TSTP Solution File: GRA002+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 00:03:08 EDT 2023

% Result   : Theorem 3.58s 1.18s
% Output   : CNFRefutation 3.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   77 (  17 unt;   0 def)
%            Number of atoms       :  289 (  39 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  340 ( 128   ~; 120   |;  63   &)
%                                         (   3 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   2 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :  241 (  26 sgn; 158   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
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(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(f15,axiom,
    ! [X1,X2,X3] :
      ( path(X1,X2,X3)
     => number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).

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

fof(f17,axiom,
    ! [X10,X11] : less_or_equal(number_of_in(X10,X11),number_of_in(X10,graph)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).

fof(f18,axiom,
    ( 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,conjecture,
    ( complete
   => ! [X3,X1,X2] :
        ( shortest_path(X1,X2,X3)
       => less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).

fof(f20,negated_conjecture,
    ~ ( complete
     => ! [X3,X1,X2] :
          ( shortest_path(X1,X2,X3)
         => less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
    inference(negated_conjecture,[],[f19]) ).

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(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(f33,plain,
    ! [X0,X1,X2] :
      ( path(X0,X1,X2)
     => number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
    inference(rectify,[],[f15]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4] :
            ( ( sequential(X3,X4)
              & on_path(X4,X0)
              & on_path(X3,X0) )
           => ? [X5] : triangle(X3,X4,X5) )
        & path(X1,X2,X0) )
     => number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(rectify,[],[f16]) ).

fof(f35,plain,
    ! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
    inference(rectify,[],[f17]) ).

fof(f36,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,[],[f18]) ).

fof(f37,plain,
    ~ ( complete
     => ! [X0,X1,X2] :
          ( shortest_path(X1,X2,X0)
         => less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
    inference(rectify,[],[f20]) ).

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(ennf_transformation,[],[f27]) ).

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(flattening,[],[f49]) ).

fof(f52,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(f56,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
      | ~ path(X0,X1,X2) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f57]) ).

fof(f59,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,[],[f36]) ).

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(flattening,[],[f59]) ).

fof(f61,plain,
    ( ? [X0,X1,X2] :
        ( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
        & shortest_path(X1,X2,X0) )
    & complete ),
    inference(ennf_transformation,[],[f37]) ).

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,[],[f52]) ).

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] :
      ( ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
     => ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
        & sequential(sK6(X0),sK7(X0))
        & on_path(sK7(X0),X0)
        & on_path(sK6(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
        & sequential(sK6(X0),sK7(X0))
        & on_path(sK7(X0),X0)
        & on_path(sK6(X0),X0) )
      | ~ path(X1,X2,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f58,f88]) ).

fof(f90,plain,
    ! [X2,X3] :
      ( ? [X5] : triangle(X2,X3,X5)
     => triangle(X2,X3,sK8(X2,X3)) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ( ! [X0,X1,X2,X3,X4] :
        ( triangle(X2,X3,sK8(X2,X3))
        | ~ sequential(X2,X3)
        | ~ precedes(X2,X3,X4)
        | ~ shortest_path(X0,X1,X4) )
    | ~ complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f60,f90]) ).

fof(f92,plain,
    ( ? [X0,X1,X2] :
        ( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
        & shortest_path(X1,X2,X0) )
   => ( ~ less_or_equal(minus(length_of(sK9),n1),number_of_in(triangles,graph))
      & shortest_path(sK10,sK11,sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ( ~ less_or_equal(minus(length_of(sK9),n1),number_of_in(triangles,graph))
    & shortest_path(sK10,sK11,sK9)
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f61,f92]) ).

fof(f125,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,[],[f50]) ).

fof(f132,plain,
    ! [X2,X0,X1] :
      ( path(X0,X1,X2)
      | ~ shortest_path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f147,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
      | ~ path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f148,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | on_path(sK6(X0),X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f149,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | on_path(sK7(X0),X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | sequential(sK6(X0),sK7(X0))
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f151,plain,
    ! [X2,X0,X1,X5] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ triangle(sK6(X0),sK7(X0),X5)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f152,plain,
    ! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
    inference(cnf_transformation,[],[f35]) ).

fof(f153,plain,
    ! [X2,X3,X0,X1,X4] :
      ( triangle(X2,X3,sK8(X2,X3))
      | ~ sequential(X2,X3)
      | ~ precedes(X2,X3,X4)
      | ~ shortest_path(X0,X1,X4)
      | ~ complete ),
    inference(cnf_transformation,[],[f91]) ).

fof(f154,plain,
    complete,
    inference(cnf_transformation,[],[f93]) ).

fof(f155,plain,
    shortest_path(sK10,sK11,sK9),
    inference(cnf_transformation,[],[f93]) ).

fof(f156,plain,
    ~ less_or_equal(minus(length_of(sK9),n1),number_of_in(triangles,graph)),
    inference(cnf_transformation,[],[f93]) ).

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,[],[f125]) ).

cnf(c_91,plain,
    ( ~ shortest_path(X0,X1,X2)
    | path(X0,X1,X2) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_102,plain,
    ( ~ path(X0,X1,X2)
    | minus(length_of(X2),n1) = number_of_in(sequential_pairs,X2) ),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_103,plain,
    ( ~ triangle(sK6(X0),sK7(X0),X1)
    | ~ path(X2,X3,X0)
    | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_104,plain,
    ( ~ path(X0,X1,X2)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
    | sequential(sK6(X2),sK7(X2)) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_105,plain,
    ( ~ path(X0,X1,X2)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
    | on_path(sK7(X2),X2) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_106,plain,
    ( ~ path(X0,X1,X2)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
    | on_path(sK6(X2),X2) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_107,plain,
    less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_108,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | ~ sequential(X0,X1)
    | ~ complete
    | triangle(X0,X1,sK8(X0,X1)) ),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_109,negated_conjecture,
    ~ less_or_equal(minus(length_of(sK9),n1),number_of_in(triangles,graph)),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_110,negated_conjecture,
    shortest_path(sK10,sK11,sK9),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_111,negated_conjecture,
    complete,
    inference(cnf_transformation,[],[f154]) ).

cnf(c_156,plain,
    ( ~ sequential(X0,X1)
    | ~ shortest_path(X3,X4,X2)
    | ~ precedes(X0,X1,X2)
    | triangle(X0,X1,sK8(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_108,c_111,c_108]) ).

cnf(c_157,plain,
    ( ~ precedes(X0,X1,X2)
    | ~ shortest_path(X3,X4,X2)
    | ~ sequential(X0,X1)
    | triangle(X0,X1,sK8(X0,X1)) ),
    inference(renaming,[status(thm)],[c_156]) ).

cnf(c_1418,plain,
    ( X0 != sK10
    | X1 != sK11
    | X2 != sK9
    | path(X0,X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_91,c_110]) ).

cnf(c_1419,plain,
    path(sK10,sK11,sK9),
    inference(unflattening,[status(thm)],[c_1418]) ).

cnf(c_3907,plain,
    path(sK10,sK11,sK9),
    inference(superposition,[status(thm)],[c_110,c_91]) ).

cnf(c_4283,plain,
    minus(length_of(sK9),n1) = number_of_in(sequential_pairs,sK9),
    inference(superposition,[status(thm)],[c_3907,c_102]) ).

cnf(c_4292,plain,
    ~ less_or_equal(number_of_in(sequential_pairs,sK9),number_of_in(triangles,graph)),
    inference(demodulation,[status(thm)],[c_109,c_4283]) ).

cnf(c_4540,plain,
    ( ~ path(sK10,sK11,sK9)
    | number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9)
    | on_path(sK6(sK9),sK9) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_4541,plain,
    ( ~ path(sK10,sK11,sK9)
    | number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9)
    | on_path(sK7(sK9),sK9) ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_5282,plain,
    ( ~ sequential(X0,X1)
    | ~ on_path(X0,sK9)
    | ~ on_path(X1,sK9)
    | precedes(X0,X1,sK9) ),
    inference(superposition,[status(thm)],[c_3907,c_81]) ).

cnf(c_8552,plain,
    ( ~ shortest_path(X0,X1,sK9)
    | ~ sequential(X2,X3)
    | ~ on_path(X2,sK9)
    | ~ on_path(X3,sK9)
    | triangle(X2,X3,sK8(X2,X3)) ),
    inference(superposition,[status(thm)],[c_5282,c_157]) ).

cnf(c_8860,plain,
    ( ~ sequential(X0,X1)
    | ~ on_path(X0,sK9)
    | ~ on_path(X1,sK9)
    | triangle(X0,X1,sK8(X0,X1)) ),
    inference(superposition,[status(thm)],[c_110,c_8552]) ).

cnf(c_8883,plain,
    ( ~ sequential(sK6(X0),sK7(X0))
    | ~ path(X1,X2,X0)
    | ~ on_path(sK6(X0),sK9)
    | ~ on_path(sK7(X0),sK9)
    | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(superposition,[status(thm)],[c_8860,c_103]) ).

cnf(c_9449,plain,
    ( ~ path(X0,X1,X2)
    | ~ on_path(sK6(X2),sK9)
    | ~ on_path(sK7(X2),sK9)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_8883,c_104]) ).

cnf(c_9459,plain,
    ( ~ on_path(sK6(sK9),sK9)
    | ~ on_path(sK7(sK9),sK9)
    | number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9) ),
    inference(superposition,[status(thm)],[c_3907,c_9449]) ).

cnf(c_9533,plain,
    number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9),
    inference(global_subsumption_just,[status(thm)],[c_9459,c_1419,c_4541,c_4540,c_9459]) ).

cnf(c_9548,plain,
    less_or_equal(number_of_in(sequential_pairs,sK9),number_of_in(triangles,graph)),
    inference(superposition,[status(thm)],[c_9533,c_107]) ).

cnf(c_9549,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_9548,c_4292]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.19/0.36  % Computer : n016.cluster.edu
% 0.19/0.36  % Model    : x86_64 x86_64
% 0.19/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36  % Memory   : 8042.1875MB
% 0.19/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36  % CPULimit : 300
% 0.19/0.36  % WCLimit  : 300
% 0.19/0.36  % DateTime : Sun Aug 27 04:17:43 EDT 2023
% 0.19/0.37  % CPUTime  : 
% 0.22/0.50  Running first-order theorem proving
% 0.22/0.50  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.58/1.18  % SZS status Started for theBenchmark.p
% 3.58/1.18  % SZS status Theorem for theBenchmark.p
% 3.58/1.18  
% 3.58/1.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.58/1.18  
% 3.58/1.18  ------  iProver source info
% 3.58/1.18  
% 3.58/1.18  git: date: 2023-05-31 18:12:56 +0000
% 3.58/1.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.58/1.18  git: non_committed_changes: false
% 3.58/1.18  git: last_make_outside_of_git: false
% 3.58/1.18  
% 3.58/1.18  ------ Parsing...
% 3.58/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.58/1.18  
% 3.58/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.58/1.18  
% 3.58/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.58/1.18  
% 3.58/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.58/1.18  ------ Proving...
% 3.58/1.18  ------ Problem Properties 
% 3.58/1.18  
% 3.58/1.18  
% 3.58/1.18  clauses                                 62
% 3.58/1.18  conjectures                             2
% 3.58/1.18  EPR                                     23
% 3.58/1.18  Horn                                    44
% 3.58/1.18  unary                                   5
% 3.58/1.18  binary                                  20
% 3.58/1.18  lits                                    187
% 3.58/1.18  lits eq                                 44
% 3.58/1.18  fd_pure                                 0
% 3.58/1.18  fd_pseudo                               0
% 3.58/1.18  fd_cond                                 0
% 3.58/1.18  fd_pseudo_cond                          5
% 3.58/1.18  AC symbols                              0
% 3.58/1.18  
% 3.58/1.18  ------ Schedule dynamic 5 is on 
% 3.58/1.18  
% 3.58/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.58/1.18  
% 3.58/1.18  
% 3.58/1.18  ------ 
% 3.58/1.18  Current options:
% 3.58/1.18  ------ 
% 3.58/1.18  
% 3.58/1.18  
% 3.58/1.18  
% 3.58/1.18  
% 3.58/1.18  ------ Proving...
% 3.58/1.18  
% 3.58/1.18  
% 3.58/1.18  % SZS status Theorem for theBenchmark.p
% 3.58/1.18  
% 3.58/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.58/1.19  
% 3.58/1.19  
%------------------------------------------------------------------------------