TSTP Solution File: GRA008+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRA008+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n013.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 : Fri May  3 02:19:23 EDT 2024

% Result   : Theorem 61.86s 9.24s
% Output   : CNFRefutation 61.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  256 (  14 unt;   0 def)
%            Number of atoms       : 1133 ( 387 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives : 1449 ( 572   ~; 595   |; 230   &)
%                                         (   7 <=>;  35  =>;   0  <=;  10 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   16 (  14 usr;   2 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-3 aty)
%            Number of variables   :  619 (  57 sgn 298   !;  60   ?)

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

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(f3,axiom,
    ( complete
   => ! [X1,X2] :
        ( ( X1 != X2
          & vertex(X2)
          & vertex(X1) )
       => ? [X0] :
            ( ( ( tail_of(X0) = X2
                & head_of(X0) = X1 )
            <~> ( tail_of(X0) = X1
                & head_of(X0) = X2 ) )
            & edge(X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_properties) ).

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(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(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(f9,axiom,
    ! [X3,X1,X2] :
      ( path(X1,X2,X3)
     => ! [X6,X7] :
          ( ( ( ? [X8] :
                  ( precedes(X8,X7,X3)
                  & sequential(X6,X8) )
              | sequential(X6,X7) )
            & on_path(X7,X3)
            & on_path(X6,X3) )
         => precedes(X6,X7,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).

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(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(f12,axiom,
    ! [X1,X2,X6,X7,X3] :
      ( ( precedes(X6,X7,X3)
        & shortest_path(X1,X2,X3) )
     => ( ~ precedes(X7,X6,X3)
        & ~ ? [X8] :
              ( head_of(X8) = head_of(X7)
              & tail_of(X8) = tail_of(X6) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).

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(f18,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(f19,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,[],[f18]) ).

fof(f20,plain,
    ( complete
   => ! [X0,X1] :
        ( ( X0 != X1
          & vertex(X1)
          & vertex(X0) )
       => ? [X2] :
            ( ( ( tail_of(X2) = X1
                & head_of(X2) = X0 )
            <~> ( tail_of(X2) = X0
                & head_of(X2) = X1 ) )
            & edge(X2) ) ) ),
    inference(rectify,[],[f3]) ).

fof(f21,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(f22,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(f25,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
    <=> ( head_of(X0) = tail_of(X1)
        & X0 != X1
        & edge(X1)
        & edge(X0) ) ),
    inference(rectify,[],[f8]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( path(X1,X2,X0)
     => ! [X3,X4] :
          ( ( ( ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
         => precedes(X3,X4,X0) ) ),
    inference(rectify,[],[f9]) ).

fof(f27,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(f28,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(f29,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( precedes(X2,X3,X4)
        & shortest_path(X0,X1,X4) )
     => ( ~ precedes(X3,X2,X4)
        & ~ ? [X5] :
              ( head_of(X3) = head_of(X5)
              & tail_of(X2) = tail_of(X5) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f30,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(f35,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,[],[f19]) ).

fof(f36,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,[],[f30]) ).

fof(f37,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f38,plain,
    ! [X0] :
      ( ( vertex(tail_of(X0))
        & vertex(head_of(X0)) )
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f39,plain,
    ( ! [X0,X1] :
        ( ? [X2] :
            ( ( ( tail_of(X2) = X1
                & head_of(X2) = X0 )
            <~> ( tail_of(X2) = X0
                & head_of(X2) = X1 ) )
            & edge(X2) )
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
    | ~ complete ),
    inference(ennf_transformation,[],[f20]) ).

fof(f40,plain,
    ( ! [X0,X1] :
        ( ? [X2] :
            ( ( ( tail_of(X2) = X1
                & head_of(X2) = X0 )
            <~> ( tail_of(X2) = X0
                & head_of(X2) = X1 ) )
            & edge(X2) )
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
    | ~ complete ),
    inference(flattening,[],[f39]) ).

fof(f41,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,[],[f21]) ).

fof(f42,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,[],[f41]) ).

fof(f43,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,[],[f22]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( precedes(X3,X4,X0)
          | ( ! [X5] :
                ( ~ precedes(X5,X4,X0)
                | ~ sequential(X3,X5) )
            & ~ sequential(X3,X4) )
          | ~ on_path(X4,X0)
          | ~ on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( precedes(X3,X4,X0)
          | ( ! [X5] :
                ( ~ precedes(X5,X4,X0)
                | ~ sequential(X3,X5) )
            & ~ sequential(X3,X4) )
          | ~ on_path(X4,X0)
          | ~ on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f48]) ).

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,[],[f27]) ).

fof(f51,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,[],[f28]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ precedes(X3,X2,X4)
        & ! [X5] :
            ( head_of(X3) != head_of(X5)
            | tail_of(X2) != tail_of(X5) ) )
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ~ precedes(X3,X2,X4)
        & ! [X5] :
            ( head_of(X3) != head_of(X5)
            | tail_of(X2) != tail_of(X5) ) )
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(flattening,[],[f52]) ).

fof(f54,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,[],[f36]) ).

fof(f55,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,[],[f54]) ).

fof(f60,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,[],[f35]) ).

fof(f61,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,[],[f60]) ).

fof(f62,plain,
    ( ! [X0,X1] :
        ( ? [X2] :
            ( ( tail_of(X2) != X0
              | head_of(X2) != X1
              | tail_of(X2) != X1
              | head_of(X2) != X0 )
            & ( ( tail_of(X2) = X0
                & head_of(X2) = X1 )
              | ( tail_of(X2) = X1
                & head_of(X2) = X0 ) )
            & edge(X2) )
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
    | ~ complete ),
    inference(nnf_transformation,[],[f40]) ).

fof(f63,plain,
    ( ! [X0,X1] :
        ( ? [X2] :
            ( ( tail_of(X2) != X0
              | head_of(X2) != X1
              | tail_of(X2) != X1
              | head_of(X2) != X0 )
            & ( ( tail_of(X2) = X0
                & head_of(X2) = X1 )
              | ( tail_of(X2) = X1
                & head_of(X2) = X0 ) )
            & edge(X2) )
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
    | ~ complete ),
    inference(flattening,[],[f62]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( tail_of(X2) != X0
            | head_of(X2) != X1
            | tail_of(X2) != X1
            | head_of(X2) != X0 )
          & ( ( tail_of(X2) = X0
              & head_of(X2) = X1 )
            | ( tail_of(X2) = X1
              & head_of(X2) = X0 ) )
          & edge(X2) )
     => ( ( tail_of(sK0(X0,X1)) != X0
          | head_of(sK0(X0,X1)) != X1
          | tail_of(sK0(X0,X1)) != X1
          | head_of(sK0(X0,X1)) != X0 )
        & ( ( tail_of(sK0(X0,X1)) = X0
            & head_of(sK0(X0,X1)) = X1 )
          | ( tail_of(sK0(X0,X1)) = X1
            & head_of(sK0(X0,X1)) = X0 ) )
        & edge(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ( ! [X0,X1] :
        ( ( ( tail_of(sK0(X0,X1)) != X0
            | head_of(sK0(X0,X1)) != X1
            | tail_of(sK0(X0,X1)) != X1
            | head_of(sK0(X0,X1)) != X0 )
          & ( ( tail_of(sK0(X0,X1)) = X0
              & head_of(sK0(X0,X1)) = X1 )
            | ( tail_of(sK0(X0,X1)) = X1
              & head_of(sK0(X0,X1)) = X0 ) )
          & edge(sK0(X0,X1)) )
        | X0 = X1
        | ~ vertex(X1)
        | ~ vertex(X0) )
    | ~ complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f63,f64]) ).

fof(f66,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 )
            & ( ? [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(nnf_transformation,[],[f43]) ).

fof(f67,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 )
            & ( ? [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(flattening,[],[f66]) ).

fof(f68,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 )
            & ( ? [X5] :
                  ( path_cons(X3,X5) = X2
                  & path(head_of(X3),X1,X5) )
              | ( 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,[],[f67]) ).

fof(f69,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 )
          & ( ? [X5] :
                ( path_cons(X3,X5) = X2
                & path(head_of(X3),X1,X5) )
            | ( path_cons(X3,empty) = X2
              & head_of(X3) = X1 ) )
          & tail_of(X3) = X0
          & edge(X3) )
     => ( ( ! [X4] :
              ( path_cons(sK1(X0,X1,X2),X4) != X2
              | ~ path(head_of(sK1(X0,X1,X2)),X1,X4) )
          | path_cons(sK1(X0,X1,X2),empty) != X2
          | head_of(sK1(X0,X1,X2)) != X1 )
        & ( ? [X5] :
              ( path_cons(sK1(X0,X1,X2),X5) = X2
              & path(head_of(sK1(X0,X1,X2)),X1,X5) )
          | ( path_cons(sK1(X0,X1,X2),empty) = X2
            & head_of(sK1(X0,X1,X2)) = X1 ) )
        & tail_of(sK1(X0,X1,X2)) = X0
        & edge(sK1(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( path_cons(sK1(X0,X1,X2),X5) = X2
          & path(head_of(sK1(X0,X1,X2)),X1,X5) )
     => ( path_cons(sK1(X0,X1,X2),sK2(X0,X1,X2)) = X2
        & path(head_of(sK1(X0,X1,X2)),X1,sK2(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ( ( ! [X4] :
              ( path_cons(sK1(X0,X1,X2),X4) != X2
              | ~ path(head_of(sK1(X0,X1,X2)),X1,X4) )
          | path_cons(sK1(X0,X1,X2),empty) != X2
          | head_of(sK1(X0,X1,X2)) != X1 )
        & ( ( path_cons(sK1(X0,X1,X2),sK2(X0,X1,X2)) = X2
            & path(head_of(sK1(X0,X1,X2)),X1,sK2(X0,X1,X2)) )
          | ( path_cons(sK1(X0,X1,X2),empty) = X2
            & head_of(sK1(X0,X1,X2)) = X1 ) )
        & tail_of(sK1(X0,X1,X2)) = X0
        & edge(sK1(X0,X1,X2))
        & vertex(X1)
        & vertex(X0) )
      | ~ path(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f68,f70,f69]) ).

fof(f74,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(f75,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,[],[f74]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(X3,X4) )
            & ( ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(X3,X4) )
            & ( ? [X5] :
                  ( precedes(X5,X4,X0)
                  & sequential(X3,X5) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f76]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(X3,X4) )
            & ( ? [X6] :
                  ( precedes(X6,X4,X0)
                  & sequential(X3,X6) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(rectify,[],[f77]) ).

fof(f79,plain,
    ! [X0,X3,X4] :
      ( ? [X6] :
          ( precedes(X6,X4,X0)
          & sequential(X3,X6) )
     => ( precedes(sK4(X0,X3,X4),X4,X0)
        & sequential(X3,sK4(X0,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ! [X3,X4] :
          ( ( ( ! [X5] :
                  ( ~ precedes(X5,X4,X0)
                  | ~ sequential(X3,X5) )
              | ~ sequential(X3,X4) )
            & ( ( precedes(sK4(X0,X3,X4),X4,X0)
                & sequential(X3,sK4(X0,X3,X4)) )
              | sequential(X3,X4) )
            & on_path(X4,X0)
            & on_path(X3,X0) )
          | ~ precedes(X3,X4,X0) )
      | ~ path(X1,X2,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78,f79]) ).

fof(f81,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) )
      & ( ( ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X0,X1,X3) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f82,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) )
      & ( ( ! [X3] :
              ( less_or_equal(length_of(X2),length_of(X3))
              | ~ path(X0,X1,X3) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(flattening,[],[f81]) ).

fof(f83,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) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X2),length_of(X4))
              | ~ path(X0,X1,X4) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(rectify,[],[f82]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ less_or_equal(length_of(X2),length_of(X3))
          & path(X0,X1,X3) )
     => ( ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2)))
        & path(X0,X1,sK5(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( ( shortest_path(X0,X1,X2)
        | ( ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2)))
          & path(X0,X1,sK5(X0,X1,X2)) )
        | X0 = X1
        | ~ path(X0,X1,X2) )
      & ( ( ! [X4] :
              ( less_or_equal(length_of(X2),length_of(X4))
              | ~ path(X0,X1,X4) )
          & X0 != X1
          & path(X0,X1,X2) )
        | ~ shortest_path(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f83,f84]) ).

fof(f88,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(sK10,sK11,X5)
      & sequential(sK10,sK11)
      & precedes(sK10,sK11,sK12)
      & shortest_path(sK8,sK9,sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ( ! [X5] : ~ triangle(sK10,sK11,X5)
    & sequential(sK10,sK11)
    & precedes(sK10,sK11,sK12)
    & shortest_path(sK8,sK9,sK12)
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f61,f88]) ).

fof(f90,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f91,plain,
    ! [X0] :
      ( vertex(head_of(X0))
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f92,plain,
    ! [X0] :
      ( vertex(tail_of(X0))
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( edge(sK0(X0,X1))
      | X0 = X1
      | ~ vertex(X1)
      | ~ vertex(X0)
      | ~ complete ),
    inference(cnf_transformation,[],[f65]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( head_of(sK0(X0,X1)) = X1
      | head_of(sK0(X0,X1)) = X0
      | X0 = X1
      | ~ vertex(X1)
      | ~ vertex(X0)
      | ~ complete ),
    inference(cnf_transformation,[],[f65]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( head_of(sK0(X0,X1)) = X1
      | tail_of(sK0(X0,X1)) = X1
      | X0 = X1
      | ~ vertex(X1)
      | ~ vertex(X0)
      | ~ complete ),
    inference(cnf_transformation,[],[f65]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( tail_of(sK0(X0,X1)) = X0
      | tail_of(sK0(X0,X1)) = X1
      | X0 = X1
      | ~ vertex(X1)
      | ~ vertex(X0)
      | ~ complete ),
    inference(cnf_transformation,[],[f65]) ).

fof(f99,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,[],[f42]) ).

fof(f102,plain,
    ! [X2,X0,X1] :
      ( vertex(X1)
      | ~ path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( edge(X0)
      | ~ sequential(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( edge(X1)
      | ~ sequential(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
      | head_of(X0) != tail_of(X1)
      | X0 = X1
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f121,plain,
    ! [X2,X3,X0,X1,X4] :
      ( precedes(X3,X4,X0)
      | ~ sequential(X3,X4)
      | ~ on_path(X4,X0)
      | ~ on_path(X3,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f122,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( precedes(X3,X4,X0)
      | ~ precedes(X5,X4,X0)
      | ~ sequential(X3,X5)
      | ~ on_path(X4,X0)
      | ~ on_path(X3,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f123,plain,
    ! [X2,X3,X0,X1,X4] :
      ( on_path(X3,X0)
      | ~ precedes(X3,X4,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f124,plain,
    ! [X2,X3,X0,X1,X4] :
      ( on_path(X4,X0)
      | ~ precedes(X3,X4,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f128,plain,
    ! [X2,X0,X1] :
      ( path(X0,X1,X2)
      | ~ shortest_path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( head_of(X3) != head_of(X5)
      | tail_of(X2) != tail_of(X5)
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f134,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X2,X4)
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f135,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,[],[f55]) ).

fof(f143,plain,
    complete,
    inference(cnf_transformation,[],[f89]) ).

fof(f144,plain,
    shortest_path(sK8,sK9,sK12),
    inference(cnf_transformation,[],[f89]) ).

fof(f145,plain,
    precedes(sK10,sK11,sK12),
    inference(cnf_transformation,[],[f89]) ).

fof(f146,plain,
    sequential(sK10,sK11),
    inference(cnf_transformation,[],[f89]) ).

fof(f147,plain,
    ! [X5] : ~ triangle(sK10,sK11,X5),
    inference(cnf_transformation,[],[f89]) ).

fof(f150,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,[],[f99]) ).

fof(f151,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,[],[f150]) ).

fof(f152,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,[],[f151]) ).

cnf(c_49,plain,
    ( head_of(X0) != tail_of(X0)
    | ~ edge(X0) ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_50,plain,
    ( ~ edge(X0)
    | vertex(tail_of(X0)) ),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_51,plain,
    ( ~ edge(X0)
    | vertex(head_of(X0)) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_53,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | ~ complete
    | tail_of(sK0(X0,X1)) = X0
    | tail_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_55,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | ~ complete
    | head_of(sK0(X0,X1)) = X1
    | tail_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_56,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | ~ complete
    | head_of(sK0(X0,X1)) = X0
    | head_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_57,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | ~ complete
    | X0 = X1
    | edge(sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_59,plain,
    ( ~ vertex(head_of(X0))
    | ~ vertex(tail_of(X0))
    | ~ edge(X0)
    | path(tail_of(X0),head_of(X0),path_cons(X0,empty)) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_67,plain,
    ( ~ path(X0,X1,X2)
    | vertex(X1) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_75,plain,
    ( head_of(X0) != tail_of(X1)
    | ~ edge(X0)
    | ~ edge(X1)
    | X0 = X1
    | sequential(X0,X1) ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_78,plain,
    ( ~ sequential(X0,X1)
    | edge(X1) ),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_79,plain,
    ( ~ sequential(X0,X1)
    | edge(X0) ),
    inference(cnf_transformation,[],[f116]) ).

cnf(c_80,plain,
    ( ~ path(X0,X1,X2)
    | ~ precedes(X3,X4,X2)
    | ~ on_path(X4,X2)
    | ~ on_path(X5,X2)
    | ~ sequential(X5,X3)
    | precedes(X5,X4,X2) ),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_81,plain,
    ( ~ path(X0,X1,X2)
    | ~ on_path(X3,X2)
    | ~ on_path(X4,X2)
    | ~ sequential(X3,X4)
    | precedes(X3,X4,X2) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_85,plain,
    ( ~ path(X0,X1,X2)
    | ~ precedes(X3,X4,X2)
    | on_path(X4,X2) ),
    inference(cnf_transformation,[],[f124]) ).

cnf(c_86,plain,
    ( ~ path(X0,X1,X2)
    | ~ precedes(X3,X4,X2)
    | on_path(X3,X2) ),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_91,plain,
    ( ~ shortest_path(X0,X1,X2)
    | path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f128]) ).

cnf(c_92,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ precedes(X1,X0,X2)
    | ~ shortest_path(X3,X4,X2) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_93,plain,
    ( head_of(X0) != head_of(X1)
    | tail_of(X1) != tail_of(X2)
    | ~ precedes(X2,X0,X3)
    | ~ shortest_path(X4,X5,X3) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_94,plain,
    ( ~ sequential(X0,X1)
    | ~ sequential(X1,X2)
    | ~ sequential(X2,X0)
    | ~ edge(X0)
    | ~ edge(X1)
    | ~ edge(X2)
    | triangle(X0,X1,X2) ),
    inference(cnf_transformation,[],[f135]) ).

cnf(c_102,negated_conjecture,
    ~ triangle(sK10,sK11,X0),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_103,negated_conjecture,
    sequential(sK10,sK11),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_104,negated_conjecture,
    precedes(sK10,sK11,sK12),
    inference(cnf_transformation,[],[f145]) ).

cnf(c_105,negated_conjecture,
    shortest_path(sK8,sK9,sK12),
    inference(cnf_transformation,[],[f144]) ).

cnf(c_106,negated_conjecture,
    complete,
    inference(cnf_transformation,[],[f143]) ).

cnf(c_144,plain,
    ( ~ vertex(X1)
    | ~ vertex(X0)
    | X0 = X1
    | edge(sK0(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_57,c_106,c_57]) ).

cnf(c_145,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | X0 = X1
    | edge(sK0(X0,X1)) ),
    inference(renaming,[status(thm)],[c_144]) ).

cnf(c_147,plain,
    ( ~ edge(X0)
    | path(tail_of(X0),head_of(X0),path_cons(X0,empty)) ),
    inference(global_subsumption_just,[status(thm)],[c_59,c_51,c_50,c_59]) ).

cnf(c_153,plain,
    ( ~ sequential(X0,X1)
    | ~ sequential(X1,X2)
    | ~ sequential(X2,X0)
    | ~ edge(X2)
    | triangle(X0,X1,X2) ),
    inference(global_subsumption_just,[status(thm)],[c_94,c_79,c_78,c_94]) ).

cnf(c_155,plain,
    ( ~ precedes(X3,X4,X2)
    | ~ path(X0,X1,X2)
    | ~ on_path(X5,X2)
    | ~ sequential(X5,X3)
    | precedes(X5,X4,X2) ),
    inference(global_subsumption_just,[status(thm)],[c_80,c_85,c_80]) ).

cnf(c_156,plain,
    ( ~ path(X0,X1,X2)
    | ~ precedes(X3,X4,X2)
    | ~ on_path(X5,X2)
    | ~ sequential(X5,X3)
    | precedes(X5,X4,X2) ),
    inference(renaming,[status(thm)],[c_155]) ).

cnf(c_157,plain,
    ( ~ vertex(X1)
    | ~ vertex(X0)
    | head_of(sK0(X0,X1)) = X0
    | head_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_56,c_106,c_56]) ).

cnf(c_158,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | head_of(sK0(X0,X1)) = X0
    | head_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(renaming,[status(thm)],[c_157]) ).

cnf(c_160,plain,
    ( ~ vertex(X1)
    | ~ vertex(X0)
    | head_of(sK0(X0,X1)) = X1
    | tail_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_55,c_106,c_55]) ).

cnf(c_161,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | head_of(sK0(X0,X1)) = X1
    | tail_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(renaming,[status(thm)],[c_160]) ).

cnf(c_164,plain,
    ( ~ vertex(X1)
    | ~ vertex(X0)
    | tail_of(sK0(X0,X1)) = X0
    | tail_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_53,c_106,c_53]) ).

cnf(c_165,plain,
    ( ~ vertex(X0)
    | ~ vertex(X1)
    | tail_of(sK0(X0,X1)) = X0
    | tail_of(sK0(X0,X1)) = X1
    | X0 = X1 ),
    inference(renaming,[status(thm)],[c_164]) ).

cnf(c_261,plain,
    ( X0 != sK10
    | X1 != sK11
    | X2 != X3
    | ~ sequential(X0,X1)
    | ~ sequential(X1,X2)
    | ~ sequential(X2,X0)
    | ~ edge(X2) ),
    inference(resolution_lifted,[status(thm)],[c_153,c_102]) ).

cnf(c_262,plain,
    ( ~ sequential(X0,sK10)
    | ~ sequential(sK11,X0)
    | ~ sequential(sK10,sK11)
    | ~ edge(X0) ),
    inference(unflattening,[status(thm)],[c_261]) ).

cnf(c_264,plain,
    ( ~ sequential(sK11,X0)
    | ~ sequential(X0,sK10)
    | ~ edge(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_262,c_103,c_262]) ).

cnf(c_265,plain,
    ( ~ sequential(X0,sK10)
    | ~ sequential(sK11,X0)
    | ~ edge(X0) ),
    inference(renaming,[status(thm)],[c_264]) ).

cnf(c_273,plain,
    ( ~ sequential(X0,sK10)
    | ~ sequential(sK11,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_265,c_78]) ).

cnf(c_525,plain,
    ( X0 != sK8
    | X1 != sK9
    | X2 != sK12
    | path(X0,X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_91,c_105]) ).

cnf(c_526,plain,
    path(sK8,sK9,sK12),
    inference(unflattening,[status(thm)],[c_525]) ).

cnf(c_983,plain,
    ( ~ sequential(X0_13,sK10)
    | ~ sequential(sK11,X0_13) ),
    inference(subtyping,[status(esa)],[c_273]) ).

cnf(c_986,plain,
    ( ~ vertex(X0_14)
    | ~ vertex(X1_14)
    | tail_of(sK0(X0_14,X1_14)) = X0_14
    | tail_of(sK0(X0_14,X1_14)) = X1_14
    | X0_14 = X1_14 ),
    inference(subtyping,[status(esa)],[c_165]) ).

cnf(c_988,plain,
    ( ~ vertex(X0_14)
    | ~ vertex(X1_14)
    | head_of(sK0(X0_14,X1_14)) = X1_14
    | tail_of(sK0(X0_14,X1_14)) = X1_14
    | X0_14 = X1_14 ),
    inference(subtyping,[status(esa)],[c_161]) ).

cnf(c_989,plain,
    ( ~ vertex(X0_14)
    | ~ vertex(X1_14)
    | head_of(sK0(X0_14,X1_14)) = X0_14
    | head_of(sK0(X0_14,X1_14)) = X1_14
    | X0_14 = X1_14 ),
    inference(subtyping,[status(esa)],[c_158]) ).

cnf(c_990,plain,
    ( ~ path(X0_14,X1_14,X0_15)
    | ~ precedes(X0_13,X1_13,X0_15)
    | ~ on_path(X2_13,X0_15)
    | ~ sequential(X2_13,X0_13)
    | precedes(X2_13,X1_13,X0_15) ),
    inference(subtyping,[status(esa)],[c_156]) ).

cnf(c_992,plain,
    ( ~ edge(X0_13)
    | path(tail_of(X0_13),head_of(X0_13),path_cons(X0_13,empty)) ),
    inference(subtyping,[status(esa)],[c_147]) ).

cnf(c_993,plain,
    ( ~ vertex(X0_14)
    | ~ vertex(X1_14)
    | X0_14 = X1_14
    | edge(sK0(X0_14,X1_14)) ),
    inference(subtyping,[status(esa)],[c_145]) ).

cnf(c_1003,plain,
    ( head_of(X0_13) != head_of(X1_13)
    | tail_of(X1_13) != tail_of(X2_13)
    | ~ precedes(X2_13,X0_13,X0_15)
    | ~ shortest_path(X0_14,X1_14,X0_15) ),
    inference(subtyping,[status(esa)],[c_93]) ).

cnf(c_1004,plain,
    ( ~ precedes(X0_13,X1_13,X0_15)
    | ~ precedes(X1_13,X0_13,X0_15)
    | ~ shortest_path(X0_14,X1_14,X0_15) ),
    inference(subtyping,[status(esa)],[c_92]) ).

cnf(c_1010,plain,
    ( ~ path(X0_14,X1_14,X0_15)
    | ~ precedes(X0_13,X1_13,X0_15)
    | on_path(X0_13,X0_15) ),
    inference(subtyping,[status(esa)],[c_86]) ).

cnf(c_1011,plain,
    ( ~ path(X0_14,X1_14,X0_15)
    | ~ precedes(X0_13,X1_13,X0_15)
    | on_path(X1_13,X0_15) ),
    inference(subtyping,[status(esa)],[c_85]) ).

cnf(c_1015,plain,
    ( ~ path(X0_14,X1_14,X0_15)
    | ~ on_path(X0_13,X0_15)
    | ~ on_path(X1_13,X0_15)
    | ~ sequential(X0_13,X1_13)
    | precedes(X0_13,X1_13,X0_15) ),
    inference(subtyping,[status(esa)],[c_81]) ).

cnf(c_1016,plain,
    ( ~ sequential(X0_13,X1_13)
    | edge(X0_13) ),
    inference(subtyping,[status(esa)],[c_79]) ).

cnf(c_1017,plain,
    ( ~ sequential(X0_13,X1_13)
    | edge(X1_13) ),
    inference(subtyping,[status(esa)],[c_78]) ).

cnf(c_1020,plain,
    ( head_of(X0_13) != tail_of(X1_13)
    | ~ edge(X0_13)
    | ~ edge(X1_13)
    | X0_13 = X1_13
    | sequential(X0_13,X1_13) ),
    inference(subtyping,[status(esa)],[c_75]) ).

cnf(c_1028,plain,
    ( ~ path(X0_14,X1_14,X0_15)
    | vertex(X1_14) ),
    inference(subtyping,[status(esa)],[c_67]) ).

cnf(c_1037,plain,
    ( ~ edge(X0_13)
    | vertex(tail_of(X0_13)) ),
    inference(subtyping,[status(esa)],[c_50]) ).

cnf(c_1038,plain,
    ( head_of(X0_13) != tail_of(X0_13)
    | ~ edge(X0_13) ),
    inference(subtyping,[status(esa)],[c_49]) ).

cnf(c_1049,plain,
    ( ~ path(X0_14,X1_14,X0_15)
    | ~ sP1_iProver_def(X0_15) ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP1_iProver_def])],[c_990]) ).

cnf(c_1065,plain,
    ( ~ shortest_path(X0_14,X1_14,X0_15)
    | ~ sP2_iProver_def(X0_15) ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_def])],[c_1003]) ).

cnf(c_1066,plain,
    ( ~ precedes(X0_13,X1_13,X0_15)
    | sP2_iProver_def(X0_15)
    | ~ sP3_iProver_def(X0_13,X1_13) ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP3_iProver_def])],[c_1003]) ).

cnf(c_1067,plain,
    ( head_of(X0_13) != head_of(X1_13)
    | tail_of(X1_13) != tail_of(X2_13)
    | sP3_iProver_def(X2_13,X0_13) ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1003]) ).

cnf(c_1071,plain,
    ( ~ precedes(X0_13,X1_13,X0_15)
    | ~ precedes(X1_13,X0_13,X0_15)
    | sP2_iProver_def(X0_15) ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1004]) ).

cnf(c_1079,plain,
    ( ~ precedes(X0_13,X1_13,X0_15)
    | on_path(X0_13,X0_15)
    | sP1_iProver_def(X0_15) ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1010]) ).

cnf(c_1082,plain,
    ( ~ precedes(X0_13,X1_13,X0_15)
    | on_path(X1_13,X0_15)
    | ~ sP4_iProver_def(X0_15) ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP4_iProver_def])],[c_1011]) ).

cnf(c_1083,plain,
    ( ~ path(X0_14,X1_14,X0_15)
    | sP4_iProver_def(X0_15) ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1011]) ).

cnf(c_1095,plain,
    ( ~ on_path(X0_13,X0_15)
    | ~ on_path(X1_13,X0_15)
    | ~ sequential(X0_13,X1_13)
    | precedes(X0_13,X1_13,X0_15)
    | sP1_iProver_def(X0_15) ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1015]) ).

cnf(c_1134,plain,
    X0_13 = X0_13,
    theory(equality) ).

cnf(c_1139,plain,
    ( X0_14 != X1_14
    | X2_14 != X1_14
    | X2_14 = X0_14 ),
    theory(equality) ).

cnf(c_1142,plain,
    ( X0_13 != X1_13
    | head_of(X0_13) = head_of(X1_13) ),
    theory(equality) ).

cnf(c_1143,plain,
    ( X0_13 != X1_13
    | tail_of(X0_13) = tail_of(X1_13) ),
    theory(equality) ).

cnf(c_1158,plain,
    ( sK10 != sK10
    | tail_of(sK10) = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_1143]) ).

cnf(c_1164,plain,
    sK10 = sK10,
    inference(instantiation,[status(thm)],[c_1134]) ).

cnf(c_1190,plain,
    ( ~ edge(sK10)
    | vertex(tail_of(sK10)) ),
    inference(instantiation,[status(thm)],[c_1037]) ).

cnf(c_1898,plain,
    ( ~ shortest_path(sK8,sK9,sK12)
    | ~ sP2_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_1065]) ).

cnf(c_1904,plain,
    ( ~ precedes(X0_13,X1_13,sK12)
    | ~ precedes(X1_13,X0_13,sK12)
    | sP2_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_1071]) ).

cnf(c_1906,plain,
    ( ~ precedes(X1_13,X0_13,sK12)
    | ~ precedes(X0_13,X1_13,sK12) ),
    inference(global_subsumption_just,[status(thm)],[c_1904,c_105,c_1898,c_1904]) ).

cnf(c_1907,plain,
    ( ~ precedes(X0_13,X1_13,sK12)
    | ~ precedes(X1_13,X0_13,sK12) ),
    inference(renaming,[status(thm)],[c_1906]) ).

cnf(c_1909,plain,
    ( ~ precedes(sK10,sK11,sK12)
    | ~ precedes(sK11,sK10,sK12) ),
    inference(instantiation,[status(thm)],[c_1907]) ).

cnf(c_2139,plain,
    ( ~ precedes(X0_13,X1_13,sK12)
    | ~ sP3_iProver_def(X0_13,X1_13)
    | sP2_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_1066]) ).

cnf(c_2140,plain,
    ( ~ sP3_iProver_def(X0_13,X1_13)
    | ~ precedes(X0_13,X1_13,sK12) ),
    inference(global_subsumption_just,[status(thm)],[c_2139,c_105,c_1898,c_2139]) ).

cnf(c_2141,plain,
    ( ~ precedes(X0_13,X1_13,sK12)
    | ~ sP3_iProver_def(X0_13,X1_13) ),
    inference(renaming,[status(thm)],[c_2140]) ).

cnf(c_2142,plain,
    ( ~ precedes(sK10,sK11,sK12)
    | ~ sP3_iProver_def(sK10,sK11) ),
    inference(instantiation,[status(thm)],[c_2141]) ).

cnf(c_2145,plain,
    ( tail_of(X0_13) != tail_of(sK10)
    | head_of(sK11) != head_of(X0_13)
    | sP3_iProver_def(sK10,sK11) ),
    inference(instantiation,[status(thm)],[c_1067]) ).

cnf(c_2146,plain,
    ( head_of(sK11) != head_of(sK10)
    | tail_of(sK10) != tail_of(sK10)
    | sP3_iProver_def(sK10,sK11) ),
    inference(instantiation,[status(thm)],[c_2145]) ).

cnf(c_2150,plain,
    ( sK11 != X0_13
    | head_of(sK11) = head_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_1142]) ).

cnf(c_2151,plain,
    ( sK11 != sK10
    | head_of(sK11) = head_of(sK10) ),
    inference(instantiation,[status(thm)],[c_2150]) ).

cnf(c_3371,plain,
    ( head_of(X0_13) != X0_14
    | tail_of(X0_13) != X0_14
    | head_of(X0_13) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_1139]) ).

cnf(c_3532,plain,
    ( head_of(X0_13) != tail_of(X1_13)
    | tail_of(X0_13) != tail_of(X1_13)
    | head_of(X0_13) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_3371]) ).

cnf(c_4109,plain,
    ( sK11 != X0_13
    | tail_of(sK11) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_1143]) ).

cnf(c_5084,plain,
    ( head_of(sK11) != tail_of(X0_13)
    | tail_of(sK11) != tail_of(X0_13)
    | head_of(sK11) = tail_of(sK11) ),
    inference(instantiation,[status(thm)],[c_3532]) ).

cnf(c_5493,plain,
    ( ~ precedes(X0_13,X1_13,sK12)
    | on_path(X0_13,sK12)
    | sP1_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_1079]) ).

cnf(c_5507,plain,
    ( ~ precedes(sK10,sK11,sK12)
    | on_path(sK10,sK12)
    | sP1_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_5493]) ).

cnf(c_5536,plain,
    ( head_of(sK11) != tail_of(X0_13)
    | ~ edge(X0_13)
    | ~ edge(sK11)
    | sK11 = X0_13
    | sequential(sK11,X0_13) ),
    inference(instantiation,[status(thm)],[c_1020]) ).

cnf(c_5537,plain,
    ( head_of(sK11) != tail_of(sK10)
    | ~ edge(sK10)
    | ~ edge(sK11)
    | sK11 = sK10
    | sequential(sK11,sK10) ),
    inference(instantiation,[status(thm)],[c_5536]) ).

cnf(c_5558,plain,
    ( ~ sequential(X0_13,sK11)
    | edge(sK11) ),
    inference(instantiation,[status(thm)],[c_1017]) ).

cnf(c_5559,plain,
    ( ~ sequential(sK10,sK11)
    | edge(sK11) ),
    inference(instantiation,[status(thm)],[c_5558]) ).

cnf(c_5583,plain,
    ( ~ sequential(X0_13,X1_13)
    | ~ on_path(X0_13,sK12)
    | ~ on_path(X1_13,sK12)
    | precedes(X0_13,X1_13,sK12)
    | sP1_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_1095]) ).

cnf(c_5658,plain,
    ( ~ path(X0_14,head_of(sK11),X0_15)
    | vertex(head_of(sK11)) ),
    inference(instantiation,[status(thm)],[c_1028]) ).

cnf(c_5666,plain,
    ( ~ sequential(sK10,sK11)
    | edge(sK10) ),
    inference(instantiation,[status(thm)],[c_1016]) ).

cnf(c_5682,plain,
    ( ~ path(tail_of(sK11),head_of(sK11),path_cons(sK11,empty))
    | vertex(head_of(sK11)) ),
    inference(instantiation,[status(thm)],[c_5658]) ).

cnf(c_5719,plain,
    ( ~ on_path(X0_13,sK12)
    | ~ sequential(sK11,X0_13)
    | ~ on_path(sK11,sK12)
    | precedes(sK11,X0_13,sK12)
    | sP1_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_5583]) ).

cnf(c_5720,plain,
    ( ~ on_path(sK10,sK12)
    | ~ on_path(sK11,sK12)
    | ~ sequential(sK11,sK10)
    | precedes(sK11,sK10,sK12)
    | sP1_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_5719]) ).

cnf(c_5734,plain,
    ( head_of(sK11) != tail_of(sK11)
    | ~ edge(sK11) ),
    inference(instantiation,[status(thm)],[c_1038]) ).

cnf(c_5763,plain,
    ( ~ edge(sK11)
    | path(tail_of(sK11),head_of(sK11),path_cons(sK11,empty)) ),
    inference(instantiation,[status(thm)],[c_992]) ).

cnf(c_6034,plain,
    ( ~ vertex(head_of(X0_13))
    | ~ vertex(X0_14)
    | head_of(sK0(head_of(X0_13),X0_14)) = head_of(X0_13)
    | head_of(sK0(head_of(X0_13),X0_14)) = X0_14
    | head_of(X0_13) = X0_14 ),
    inference(instantiation,[status(thm)],[c_989]) ).

cnf(c_6228,plain,
    ( ~ vertex(head_of(X0_13))
    | ~ vertex(tail_of(X1_13))
    | head_of(sK0(head_of(X0_13),tail_of(X1_13))) = head_of(X0_13)
    | head_of(sK0(head_of(X0_13),tail_of(X1_13))) = tail_of(X1_13)
    | head_of(X0_13) = tail_of(X1_13) ),
    inference(instantiation,[status(thm)],[c_6034]) ).

cnf(c_6332,plain,
    ( ~ vertex(tail_of(sK10))
    | ~ vertex(X0_14)
    | head_of(sK0(X0_14,tail_of(sK10))) = tail_of(sK10)
    | head_of(sK0(X0_14,tail_of(sK10))) = X0_14
    | X0_14 = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_989]) ).

cnf(c_6339,plain,
    ( ~ vertex(X0_14)
    | head_of(sK0(X0_14,tail_of(sK10))) = tail_of(sK10)
    | head_of(sK0(X0_14,tail_of(sK10))) = X0_14
    | X0_14 = tail_of(sK10) ),
    inference(global_subsumption_just,[status(thm)],[c_6332,c_103,c_1190,c_5666,c_6332]) ).

cnf(c_7167,plain,
    ( ~ vertex(head_of(X0_13))
    | head_of(sK0(head_of(X0_13),tail_of(sK10))) = head_of(X0_13)
    | head_of(sK0(head_of(X0_13),tail_of(sK10))) = tail_of(sK10)
    | head_of(X0_13) = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_6339]) ).

cnf(c_7177,plain,
    ( ~ vertex(tail_of(X0_13))
    | ~ vertex(head_of(sK11))
    | head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
    | head_of(sK0(head_of(sK11),tail_of(X0_13))) = head_of(sK11)
    | head_of(sK11) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_6228]) ).

cnf(c_7179,plain,
    ( ~ vertex(tail_of(X0_13))
    | head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
    | head_of(sK0(head_of(sK11),tail_of(X0_13))) = head_of(sK11)
    | head_of(sK11) = tail_of(X0_13) ),
    inference(global_subsumption_just,[status(thm)],[c_7177,c_103,c_5559,c_5682,c_5763,c_7177]) ).

cnf(c_7181,plain,
    ( ~ vertex(tail_of(sK10))
    | head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
    | head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
    | head_of(sK11) = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_7179]) ).

cnf(c_8698,plain,
    ( ~ vertex(head_of(sK11))
    | head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
    | head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
    | head_of(sK11) = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_7167]) ).

cnf(c_8699,plain,
    ( head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
    | head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
    | head_of(sK11) = tail_of(sK10) ),
    inference(global_subsumption_just,[status(thm)],[c_8698,c_103,c_1190,c_5666,c_7181]) ).

cnf(c_165490,plain,
    ( ~ precedes(X0_13,sK11,sK12)
    | ~ sP4_iProver_def(sK12)
    | on_path(sK11,sK12) ),
    inference(instantiation,[status(thm)],[c_1082]) ).

cnf(c_165491,plain,
    ( ~ precedes(sK10,sK11,sK12)
    | ~ sP4_iProver_def(sK12)
    | on_path(sK11,sK12) ),
    inference(instantiation,[status(thm)],[c_165490]) ).

cnf(c_165492,plain,
    ( ~ sP4_iProver_def(sK12)
    | on_path(sK11,sK12) ),
    inference(global_subsumption_just,[status(thm)],[c_165490,c_104,c_165491]) ).

cnf(c_165509,plain,
    ( ~ path(X0_14,X1_14,sK12)
    | sP4_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_1083]) ).

cnf(c_165820,plain,
    ( ~ path(sK8,sK9,sK12)
    | sP4_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_165509]) ).

cnf(c_165823,plain,
    ( ~ path(sK8,sK9,sK12)
    | ~ sP1_iProver_def(sK12) ),
    inference(instantiation,[status(thm)],[c_1049]) ).

cnf(c_165944,plain,
    ( head_of(sK11) != tail_of(X0_13)
    | ~ edge(X0_13)
    | ~ edge(sK11)
    | sK11 = X0_13
    | sequential(sK11,X0_13) ),
    inference(instantiation,[status(thm)],[c_1020]) ).

cnf(c_165945,plain,
    ( head_of(sK11) != tail_of(X0_13)
    | ~ edge(X0_13)
    | sequential(sK11,X0_13) ),
    inference(global_subsumption_just,[status(thm)],[c_165944,c_103,c_4109,c_5084,c_5536,c_5559,c_5734]) ).

cnf(c_165960,plain,
    ( ~ vertex(tail_of(X0_13))
    | ~ vertex(head_of(sK11))
    | head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
    | tail_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
    | head_of(sK11) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_988]) ).

cnf(c_165962,plain,
    ( ~ vertex(tail_of(X0_13))
    | ~ vertex(head_of(sK11))
    | tail_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
    | tail_of(sK0(head_of(sK11),tail_of(X0_13))) = head_of(sK11)
    | head_of(sK11) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_986]) ).

cnf(c_165963,plain,
    ( ~ vertex(tail_of(X0_13))
    | ~ vertex(head_of(sK11))
    | head_of(sK11) = tail_of(X0_13)
    | edge(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_993]) ).

cnf(c_165964,plain,
    ( ~ vertex(head_of(sK11))
    | ~ vertex(tail_of(sK10))
    | head_of(sK11) = tail_of(sK10)
    | edge(sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_165963]) ).

cnf(c_165968,plain,
    ( ~ vertex(head_of(sK11))
    | ~ vertex(tail_of(sK10))
    | tail_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
    | tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
    | head_of(sK11) = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_165962]) ).

cnf(c_165976,plain,
    ( ~ vertex(head_of(sK11))
    | ~ vertex(tail_of(sK10))
    | head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
    | tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
    | head_of(sK11) = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_165960]) ).

cnf(c_165980,plain,
    ( tail_of(X0_13) != X0_14
    | head_of(sK11) != X0_14
    | head_of(sK11) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_1139]) ).

cnf(c_165995,plain,
    ( head_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(sK0(head_of(sK11),tail_of(X0_13)))
    | ~ edge(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_1038]) ).

cnf(c_165996,plain,
    ( head_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK0(head_of(sK11),tail_of(sK10)))
    | ~ edge(sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_165995]) ).

cnf(c_166007,plain,
    ( tail_of(sK0(head_of(sK11),tail_of(X0_13))) != head_of(sK11)
    | head_of(sK11) != head_of(sK11)
    | head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_165980]) ).

cnf(c_166008,plain,
    ( tail_of(sK0(head_of(sK11),tail_of(X0_13))) != head_of(sK11)
    | head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(equality_resolution_simp,[status(thm)],[c_166007]) ).

cnf(c_166009,plain,
    ( tail_of(sK0(head_of(sK11),tail_of(sK10))) != head_of(sK11)
    | head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_166008]) ).

cnf(c_166027,plain,
    ( head_of(X0_13) != X0_14
    | head_of(sK11) != X0_14
    | head_of(sK11) = head_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_1139]) ).

cnf(c_166036,plain,
    ( head_of(sK0(head_of(sK11),tail_of(X0_13))) != X0_14
    | tail_of(sK0(head_of(sK11),tail_of(X0_13))) != X0_14
    | head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_1139]) ).

cnf(c_166038,plain,
    ( head_of(sK11) != tail_of(sK0(head_of(sK11),tail_of(X0_13)))
    | ~ edge(sK0(head_of(sK11),tail_of(X0_13)))
    | sequential(sK11,sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_165945]) ).

cnf(c_166039,plain,
    ( head_of(sK11) != tail_of(sK0(head_of(sK11),tail_of(sK10)))
    | ~ edge(sK0(head_of(sK11),tail_of(sK10)))
    | sequential(sK11,sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_166038]) ).

cnf(c_166104,plain,
    ( head_of(X0_13) != head_of(X1_13)
    | head_of(sK11) != head_of(X1_13)
    | head_of(sK11) = head_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_166027]) ).

cnf(c_166106,plain,
    ( head_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(X0_13)
    | tail_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(X0_13)
    | head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_166036]) ).

cnf(c_166107,plain,
    ( head_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
    | tail_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
    | head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_166106]) ).

cnf(c_166115,plain,
    ( ~ sequential(sK0(head_of(sK11),tail_of(X0_13)),sK10)
    | ~ sequential(sK11,sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_983]) ).

cnf(c_166116,plain,
    ( ~ sequential(sK0(head_of(sK11),tail_of(sK10)),sK10)
    | ~ sequential(sK11,sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_166115]) ).

cnf(c_166262,plain,
    ( head_of(X0_13) != head_of(sK11)
    | head_of(sK11) != head_of(sK11)
    | head_of(sK11) = head_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_166104]) ).

cnf(c_166263,plain,
    ( head_of(X0_13) != head_of(sK11)
    | head_of(sK11) = head_of(X0_13) ),
    inference(equality_resolution_simp,[status(thm)],[c_166262]) ).

cnf(c_166291,plain,
    ( sK0(head_of(sK11),tail_of(X0_13)) != X0_13
    | tail_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13) ),
    inference(instantiation,[status(thm)],[c_1143]) ).

cnf(c_166292,plain,
    ( sK0(head_of(sK11),tail_of(sK10)) != sK10
    | tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10) ),
    inference(instantiation,[status(thm)],[c_166291]) ).

cnf(c_166628,plain,
    ( head_of(sK0(head_of(sK11),X0_14)) != head_of(sK11)
    | head_of(sK11) = head_of(sK0(head_of(sK11),X0_14)) ),
    inference(instantiation,[status(thm)],[c_166263]) ).

cnf(c_166650,plain,
    ( head_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(X0_13)
    | ~ edge(sK0(head_of(sK11),tail_of(X0_13)))
    | ~ edge(X0_13)
    | sK0(head_of(sK11),tail_of(X0_13)) = X0_13
    | sequential(sK0(head_of(sK11),tail_of(X0_13)),X0_13) ),
    inference(instantiation,[status(thm)],[c_1020]) ).

cnf(c_166651,plain,
    ( head_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
    | ~ edge(sK0(head_of(sK11),tail_of(sK10)))
    | ~ edge(sK10)
    | sK0(head_of(sK11),tail_of(sK10)) = sK10
    | sequential(sK0(head_of(sK11),tail_of(sK10)),sK10) ),
    inference(instantiation,[status(thm)],[c_166650]) ).

cnf(c_168228,plain,
    ( head_of(sK0(head_of(sK11),tail_of(X0_13))) != head_of(sK11)
    | head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_166628]) ).

cnf(c_168229,plain,
    ( head_of(sK0(head_of(sK11),tail_of(sK10))) != head_of(sK11)
    | head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_168228]) ).

cnf(c_168984,plain,
    ( tail_of(X0_13) != tail_of(sK10)
    | head_of(sK11) != head_of(X0_13)
    | sP3_iProver_def(sK10,sK11) ),
    inference(instantiation,[status(thm)],[c_1067]) ).

cnf(c_168985,plain,
    ( head_of(sK11) != head_of(X0_13)
    | tail_of(X0_13) != tail_of(sK10) ),
    inference(global_subsumption_just,[status(thm)],[c_168984,c_104,c_2142,c_2145]) ).

cnf(c_168986,plain,
    ( tail_of(X0_13) != tail_of(sK10)
    | head_of(sK11) != head_of(X0_13) ),
    inference(renaming,[status(thm)],[c_168985]) ).

cnf(c_169381,plain,
    ( tail_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(sK10)
    | head_of(sK11) != head_of(sK0(head_of(sK11),tail_of(X0_13))) ),
    inference(instantiation,[status(thm)],[c_168986]) ).

cnf(c_169382,plain,
    ( tail_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
    | head_of(sK11) != head_of(sK0(head_of(sK11),tail_of(sK10))) ),
    inference(instantiation,[status(thm)],[c_169381]) ).

cnf(c_169383,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_169382,c_168229,c_166651,c_166292,c_166116,c_166107,c_166039,c_166009,c_165996,c_165976,c_165968,c_165964,c_165823,c_165820,c_165492,c_8699,c_5763,c_5720,c_5682,c_5666,c_5559,c_5537,c_5507,c_2151,c_2146,c_2142,c_1909,c_1190,c_1164,c_1158,c_526,c_104,c_103]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRA008+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May  2 21:19:49 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 46.51/7.23  % SZS status Started for theBenchmark.p
% 46.51/7.23  ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!96 (|16777216|) |16777216|) supplied sort is |16777229|")
% 46.51/7.23  Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!96 (|16777216|) |16777216|) supplied sort is |16777229|")
% 46.51/7.23  ERROR - cmd was:  ulimit -v 4096000; ./res/iproveropt_static_z3 --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --proof_out true --sat_out_model pos  --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 2.00" --time_out_real 2.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_10emtf71/ul5adb5b 2>> /export/starexec/sandbox/tmp/iprover_out_10emtf71/ul5adb5b_error
% 61.86/9.24  % SZS status Theorem for theBenchmark.p
% 61.86/9.24  
% 61.86/9.24  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.86/9.24  
% 61.86/9.24  ------  iProver source info
% 61.86/9.24  
% 61.86/9.24  git: date: 2024-05-02 19:28:25 +0000
% 61.86/9.24  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.86/9.24  git: non_committed_changes: false
% 61.86/9.24  
% 61.86/9.24  ------ Parsing...
% 61.86/9.24  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 61.86/9.24  
% 61.86/9.24  ------ Preprocessing... sf_s  rm: 2 0s  sf_e  pe_s  pe:1:0s pe_e  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 61.86/9.24  
% 61.86/9.24  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  scvd_s sp: 17 0s scvd_e  snvd_s sp: 0 0s snvd_e 
% 61.86/9.24  
% 61.86/9.24  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 61.86/9.24  ------ Proving...
% 61.86/9.24  ------ Problem Properties 
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  clauses                                 61
% 61.86/9.24  conjectures                             3
% 61.86/9.24  EPR                                     23
% 61.86/9.24  Horn                                    35
% 61.86/9.24  unary                                   6
% 61.86/9.24  binary                                  18
% 61.86/9.24  lits                                    182
% 61.86/9.24  lits eq                                 44
% 61.86/9.24  fd_pure                                 0
% 61.86/9.24  fd_pseudo                               0
% 61.86/9.24  fd_cond                                 0
% 61.86/9.24  fd_pseudo_cond                          5
% 61.86/9.24  AC symbols                              0
% 61.86/9.24  
% 61.86/9.24  ------ Input Options Time Limit: Unbounded
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ 
% 61.86/9.24  Current options:
% 61.86/9.24  ------ 
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  ------ Proving...
% 61.86/9.24  
% 61.86/9.24  
% 61.86/9.24  % SZS status Theorem for theBenchmark.p
% 61.86/9.24  
% 61.86/9.24  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.86/9.24  
% 61.86/9.26  
%------------------------------------------------------------------------------