK10(X2,X3))
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4)
      | ~ complete ),
    inference(cnf_transformation,[],[f78]) ).

fof(f327,plain,
    ( head_of(sK10(sK7,sK8)) != head_of(sK8)
    | ~ edge(sK10(sK7,sK8)) ),
    inference(superposition,[],[f124,f324]) ).

fof(f757,plain,
    ( tail_of(sK7) = head_of(sK8)
    | ~ spl19_11 ),
    inference(superposition,[],[f306,f346]) ).

fof(f786,plain,
    ~ spl19_11,
    inference(avatar_contradiction_clause,[],[f785]) ).

fof(f785,plain,
    ( $false
    | ~ spl19_11 ),
    inference(trivial_inequality_removal,[],[f760]) ).

fof(f760,plain,
    ( head_of(sK8) != head_of(sK8)
    | ~ spl19_11 ),
    inference(superposition,[],[f329,f346]) ).

fof(f746,plain,
    ( spl19_11
    | spl19_12 ),
    inference(avatar_contradiction_clause,[],[f745]) ).

fof(f745,plain,
    ( $false
    | spl19_11
    | spl19_12 ),
    inference(subsumption_resolution,[],[f714,f112]) ).

fof(f714,plain,
    ( ~ sequential(sK7,sK8)
    | spl19_11
    | spl19_12 ),
    inference(superposition,[],[f349,f705]) ).

fof(f705,plain,
    ( sK7 = sK10(sK7,sK8)
    | spl19_11 ),
    inference(subsumption_resolution,[],[f704,f192]) ).

fof(f192,plain,
    edge(sK7),
    inference(resolution,[],[f128,f112]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ~ sequential(X0,X1)
      | edge(X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f704,plain,
    ( sK7 = sK10(sK7,sK8)
    | ~ edge(sK7)
    | spl19_11 ),
    inference(trivial_inequality_removal,[],[f703]) ).

fof(f703,plain,
    ( tail_of(sK7) != tail_of(sK7)
    | sK7 = sK10(sK7,sK8)
    | ~ edge(sK7)
    | spl19_11 ),
    inference(resolution,[],[f701,f336]) ).

fof(f336,plain,
    ! [X0] :
      ( sequential(sK10(sK7,sK8),X0)
      | tail_of(X0) != tail_of(sK7)
      | sK10(sK7,sK8) = X0
      | ~ edge(X0) ),
    inference(subsumption_resolution,[],[f332,f255]) ).

fof(f332,plain,
    ! [X0] :
      ( tail_of(X0) != tail_of(sK7)
      | sequential(sK10(sK7,sK8),X0)
      | sK10(sK7,sK8) = X0
      | ~ edge(X0)
      | ~ edge(sK10(sK7,sK8)) ),
    inference(superposition,[],[f132,f306]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( head_of(X0) != tail_of(X1)
      | sequential(X0,X1)
      | X0 = X1
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f701,plain,
    ( ~ sequential(sK10(sK7,sK8),sK7)
    | spl19_11 ),
    inference(subsumption_resolution,[],[f700,f193]) ).

fof(f700,plain,
    ( ~ sequential(sK10(sK7,sK8),sK7)
    | ~ edge(sK8)
    | spl19_11 ),
    inference(subsumption_resolution,[],[f699,f345]) ).

fof(f345,plain,
    ( sK8 != sK10(sK7,sK8)
    | spl19_11 ),
    inference(avatar_component_clause,[],[f344]) ).

fof(f699,plain,
    ( ~ sequential(sK10(sK7,sK8),sK7)
    | sK8 = sK10(sK7,sK8)
    | ~ edge(sK8) ),
    inference(trivial_inequality_removal,[],[f697]) ).

fof(f697,plain,
    ( ~ sequential(sK10(sK7,sK8),sK7)
    | head_of(sK8) != head_of(sK8)
    | sK8 = sK10(sK7,sK8)
    | ~ edge(sK8) ),
    inference(resolution,[],[f694,f339]) ).

fof(f339,plain,
    ! [X0] :
      ( sequential(X0,sK10(sK7,sK8))
      | head_of(X0) != head_of(sK8)
      | sK10(sK7,sK8) = X0
      | ~ edge(X0) ),
    inference(subsumption_resolution,[],[f335,f255]) ).

fof(f335,plain,
    ! [X0] :
      ( head_of(X0) != head_of(sK8)
      | sequential(X0,sK10(sK7,sK8))
      | sK10(sK7,sK8) = X0
      | ~ edge(sK10(sK7,sK8))
      | ~ edge(X0) ),
    inference(superposition,[],[f132,f324]) ).

fof(f694,plain,
    ! [X0] :
      ( ~ sequential(sK8,X0)
      | ~ sequential(X0,sK7) ),
    inference(subsumption_resolution,[],[f692,f112]) ).

fof(f692,plain,
    ! [X0] :
      ( ~ sequential(X0,sK7)
      | ~ sequential(sK8,X0)
      | ~ sequential(sK7,sK8) ),
    inference(resolution,[],[f667,f113]) ).

fof(f667,plain,
    ! [X2,X0,X1] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1) ),
    inference(subsumption_resolution,[],[f666,f128]) ).

fof(f666,plain,
    ! [X2,X0,X1] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1)
      | ~ edge(X0) ),
    inference(subsumption_resolution,[],[f665,f128]) ).

fof(f665,plain,
    ! [X2,X0,X1] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1)
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(subsumption_resolution,[],[f160,f128]) ).

fof(f160,plain,
    ! [X2,X0,X1] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1)
      | ~ edge(X2)
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1)
      | ~ edge(X2)
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( triangle(X0,X1,X2)
      | ~ sequential(X2,X0)
      | ~ sequential(X1,X2)
      | ~ sequential(X0,X1)
      | ~ edge(X2)
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( sequential(X2,X0)
        & sequential(X1,X2)
        & sequential(X0,X1)
        & edge(X2)
        & edge(X1)
        & edge(X0) )
     => triangle(X0,X1,X2) ),
    inference(unused_predicate_definition_removal,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( triangle(X0,X1,X2)
    <=> ( sequential(X2,X0)
        & sequential(X1,X2)
        & sequential(X0,X1)
        & edge(X2)
        & edge(X1)
        & edge(X0) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X6,X7,X8] :
      ( triangle(X6,X7,X8)
    <=> ( sequential(X8,X6)
        & sequential(X7,X8)
        & sequential(X6,X7)
        & edge(X8)
        & edge(X7)
        & edge(X6) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).

fof(f349,plain,
    ( ~ sequential(sK10(sK7,sK8),sK8)
    | spl19_12 ),
    inference(avatar_component_clause,[],[f348]) ).

fof(f348,plain,
    ( spl19_12
  <=> sequential(sK10(sK7,sK8),sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).

fof(f742,plain,
    spl19_11,
    inference(avatar_contradiction_clause,[],[f741]) ).

fof(f741,plain,
    ( $false
    | spl19_11 ),
    inference(subsumption_resolution,[],[f709,f330]) ).

fof(f709,plain,
    ( tail_of(sK7) = head_of(sK8)
    | spl19_11 ),
    inference(superposition,[],[f324,f705]) ).

fof(f740,plain,
    ( ~ spl19_2
    | spl19_9
    | spl19_11 ),
    inference(avatar_contradiction_clause,[],[f739]) ).

fof(f739,plain,
    ( $false
    | ~ spl19_2
    | spl19_9
    | spl19_11 ),
    inference(subsumption_resolution,[],[f708,f217]) ).

fof(f217,plain,
    ( on_path(sK7,sK9)
    | ~ spl19_2 ),
    inference(avatar_component_clause,[],[f215]) ).

fof(f215,plain,
    ( spl19_2
  <=> on_path(sK7,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).

fof(f708,plain,
    ( ~ on_path(sK7,sK9)
    | spl19_9
    | spl19_11 ),
    inference(superposition,[],[f313,f705]) ).

fof(f738,plain,
    ( spl19_11
    | spl19_13 ),
    inference(avatar_contradiction_clause,[],[f737]) ).

fof(f737,plain,
    ( $false
    | spl19_11
    | spl19_13 ),
    inference(subsumption_resolution,[],[f707,f354]) ).

fof(f354,plain,
    ( head_of(sK7) != tail_of(sK7)
    | spl19_13 ),
    inference(avatar_component_clause,[],[f352]) ).

fof(f352,plain,
    ( spl19_13
  <=> head_of(sK7) = tail_of(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_13])]) ).

fof(f707,plain,
    ( head_of(sK7) = tail_of(sK7)
    | spl19_11 ),
    inference(superposition,[],[f306,f705]) ).

fof(f690,plain,
    ( ~ spl19_3
    | spl19_25 ),
    inference(avatar_contradiction_clause,[],[f689]) ).

fof(f689,plain,
    ( $false
    | ~ spl19_3
    | spl19_25 ),
    inference(subsumption_resolution,[],[f688,f224]) ).

fof(f688,plain,
    ( ~ on_path(sK8,sK9)
    | spl19_25 ),
    inference(resolution,[],[f685,f229]) ).

fof(f229,plain,
    ! [X0] :
      ( in_path(head_of(X0),sK9)
      | ~ on_path(X0,sK9) ),
    inference(resolution,[],[f172,f202]) ).

fof(f202,plain,
    path(sK5,sK6,sK9),
    inference(resolution,[],[f200,f110]) ).

fof(f200,plain,
    ! [X2,X0,X1] :
      ( ~ shortest_path(X0,X1,X2)
      | path(X0,X1,X2) ),
    inference(resolution,[],[f166,f161]) ).

fof(f161,plain,
    ! [X2,X0,X1] :
      ( ~ sP4(X0,X1,X2)
      | path(X2,X1,X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ( ~ less_or_equal(length_of(X0),length_of(sK17(X0,X1,X2)))
          & path(X2,X1,sK17(X0,X1,X2)) )
        | X1 = X2
        | ~ path(X2,X1,X0) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X0),length_of(X4))
              | ~ path(X2,X1,X4) )
          & X1 != X2
          & path(X2,X1,X0) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f103,f104]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ less_or_equal(length_of(X0),length_of(X3))
          & path(X2,X1,X3) )
     => ( ~ less_or_equal(length_of(X0),length_of(sK17(X0,X1,X2)))
        & path(X2,X1,sK17(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ? [X3] :
            ( ~ less_or_equal(length_of(X0),length_of(X3))
            & path(X2,X1,X3) )
        | X1 = X2
        | ~ path(X2,X1,X0) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X0),length_of(X4))
              | ~ path(X2,X1,X4) )
          & X1 != X2
          & path(X2,X1,X0) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(rectify,[],[f102]) ).

fof(f102,plain,
    ! [X2,X1,X0] :
      ( ( sP4(X2,X1,X0)
        | ? [X3] :
            ( ~ less_or_equal(length_of(X2),length_of(X3))
            & path(X0,X1,X3) )
        | X0 = X1
        | ~ path(X0,X1,X2) )
      & ( ( ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X0,X1,X3) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ sP4(X2,X1,X0) ) ),
    inference(flattening,[],[f101]) ).

fof(f101,plain,
    ! [X2,X1,X0] :
      ( ( sP4(X2,X1,X0)
        | ? [X3] :
            ( ~ less_or_equal(length_of(X2),length_of(X3))
            & path(X0,X1,X3) )
        | X0 = X1
        | ~ path(X0,X1,X2) )
      & ( ( ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X0,X1,X3) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ sP4(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X2,X1,X0] :
      ( sP4(X2,X1,X0)
    <=> ( ! [X3] :
            ( less_or_equal(length_of(X2),length_of(X3))
            | ~ path(X0,X1,X3) )
        & X0 != X1
        & path(X0,X1,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f166,plain,
    ! [X2,X0,X1] :
      ( sP4(X2,X1,X0)
      | ~ shortest_path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X0,X1,X2)
        | ~ sP4(X2,X1,X0) )
      & ( sP4(X2,X1,X0)
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( shortest_path(X0,X1,X2)
    <=> sP4(X2,X1,X0) ),
    inference(definition_folding,[],[f59,f73]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( shortest_path(X0,X1,X2)
    <=> ( ! [X3] :
            ( less_or_equal(length_of(X2),length_of(X3))
            | ~ path(X0,X1,X3) )
        & X0 != X1
        & path(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( shortest_path(X0,X1,X2)
    <=> ( ! [X3] :
            ( path(X0,X1,X3)
           => less_or_equal(length_of(X2),length_of(X3)) )
        & X0 != X1
        & path(X0,X1,X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X2,X9] :
      ( shortest_path(X1,X2,X9)
    <=> ( ! [X3] :
            ( path(X1,X2,X3)
           => less_or_equal(length_of(X9),length_of(X3)) )
        & X1 != X2
        & path(X1,X2,X9) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).

fof(f172,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X0,X1,X2)
      | ~ on_path(X3,X2)
      | in_path(head_of(X3),X2) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2,X3] :
      ( ( in_path(tail_of(X3),X2)
        & in_path(head_of(X3),X2)
        & edge(X3) )
      | ~ on_path(X3,X2)
      | ~ path(X0,X1,X2) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2,X3] :
      ( ( in_path(tail_of(X3),X2)
        & in_path(head_of(X3),X2)
        & edge(X3) )
      | ~ on_path(X3,X2)
      | ~ path(X0,X1,X2) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( ( on_path(X3,X2)
        & path(X0,X1,X2) )
     => ( in_path(tail_of(X3),X2)
        & in_path(head_of(X3),X2)
        & edge(X3) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X2,X3,X0] :
      ( ( on_path(X0,X3)
        & path(X1,X2,X3) )
     => ( in_path(tail_of(X0),X3)
        & in_path(head_of(X0),X3)
        & edge(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).

fof(f685,plain,
    ( ~ in_path(head_of(sK8),sK9)
    | spl19_25 ),
    inference(avatar_component_clause,[],[f684]) ).

fof(f684,plain,
    ( spl19_25
  <=> in_path(head_of(sK8),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).

fof(f687,plain,
    ( ~ spl19_24
    | spl19_25 ),
    inference(avatar_split_clause,[],[f603,f684,f680]) ).

fof(f680,plain,
    ( spl19_24
  <=> on_path(sK12(tail_of(sK7),path_cons(sK10(sK7,sK8),empty),head_of(sK8)),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_24])]) ).

fof(f603,plain,
    ( in_path(head_of(sK8),sK9)
    | ~ on_path(sK12(tail_of(sK7),path_cons(sK10(sK7,sK8),empty),head_of(sK8)),sK9) ),
    inference(superposition,[],[f230,f486]) ).

fof(f486,plain,
    head_of(sK8) = tail_of(sK12(tail_of(sK7),path_cons(sK10(sK7,sK8),empty),head_of(sK8))),
    inference(resolution,[],[f444,f209]) ).

fof(f209,plain,
    ! [X2,X0,X1] :
      ( ~ path(X2,X0,X1)
      | tail_of(sK12(X0,X1,X2)) = X2 ),
    inference(resolution,[],[f136,f145]) ).

fof(f145,plain,
    ! [X2,X0,X1] :
      ( sP2(X1,X2,X0)
      | ~ path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X1,X2,X0)
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(definition_folding,[],[f49,f69,f68]) ).

fof(f68,plain,
    ! [X2,X3,X1] :
      ( ( ( path_cons(X3,empty) = X2
          & head_of(X3) = X1 )
      <~> ? [X4] :
            ( path_cons(X3,X4) = X2
            & path(head_of(X3),X1,X4) ) )
      | ~ sP1(X2,X3,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f69,plain,
    ! [X1,X2,X0] :
      ( ? [X3] :
          ( sP1(X2,X3,X1)
          & tail_of(X3) = X0
          & edge(X3) )
      | ~ sP2(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( ( ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 )
            <~> ? [X4] :
                  ( path_cons(X3,X4) = X2
                  & path(head_of(X3),X1,X4) ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( path(X0,X1,X2)
     => ( ? [X3] :
            ( ( ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 )
            <~> ? [X4] :
                  ( path_cons(X3,X4) = X2
                  & path(head_of(X3),X1,X4) ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X2,X3] :
      ( path(X1,X2,X3)
     => ( ? [X0] :
            ( ( ( path_cons(X0,empty) = X3
                & head_of(X0) = X2 )
            <~> ? [X4] :
                  ( path_cons(X0,X4) = X3
                  & path(head_of(X0),X2,X4) ) )
            & tail_of(X0) = X1
            & edge(X0) )
        & vertex(X2)
        & vertex(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_properties) ).

fof(f136,plain,
    ! [X2,X0,X1] :
      ( ~ sP2(X0,X1,X2)
      | tail_of(sK12(X0,X1,X2)) = X2 ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X1,sK12(X0,X1,X2),X0)
        & tail_of(sK12(X0,X1,X2)) = X2
        & edge(sK12(X0,X1,X2)) )
      | ~ sP2(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f87,f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( sP1(X1,X3,X0)
          & tail_of(X3) = X2
          & edge(X3) )
     => ( sP1(X1,sK12(X0,X1,X2),X0)
        & tail_of(sK12(X0,X1,X2)) = X2
        & edge(sK12(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( sP1(X1,X3,X0)
          & tail_of(X3) = X2
          & edge(X3) )
      | ~ sP2(X0,X1,X2) ),
    inference(rectify,[],[f86]) ).

fof(f86,plain,
    ! [X1,X2,X0] :
      ( ? [X3] :
          ( sP1(X2,X3,X1)
          & tail_of(X3) = X0
          & edge(X3) )
      | ~ sP2(X1,X2,X0) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f444,plain,
    path(head_of(sK8),tail_of(sK7),path_cons(sK10(sK7,sK8),empty)),
    inference(forward_demodulation,[],[f443,f306]) ).

fof(f443,plain,
    path(head_of(sK8),head_of(sK10(sK7,sK8)),path_cons(sK10(sK7,sK8),empty)),
    inference(subsumption_resolution,[],[f439,f255]) ).

fof(f439,plain,
    ( path(head_of(sK8),head_of(sK10(sK7,sK8)),path_cons(sK10(sK7,sK8),empty))
    | ~ edge(sK10(sK7,sK8)) ),
    inference(superposition,[],[f423,f324]) ).

fof(f423,plain,
    ! [X3] :
      ( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
      | ~ edge(X3) ),
    inference(subsumption_resolution,[],[f422,f126]) ).

fof(f126,plain,
    ! [X0] :
      ( vertex(tail_of(X0))
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ( vertex(tail_of(X0))
        & vertex(head_of(X0)) )
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( edge(X0)
     => ( vertex(tail_of(X0))
        & vertex(head_of(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',edge_ends_are_vertices) ).

fof(f422,plain,
    ! [X3] :
      ( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
      | ~ edge(X3)
      | ~ vertex(tail_of(X3)) ),
    inference(subsumption_resolution,[],[f185,f125]) ).

fof(f125,plain,
    ! [X0] :
      ( vertex(head_of(X0))
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f185,plain,
    ! [X3] :
      ( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
      | ~ edge(X3)
      | ~ vertex(head_of(X3))
      | ~ vertex(tail_of(X3)) ),
    inference(equality_resolution,[],[f184]) ).

fof(f184,plain,
    ! [X3,X0] :
      ( path(X0,head_of(X3),path_cons(X3,empty))
      | tail_of(X3) != X0
      | ~ edge(X3)
      | ~ vertex(head_of(X3))
      | ~ vertex(X0) ),
    inference(equality_resolution,[],[f183]) ).

fof(f183,plain,
    ! [X3,X0,X1] :
      ( path(X0,X1,path_cons(X3,empty))
      | head_of(X3) != X1
      | tail_of(X3) != X0
      | ~ edge(X3)
      | ~ vertex(X1)
      | ~ vertex(X0) ),
    inference(equality_resolution,[],[f154]) ).

fof(f154,plain,
    ! [X2,X3,X0,X1] :
      ( path(X0,X1,X2)
      | path_cons(X3,empty) != X2
      | head_of(X3) != X1
      | tail_of(X3) != X0
      | ~ edge(X3)
      | ~ vertex(X1)
      | ~ vertex(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1,X2] :
      ( path(X0,X1,X2)
      | ! [X3] :
          ( ( ! [X4] :
                ( path_cons(X3,X4) != X2
                | ~ path(head_of(X3),X1,X4) )
            & ( path_cons(X3,empty) != X2
              | head_of(X3) != X1 ) )
          | tail_of(X3) != X0
          | ~ edge(X3) )
      | ~ vertex(X1)
      | ~ vertex(X0) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( path(X0,X1,X2)
      | ! [X3] :
          ( ( ! [X4] :
                ( path_cons(X3,X4) != X2
                | ~ path(head_of(X3),X1,X4) )
            & ( path_cons(X3,empty) != X2
              | head_of(X3) != X1 ) )
          | tail_of(X3) != X0
          | ~ edge(X3) )
      | ~ vertex(X1)
      | ~ vertex(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( ? [X3] :
            ( ( ? [X4] :
                  ( path_cons(X3,X4) = X2
                  & path(head_of(X3),X1,X4) )
              | ( path_cons(X3,empty) = X2
                & head_of(X3) = X1 ) )
            & tail_of(X3) = X0
            & edge(X3) )
        & vertex(X1)
        & vertex(X0) )
     => path(X0,X1,X2) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X2,X3] :
      ( ( ? [X0] :
            ( ( ? [X4] :
                  ( path_cons(X0,X4) = X3
                  & path(head_of(X0),X2,X4) )
              | ( path_cons(X0,empty) = X3
                & head_of(X0) = X2 ) )
            & tail_of(X0) = X1
            & edge(X0) )
        & vertex(X2)
        & vertex(X1) )
     => path(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_defn) ).

fof(f230,plain,
    ! [X0] :
      ( in_path(tail_of(X0),sK9)
      | ~ on_path(X0,sK9) ),
    inference(resolution,[],[f173,f202]) ).

fof(f173,plain,
    ! [X2,X3,X0,X1] :
      ( ~ path(X0,X1,X2)
      | ~ on_path(X3,X2)
      | in_path(tail_of(X3),X2) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f627,plain,
    ( ~ spl19_22
    | spl19_23 ),
    inference(avatar_split_clause,[],[f613,f624,f620]) ).

fof(f620,plain,
    ( spl19_22
  <=> on_path(sK8,path_cons(sK10(sK7,sK8),empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_22])]) ).

fof(f624,plain,
    ( spl19_23
  <=> in_path(head_of(sK7),path_cons(sK10(sK7,sK8),empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_23])]) ).

fof(f613,plain,
    ( in_path(head_of(sK7),path_cons(sK10(sK7,sK8),empty))
    | ~ on_path(sK8,path_cons(sK10(sK7,sK8),empty)) ),
    inference(superposition,[],[f485,f194]) ).

fof(f485,plain,
    ! [X0] :
      ( in_path(tail_of(X0),path_cons(sK10(sK7,sK8),empty))
      | ~ on_path(X0,path_cons(sK10(sK7,sK8),empty)) ),
    inference(resolution,[],[f444,f173]) ).

fof(f570,plain,
    ( ~ spl19_20
    | spl19_21 ),
    inference(avatar_split_clause,[],[f492,f567,f563]) ).

fof(f563,plain,
    ( spl19_20
  <=> on_path(sK12(sK6,sK9,sK5),path_cons(sK8,empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_20])]) ).

fof(f567,plain,
    ( spl19_21
  <=> in_path(sK5,path_cons(sK8,empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_21])]) ).

fof(f492,plain,
    ( in_path(sK5,path_cons(sK8,empty))
    | ~ on_path(sK12(sK6,sK9,sK5),path_cons(sK8,empty)) ),
    inference(superposition,[],[f458,f241]) ).

fof(f241,plain,
    sK5 = tail_of(sK12(sK6,sK9,sK5)),
    inference(resolution,[],[f209,f202]) ).

fof(f458,plain,
    ! [X0] :
      ( in_path(tail_of(X0),path_cons(sK8,empty))
      | ~ on_path(X0,path_cons(sK8,empty)) ),
    inference(resolution,[],[f441,f173]) ).

fof(f441,plain,
    path(head_of(sK7),head_of(sK8),path_cons(sK8,empty)),
    inference(subsumption_resolution,[],[f437,f193]) ).

fof(f437,plain,
    ( path(head_of(sK7),head_of(sK8),path_cons(sK8,empty))
    | ~ edge(sK8) ),
    inference(superposition,[],[f423,f194]) ).

fof(f560,plain,
    ( ~ spl19_18
    | spl19_19 ),
    inference(avatar_split_clause,[],[f489,f557,f553]) ).

fof(f553,plain,
    ( spl19_18
  <=> on_path(sK10(sK7,sK8),path_cons(sK8,empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).

fof(f557,plain,
    ( spl19_19
  <=> in_path(tail_of(sK7),path_cons(sK8,empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_19])]) ).

fof(f489,plain,
    ( in_path(tail_of(sK7),path_cons(sK8,empty))
    | ~ on_path(sK10(sK7,sK8),path_cons(sK8,empty)) ),
    inference(superposition,[],[f457,f306]) ).

fof(f457,plain,
    ! [X0] :
      ( in_path(head_of(X0),path_cons(sK8,empty))
      | ~ on_path(X0,path_cons(sK8,empty)) ),
    inference(resolution,[],[f441,f172]) ).

fof(f503,plain,
    ( ~ spl19_16
    | spl19_17 ),
    inference(avatar_split_clause,[],[f491,f500,f496]) ).

fof(f496,plain,
    ( spl19_16
  <=> on_path(sK8,path_cons(sK8,empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_16])]) ).

fof(f500,plain,
    ( spl19_17
  <=> in_path(head_of(sK7),path_cons(sK8,empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_17])]) ).

fof(f491,plain,
    ( in_path(head_of(sK7),path_cons(sK8,empty))
    | ~ on_path(sK8,path_cons(sK8,empty)) ),
    inference(superposition,[],[f458,f194]) ).

fof(f365,plain,
    ( spl19_14
    | spl19_15 ),
    inference(avatar_split_clause,[],[f356,f362,f358]) ).

fof(f358,plain,
    ( spl19_14
  <=> number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_14])]) ).

fof(f362,plain,
    ( spl19_15
  <=> on_path(sK15(sK9),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_15])]) ).

fof(f356,plain,
    ( on_path(sK15(sK9),sK9)
    | number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) ),
    inference(resolution,[],[f156,f202]) ).

fof(f156,plain,
    ! [X2,X0,X1] :
      ( ~ path(X1,X2,X0)
      | on_path(sK15(X0),X0)
      | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ( ! [X5] : ~ triangle(sK15(X0),sK16(X0),X5)
        & sequential(sK15(X0),sK16(X0))
        & on_path(sK16(X0),X0)
        & on_path(sK15(X0),X0) )
      | ~ path(X1,X2,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f56,f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
     => ( ! [X5] : ~ triangle(sK15(X0),sK16(X0),X5)
        & sequential(sK15(X0),sK16(X0))
        & on_path(sK16(X0),X0)
        & on_path(sK15(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4] :
            ( ( sequential(X3,X4)
              & on_path(X4,X0)
              & on_path(X3,X0) )
           => ? [X5] : triangle(X3,X4,X5) )
        & path(X1,X2,X0) )
     => number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3,X1,X2] :
      ( ( ! [X6,X7] :
            ( ( sequential(X6,X7)
              & on_path(X7,X3)
              & on_path(X6,X3) )
           => ? [X8] : triangle(X6,X7,X8) )
        & path(X1,X2,X3) )
     => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).

fof(f355,plain,
    ( spl19_11
    | spl19_12
    | ~ spl19_13 ),
    inference(avatar_split_clause,[],[f342,f352,f348,f344]) ).

fof(f342,plain,
    ( head_of(sK7) != tail_of(sK7)
    | sequential(sK10(sK7,sK8),sK8)
    | sK8 = sK10(sK7,sK8) ),
    inference(subsumption_resolution,[],[f340,f255]) ).

fof(f340,plain,
    ( head_of(sK7) != tail_of(sK7)
    | sequential(sK10(sK7,sK8),sK8)
    | sK8 = sK10(sK7,sK8)
    | ~ edge(sK10(sK7,sK8)) ),
    inference(superposition,[],[f337,f306]) ).

fof(f337,plain,
    ! [X0] :
      ( head_of(X0) != head_of(sK7)
      | sequential(X0,sK8)
      | sK8 = X0
      | ~ edge(X0) ),
    inference(subsumption_resolution,[],[f333,f193]) ).

fof(f333,plain,
    ! [X0] :
      ( head_of(X0) != head_of(sK7)
      | sequential(X0,sK8)
      | sK8 = X0
      | ~ edge(sK8)
      | ~ edge(X0) ),
    inference(superposition,[],[f132,f194]) ).

fof(f321,plain,
    ( ~ spl19_2
    | spl19_10 ),
    inference(avatar_contradiction_clause,[],[f320]) ).

fof(f320,plain,
    ( $false
    | ~ spl19_2
    | spl19_10 ),
    inference(subsumption_resolution,[],[f319,f217]) ).

fof(f319,plain,
    ( ~ on_path(sK7,sK9)
    | spl19_10 ),
    inference(resolution,[],[f316,f230]) ).

fof(f316,plain,
    ( ~ in_path(tail_of(sK7),sK9)
    | spl19_10 ),
    inference(avatar_component_clause,[],[f315]) ).

fof(f315,plain,
    ( spl19_10
  <=> in_path(tail_of(sK7),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).

fof(f318,plain,
    ( ~ spl19_9
    | spl19_10 ),
    inference(avatar_split_clause,[],[f308,f315,f311]) ).

fof(f308,plain,
    ( in_path(tail_of(sK7),sK9)
    | ~ on_path(sK10(sK7,sK8),sK9) ),
    inference(superposition,[],[f229,f306]) ).

fof(f275,plain,
    ( spl19_1
    | spl19_8 ),
    inference(avatar_split_clause,[],[f270,f272,f212]) ).

fof(f212,plain,
    ( spl19_1
  <=> ! [X0,X1] : ~ path(X0,X1,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).

fof(f272,plain,
    ( spl19_8
  <=> sP3(sK9,sK8,sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).

fof(f270,plain,
    ! [X0,X1] :
      ( sP3(sK9,sK8,sK7)
      | ~ path(X0,X1,sK9) ),
    inference(resolution,[],[f151,f111]) ).

fof(f151,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | sP3(X0,X4,X3)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( sP3(X0,X4,X3)
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(definition_folding,[],[f50,f71]) ).

fof(f71,plain,
    ! [X0,X4,X3] :
      ( ( sequential(X3,X4)
      <~> ? [X5] :
            ( precedes(X5,X4,X0)
            & sequential(X3,X5) ) )
      | ~ sP3(X0,X4,X3) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( sequential(X3,X4)
            <~> ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) ) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( path(X1,X2,X0)
     => ! [X3,X4] :
          ( precedes(X3,X4,X0)
         => ( ( sequential(X3,X4)
            <~> ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) ) )
            & on_path(X4,X0)
            & on_path(X3,X0) ) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X3,X1,X2] :
      ( path(X1,X2,X3)
     => ! [X6,X7] :
          ( precedes(X6,X7,X3)
         => ( ( sequential(X6,X7)
            <~> ? [X8] :
                  ( precedes(X8,X7,X3)
                  & sequential(X6,X8) ) )
            & on_path(X7,X3)
            & on_path(X6,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).

fof(f268,plain,
    spl19_6,
    inference(avatar_contradiction_clause,[],[f267]) ).

fof(f267,plain,
    ( $false
    | spl19_6 ),
    inference(subsumption_resolution,[],[f266,f202]) ).

fof(f266,plain,
    ( ~ path(sK5,sK6,sK9)
    | spl19_6 ),
    inference(resolution,[],[f265,f145]) ).

fof(f265,plain,
    ( ~ sP2(sK6,sK9,sK5)
    | spl19_6 ),
    inference(resolution,[],[f259,f135]) ).

fof(f135,plain,
    ! [X2,X0,X1] :
      ( edge(sK12(X0,X1,X2))
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f259,plain,
    ( ~ edge(sK12(sK6,sK9,sK5))
    | spl19_6 ),
    inference(avatar_component_clause,[],[f257]) ).

fof(f257,plain,
    ( spl19_6
  <=> edge(sK12(sK6,sK9,sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).

fof(f264,plain,
    ( ~ spl19_6
    | ~ spl19_7 ),
    inference(avatar_split_clause,[],[f243,f261,f257]) ).

fof(f261,plain,
    ( spl19_7
  <=> sK5 = head_of(sK12(sK6,sK9,sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).

fof(f243,plain,
    ( sK5 != head_of(sK12(sK6,sK9,sK5))
    | ~ edge(sK12(sK6,sK9,sK5)) ),
    inference(superposition,[],[f124,f241]) ).

fof(f253,plain,
    ( ~ spl19_4
    | spl19_5 ),
    inference(avatar_split_clause,[],[f242,f250,f246]) ).

fof(f246,plain,
    ( spl19_4
  <=> on_path(sK12(sK6,sK9,sK5),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).

fof(f250,plain,
    ( spl19_5
  <=> in_path(sK5,sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).

fof(f242,plain,
    ( in_path(sK5,sK9)
    | ~ on_path(sK12(sK6,sK9,sK5),sK9) ),
    inference(superposition,[],[f230,f241]) ).

fof(f227,plain,
    ~ spl19_1,
    inference(avatar_contradiction_clause,[],[f226]) ).

fof(f226,plain,
    ( $false
    | ~ spl19_1 ),
    inference(resolution,[],[f213,f202]) ).

fof(f213,plain,
    ( ! [X0,X1] : ~ path(X0,X1,sK9)
    | ~ spl19_1 ),
    inference(avatar_component_clause,[],[f212]) ).

fof(f225,plain,
    ( spl19_1
    | spl19_3 ),
    inference(avatar_split_clause,[],[f220,f222,f212]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( on_path(sK8,sK9)
      | ~ path(X0,X1,sK9) ),
    inference(resolution,[],[f150,f111]) ).

fof(f150,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | on_path(X4,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f218,plain,
    ( spl19_1
    | spl19_2 ),
    inference(avatar_split_clause,[],[f210,f215,f212]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( on_path(sK7,sK9)
      | ~ path(X0,X1,sK9) ),
    inference(resolution,[],[f149,f111]) ).

fof(f149,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X4,X0)
      | on_path(X3,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f72]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GRA008+2 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 18 12:42:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (15344)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37  % (15348)WARNING: value z3 for option sas not known
% 0.21/0.37  % (15345)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37  % (15349)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37  % (15348)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.37  % (15350)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.37  % (15352)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.37  % (15351)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.37  TRYING [1]
% 0.21/0.38  TRYING [1]
% 0.21/0.38  % (15347)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38  TRYING [2]
% 0.21/0.38  TRYING [2]
% 0.21/0.38  TRYING [3]
% 0.21/0.38  TRYING [3]
% 0.21/0.40  % (15348)First to succeed.
% 0.21/0.40  % (15348)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15344"
% 0.21/0.40  % (15348)Refutation found. Thanks to Tanya!
% 0.21/0.40  % SZS status Theorem for theBenchmark
% 0.21/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41  % (15348)------------------------------
% 0.21/0.41  % (15348)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41  % (15348)Termination reason: Refutation
% 0.21/0.41  
% 0.21/0.41  % (15348)Memory used [KB]: 1256
% 0.21/0.41  % (15348)Time elapsed: 0.035 s
% 0.21/0.41  % (15348)Instructions burned: 55 (million)
% 0.21/0.41  % (15344)Success in time 0.04 s
%------------------------------------------------------------------------------