TSTP Solution File: GRA008+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 02:19:24 EDT 2024

% Result   : Theorem 7.43s 1.69s
% Output   : CNFRefutation 7.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  134 (  27 unt;   0 def)
%            Number of atoms       :  532 (  89 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  651 ( 253   ~; 224   |; 136   &)
%                                         (   7 <=>;  28  =>;   0  <=;   3 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   2 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :  390 (  46 sgn 238   !;  38   ?)

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

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,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(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(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(f26,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
    <=> ( head_of(X0) = tail_of(X1)
        & X0 != X1
        & edge(X1)
        & edge(X0) ) ),
    inference(rectify,[],[f8]) ).

fof(f27,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(f28,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(f29,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(f30,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(f31,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(f36,plain,
    ( complete
   => ! [X0,X1,X2,X3,X4] :
        ( ( precedes(X2,X3,X4)
          & shortest_path(X0,X1,X4) )
       => ? [X5] :
            ( tail_of(X2) = head_of(X5)
            & head_of(X3) = tail_of(X5)
            & edge(X5) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f37,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(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,[],[f31]) ).

fof(f39,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f50,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,[],[f27]) ).

fof(f51,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,[],[f50]) ).

fof(f52,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,[],[f28]) ).

fof(f53,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,[],[f29]) ).

fof(f54,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,[],[f30]) ).

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

fof(f56,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(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(flattening,[],[f56]) ).

fof(f62,plain,
    ( ! [X0,X1,X2,X3,X4] :
        ( ? [X5] :
            ( tail_of(X2) = head_of(X5)
            & head_of(X3) = tail_of(X5)
            & edge(X5) )
        | ~ precedes(X2,X3,X4)
        | ~ shortest_path(X0,X1,X4) )
    | ~ complete ),
    inference(ennf_transformation,[],[f36]) ).

fof(f63,plain,
    ( ! [X0,X1,X2,X3,X4] :
        ( ? [X5] :
            ( tail_of(X2) = head_of(X5)
            & head_of(X3) = tail_of(X5)
            & edge(X5) )
        | ~ precedes(X2,X3,X4)
        | ~ shortest_path(X0,X1,X4) )
    | ~ complete ),
    inference(flattening,[],[f62]) ).

fof(f64,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,[],[f37]) ).

fof(f65,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,[],[f64]) ).

fof(f78,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,[],[f26]) ).

fof(f79,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,[],[f78]) ).

fof(f80,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,[],[f52]) ).

fof(f81,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,[],[f80]) ).

fof(f82,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,[],[f81]) ).

fof(f83,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(f84,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])],[f82,f83]) ).

fof(f85,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,[],[f53]) ).

fof(f86,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,[],[f85]) ).

fof(f87,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,[],[f86]) ).

fof(f88,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(f89,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])],[f87,f88]) ).

fof(f92,plain,
    ! [X2,X3] :
      ( ? [X5] :
          ( tail_of(X2) = head_of(X5)
          & head_of(X3) = tail_of(X5)
          & edge(X5) )
     => ( tail_of(X2) = head_of(sK8(X2,X3))
        & head_of(X3) = tail_of(sK8(X2,X3))
        & edge(sK8(X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ( ! [X0,X1,X2,X3,X4] :
        ( ( tail_of(X2) = head_of(sK8(X2,X3))
          & head_of(X3) = tail_of(sK8(X2,X3))
          & edge(sK8(X2,X3)) )
        | ~ precedes(X2,X3,X4)
        | ~ shortest_path(X0,X1,X4) )
    | ~ complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f63,f92]) ).

fof(f94,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(sK11,sK12,X5)
      & sequential(sK11,sK12)
      & precedes(sK11,sK12,sK13)
      & shortest_path(sK9,sK10,sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ( ! [X5] : ~ triangle(sK11,sK12,X5)
    & sequential(sK11,sK12)
    & precedes(sK11,sK12,sK13)
    & shortest_path(sK9,sK10,sK13)
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f65,f94]) ).

fof(f96,plain,
    ! [X0] :
      ( head_of(X0) != tail_of(X0)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( edge(X0)
      | ~ sequential(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( edge(X1)
      | ~ sequential(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( sequential(X0,X1)
      | head_of(X0) != tail_of(X1)
      | X0 = X1
      | ~ edge(X1)
      | ~ edge(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f127,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,[],[f51]) ).

fof(f129,plain,
    ! [X2,X3,X0,X1,X4] :
      ( on_path(X3,X0)
      | ~ precedes(X3,X4,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f130,plain,
    ! [X2,X3,X0,X1,X4] :
      ( on_path(X4,X0)
      | ~ precedes(X3,X4,X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f134,plain,
    ! [X2,X0,X1] :
      ( path(X0,X1,X2)
      | ~ shortest_path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f140,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ precedes(X3,X2,X4)
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f141,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,[],[f57]) ).

fof(f149,plain,
    ! [X2,X3,X0,X1,X4] :
      ( edge(sK8(X2,X3))
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4)
      | ~ complete ),
    inference(cnf_transformation,[],[f93]) ).

fof(f150,plain,
    ! [X2,X3,X0,X1,X4] :
      ( head_of(X3) = tail_of(sK8(X2,X3))
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4)
      | ~ complete ),
    inference(cnf_transformation,[],[f93]) ).

fof(f151,plain,
    ! [X2,X3,X0,X1,X4] :
      ( tail_of(X2) = head_of(sK8(X2,X3))
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4)
      | ~ complete ),
    inference(cnf_transformation,[],[f93]) ).

fof(f152,plain,
    complete,
    inference(cnf_transformation,[],[f95]) ).

fof(f153,plain,
    shortest_path(sK9,sK10,sK13),
    inference(cnf_transformation,[],[f95]) ).

fof(f154,plain,
    precedes(sK11,sK12,sK13),
    inference(cnf_transformation,[],[f95]) ).

fof(f155,plain,
    sequential(sK11,sK12),
    inference(cnf_transformation,[],[f95]) ).

fof(f156,plain,
    ! [X5] : ~ triangle(sK11,sK12,X5),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_49,plain,
    ( head_of(X0) != tail_of(X0)
    | ~ edge(X0) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_75,plain,
    ( head_of(X0) != tail_of(X1)
    | ~ edge(X0)
    | ~ edge(X1)
    | X0 = X1
    | sequential(X0,X1) ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_78,plain,
    ( ~ sequential(X0,X1)
    | edge(X1) ),
    inference(cnf_transformation,[],[f123]) ).

cnf(c_79,plain,
    ( ~ sequential(X0,X1)
    | edge(X0) ),
    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,[],[f127]) ).

cnf(c_85,plain,
    ( ~ path(X0,X1,X2)
    | ~ precedes(X3,X4,X2)
    | on_path(X4,X2) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_86,plain,
    ( ~ path(X0,X1,X2)
    | ~ precedes(X3,X4,X2)
    | on_path(X3,X2) ),
    inference(cnf_transformation,[],[f129]) ).

cnf(c_91,plain,
    ( ~ shortest_path(X0,X1,X2)
    | path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_92,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ precedes(X1,X0,X2)
    | ~ shortest_path(X3,X4,X2) ),
    inference(cnf_transformation,[],[f140]) ).

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,[],[f141]) ).

cnf(c_102,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | ~ complete
    | head_of(sK8(X0,X1)) = tail_of(X0) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_103,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | ~ complete
    | tail_of(sK8(X0,X1)) = head_of(X1) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_104,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | ~ complete
    | edge(sK8(X0,X1)) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_105,negated_conjecture,
    ~ triangle(sK11,sK12,X0),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_106,negated_conjecture,
    sequential(sK11,sK12),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_107,negated_conjecture,
    precedes(sK11,sK12,sK13),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_108,negated_conjecture,
    shortest_path(sK9,sK10,sK13),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_109,negated_conjecture,
    complete,
    inference(cnf_transformation,[],[f152]) ).

cnf(c_147,plain,
    ( ~ shortest_path(X3,X4,X2)
    | ~ precedes(X0,X1,X2)
    | edge(sK8(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_104,c_109,c_104]) ).

cnf(c_148,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | edge(sK8(X0,X1)) ),
    inference(renaming,[status(thm)],[c_147]) ).

cnf(c_155,plain,
    ( ~ shortest_path(X3,X4,X2)
    | ~ precedes(X0,X1,X2)
    | tail_of(sK8(X0,X1)) = head_of(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_103,c_109,c_103]) ).

cnf(c_156,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | tail_of(sK8(X0,X1)) = head_of(X1) ),
    inference(renaming,[status(thm)],[c_155]) ).

cnf(c_157,plain,
    ( ~ shortest_path(X3,X4,X2)
    | ~ precedes(X0,X1,X2)
    | head_of(sK8(X0,X1)) = tail_of(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_102,c_109,c_102]) ).

cnf(c_158,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | head_of(sK8(X0,X1)) = tail_of(X0) ),
    inference(renaming,[status(thm)],[c_157]) ).

cnf(c_162,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_207,plain,
    ( ~ sequential(X0,X1)
    | ~ sequential(X1,X2)
    | ~ sequential(X2,X0)
    | triangle(X0,X1,X2) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_162,c_78]) ).

cnf(c_985,plain,
    ( X0 != sK11
    | X1 != sK12
    | X2 != X3
    | ~ sequential(X0,X1)
    | ~ sequential(X1,X2)
    | ~ sequential(X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_207,c_105]) ).

cnf(c_986,plain,
    ( ~ sequential(X0,sK11)
    | ~ sequential(sK12,X0)
    | ~ sequential(sK11,sK12) ),
    inference(unflattening,[status(thm)],[c_985]) ).

cnf(c_988,plain,
    ( ~ sequential(sK12,X0)
    | ~ sequential(X0,sK11) ),
    inference(global_subsumption_just,[status(thm)],[c_986,c_106,c_986]) ).

cnf(c_989,plain,
    ( ~ sequential(X0,sK11)
    | ~ sequential(sK12,X0) ),
    inference(renaming,[status(thm)],[c_988]) ).

cnf(c_2742,negated_conjecture,
    shortest_path(sK9,sK10,sK13),
    inference(demodulation,[status(thm)],[c_108]) ).

cnf(c_2743,negated_conjecture,
    precedes(sK11,sK12,sK13),
    inference(demodulation,[status(thm)],[c_107]) ).

cnf(c_2744,negated_conjecture,
    sequential(sK11,sK12),
    inference(demodulation,[status(thm)],[c_106]) ).

cnf(c_3733,plain,
    edge(sK12),
    inference(superposition,[status(thm)],[c_2744,c_78]) ).

cnf(c_3738,plain,
    edge(sK11),
    inference(superposition,[status(thm)],[c_2744,c_79]) ).

cnf(c_3751,plain,
    path(sK9,sK10,sK13),
    inference(superposition,[status(thm)],[c_2742,c_91]) ).

cnf(c_3929,plain,
    ( ~ precedes(X0,X1,sK13)
    | on_path(X1,sK13) ),
    inference(superposition,[status(thm)],[c_3751,c_85]) ).

cnf(c_3984,plain,
    on_path(sK12,sK13),
    inference(superposition,[status(thm)],[c_2743,c_3929]) ).

cnf(c_4057,plain,
    ( ~ precedes(X0,X1,sK13)
    | on_path(X0,sK13) ),
    inference(superposition,[status(thm)],[c_3751,c_86]) ).

cnf(c_4118,plain,
    on_path(sK11,sK13),
    inference(superposition,[status(thm)],[c_2743,c_4057]) ).

cnf(c_4172,plain,
    ( ~ shortest_path(X0,X1,sK13)
    | ~ precedes(sK12,sK11,sK13) ),
    inference(superposition,[status(thm)],[c_2743,c_92]) ).

cnf(c_4735,plain,
    ( ~ shortest_path(X0,X1,sK13)
    | edge(sK8(sK11,sK12)) ),
    inference(superposition,[status(thm)],[c_2743,c_148]) ).

cnf(c_4743,plain,
    edge(sK8(sK11,sK12)),
    inference(superposition,[status(thm)],[c_2742,c_4735]) ).

cnf(c_4867,plain,
    ( ~ sequential(X0,X1)
    | ~ on_path(X0,sK13)
    | ~ on_path(X1,sK13)
    | precedes(X0,X1,sK13) ),
    inference(superposition,[status(thm)],[c_3751,c_81]) ).

cnf(c_5131,plain,
    ( ~ shortest_path(X0,X1,sK13)
    | ~ on_path(sK11,sK13)
    | ~ on_path(sK12,sK13)
    | ~ sequential(sK12,sK11) ),
    inference(superposition,[status(thm)],[c_4867,c_4172]) ).

cnf(c_5136,plain,
    ( ~ shortest_path(X0,X1,sK13)
    | ~ sequential(sK12,sK11) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5131,c_3984,c_4118]) ).

cnf(c_5188,plain,
    ~ sequential(sK12,sK11),
    inference(superposition,[status(thm)],[c_2742,c_5136]) ).

cnf(c_7630,plain,
    ( ~ shortest_path(X0,X1,sK13)
    | tail_of(sK8(sK11,sK12)) = head_of(sK12) ),
    inference(superposition,[status(thm)],[c_2743,c_156]) ).

cnf(c_7697,plain,
    tail_of(sK8(sK11,sK12)) = head_of(sK12),
    inference(superposition,[status(thm)],[c_2742,c_7630]) ).

cnf(c_7709,plain,
    ( head_of(sK8(sK11,sK12)) != head_of(sK12)
    | ~ edge(sK8(sK11,sK12)) ),
    inference(superposition,[status(thm)],[c_7697,c_49]) ).

cnf(c_7712,plain,
    ( head_of(X0) != head_of(sK12)
    | ~ edge(sK8(sK11,sK12))
    | ~ edge(X0)
    | sK8(sK11,sK12) = X0
    | sequential(X0,sK8(sK11,sK12)) ),
    inference(superposition,[status(thm)],[c_7697,c_75]) ).

cnf(c_7715,plain,
    head_of(sK8(sK11,sK12)) != head_of(sK12),
    inference(forward_subsumption_resolution,[status(thm)],[c_7709,c_4743]) ).

cnf(c_7737,plain,
    ( head_of(X0) != head_of(sK12)
    | ~ edge(X0)
    | sK8(sK11,sK12) = X0
    | sequential(X0,sK8(sK11,sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_7712,c_4743]) ).

cnf(c_8452,plain,
    ( ~ edge(sK12)
    | sK8(sK11,sK12) = sK12
    | sequential(sK12,sK8(sK11,sK12)) ),
    inference(equality_resolution,[status(thm)],[c_7737]) ).

cnf(c_8453,plain,
    ( sK8(sK11,sK12) = sK12
    | sequential(sK12,sK8(sK11,sK12)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8452,c_3733]) ).

cnf(c_8582,plain,
    ( ~ shortest_path(X0,X1,sK13)
    | head_of(sK8(sK11,sK12)) = tail_of(sK11) ),
    inference(superposition,[status(thm)],[c_2743,c_158]) ).

cnf(c_8626,plain,
    head_of(sK8(sK11,sK12)) = tail_of(sK11),
    inference(superposition,[status(thm)],[c_2742,c_8582]) ).

cnf(c_8632,plain,
    head_of(sK12) != tail_of(sK11),
    inference(demodulation,[status(thm)],[c_7715,c_8626]) ).

cnf(c_8650,plain,
    ( tail_of(X0) != tail_of(sK11)
    | ~ edge(sK8(sK11,sK12))
    | ~ edge(X0)
    | sK8(sK11,sK12) = X0
    | sequential(sK8(sK11,sK12),X0) ),
    inference(superposition,[status(thm)],[c_8626,c_75]) ).

cnf(c_8683,plain,
    ( tail_of(X0) != tail_of(sK11)
    | ~ edge(X0)
    | sK8(sK11,sK12) = X0
    | sequential(sK8(sK11,sK12),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8650,c_4743]) ).

cnf(c_9427,plain,
    ( ~ edge(sK11)
    | sK8(sK11,sK12) = sK11
    | sequential(sK8(sK11,sK12),sK11) ),
    inference(equality_resolution,[status(thm)],[c_8683]) ).

cnf(c_9428,plain,
    ( sK8(sK11,sK12) = sK11
    | sequential(sK8(sK11,sK12),sK11) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9427,c_3738]) ).

cnf(c_9453,plain,
    ( ~ sequential(sK12,sK8(sK11,sK12))
    | sK8(sK11,sK12) = sK11 ),
    inference(superposition,[status(thm)],[c_9428,c_989]) ).

cnf(c_9491,plain,
    ( sK8(sK11,sK12) = sK11
    | sK8(sK11,sK12) = sK12 ),
    inference(superposition,[status(thm)],[c_8453,c_9453]) ).

cnf(c_9585,plain,
    ( sK8(sK11,sK12) = sK11
    | sequential(sK12,sK11) ),
    inference(superposition,[status(thm)],[c_9491,c_9428]) ).

cnf(c_9624,plain,
    sK8(sK11,sK12) = sK11,
    inference(forward_subsumption_resolution,[status(thm)],[c_9585,c_5188]) ).

cnf(c_9663,plain,
    head_of(sK12) = tail_of(sK11),
    inference(demodulation,[status(thm)],[c_7697,c_9624]) ).

cnf(c_9668,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_9663,c_8632]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n029.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 21:44:22 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  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
% 7.43/1.69  % SZS status Started for theBenchmark.p
% 7.43/1.69  % SZS status Theorem for theBenchmark.p
% 7.43/1.69  
% 7.43/1.69  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.43/1.69  
% 7.43/1.69  ------  iProver source info
% 7.43/1.69  
% 7.43/1.69  git: date: 2024-05-02 19:28:25 +0000
% 7.43/1.69  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.43/1.69  git: non_committed_changes: false
% 7.43/1.69  
% 7.43/1.69  ------ Parsing...
% 7.43/1.69  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.43/1.69  
% 7.43/1.69  ------ Preprocessing... sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 7.43/1.69  
% 7.43/1.69  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.43/1.69  
% 7.43/1.69  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.43/1.69  ------ Proving...
% 7.43/1.69  ------ Problem Properties 
% 7.43/1.69  
% 7.43/1.69  
% 7.43/1.69  clauses                                 59
% 7.43/1.69  conjectures                             3
% 7.43/1.69  EPR                                     19
% 7.43/1.69  Horn                                    41
% 7.43/1.69  unary                                   6
% 7.43/1.69  binary                                  15
% 7.43/1.69  lits                                    180
% 7.43/1.69  lits eq                                 46
% 7.43/1.69  fd_pure                                 0
% 7.43/1.69  fd_pseudo                               0
% 7.43/1.69  fd_cond                                 0
% 7.43/1.69  fd_pseudo_cond                          5
% 7.43/1.69  AC symbols                              0
% 7.43/1.69  
% 7.43/1.69  ------ Schedule dynamic 5 is on 
% 7.43/1.69  
% 7.43/1.69  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.43/1.69  
% 7.43/1.69  
% 7.43/1.69  ------ 
% 7.43/1.69  Current options:
% 7.43/1.69  ------ 
% 7.43/1.69  
% 7.43/1.69  
% 7.43/1.69  
% 7.43/1.69  
% 7.43/1.69  ------ Proving...
% 7.43/1.69  
% 7.43/1.69  
% 7.43/1.69  % SZS status Theorem for theBenchmark.p
% 7.43/1.69  
% 7.43/1.69  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.43/1.69  
% 7.43/1.70  
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