TSTP Solution File: MGT028+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n007.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 : Wed Aug 31 17:50:58 EDT 2022

% Result   : Theorem 0.21s 0.50s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   94 (   6 unt;   0 def)
%            Number of atoms       :  479 (   2 equ)
%            Maximal formula atoms :   15 (   5 avg)
%            Number of connectives :  662 ( 277   ~; 277   |;  81   &)
%                                         (   6 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   7 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-2 aty)
%            Number of variables   :  158 ( 130   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f129,plain,
    $false,
    inference(avatar_sat_refutation,[],[f53,f76,f100,f107,f113,f119,f124,f128]) ).

fof(f128,plain,
    ( ~ spl7_2
    | ~ spl7_3
    | ~ spl7_5 ),
    inference(avatar_contradiction_clause,[],[f127]) ).

fof(f127,plain,
    ( $false
    | ~ spl7_2
    | ~ spl7_3
    | ~ spl7_5 ),
    inference(subsumption_resolution,[],[f126,f94]) ).

fof(f94,plain,
    ( in_environment(sK1,sK0(sK1))
    | ~ spl7_5 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f93,plain,
    ( spl7_5
  <=> in_environment(sK1,sK0(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).

fof(f126,plain,
    ( ~ in_environment(sK1,sK0(sK1))
    | ~ spl7_2
    | ~ spl7_3 ),
    inference(duplicate_literal_removal,[],[f125]) ).

fof(f125,plain,
    ( ~ in_environment(sK1,sK0(sK1))
    | ~ in_environment(sK1,sK0(sK1))
    | ~ spl7_2
    | ~ spl7_3 ),
    inference(resolution,[],[f75,f52]) ).

fof(f52,plain,
    ( ! [X0] :
        ( greater_or_equal(sK4(sK1,X0),X0)
        | ~ in_environment(sK1,X0) )
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f51,plain,
    ( spl7_2
  <=> ! [X0] :
        ( ~ in_environment(sK1,X0)
        | greater_or_equal(sK4(sK1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f75,plain,
    ( ! [X0] :
        ( ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
        | ~ in_environment(sK1,X0) )
    | ~ spl7_3 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f74,plain,
    ( spl7_3
  <=> ! [X0] :
        ( ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
        | ~ in_environment(sK1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).

fof(f124,plain,
    ( ~ spl7_1
    | ~ spl7_6 ),
    inference(avatar_split_clause,[],[f121,f105,f47]) ).

fof(f47,plain,
    ( spl7_1
  <=> greater(sK3(sK1),sF5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f105,plain,
    ( spl7_6
  <=> ! [X0] :
        ( ~ greater(X0,sF5)
        | ~ greater_or_equal(sK2(X0),sK3(sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).

fof(f121,plain,
    ( ~ greater(sK3(sK1),sF5)
    | ~ spl7_6 ),
    inference(duplicate_literal_removal,[],[f120]) ).

fof(f120,plain,
    ( ~ greater(sK3(sK1),sF5)
    | ~ greater(sK3(sK1),sF5)
    | ~ spl7_6 ),
    inference(resolution,[],[f106,f39]) ).

fof(f39,plain,
    ! [X1] :
      ( greater_or_equal(sK2(X1),X1)
      | ~ greater(X1,sF5) ),
    inference(definition_folding,[],[f29,f37]) ).

fof(f37,plain,
    appear(efficient_producers,sK1) = sF5,
    introduced(function_definition,[]) ).

fof(f29,plain,
    ! [X1] :
      ( greater_or_equal(sK2(X1),X1)
      | ~ greater(X1,appear(efficient_producers,sK1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ! [X1] :
        ( ( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
          & greater_or_equal(sK2(X1),X1)
          & ~ greater(zero,growth_rate(first_movers,sK2(X1))) )
        | ~ greater(X1,appear(efficient_producers,sK1)) )
    & environment(sK1)
    & stable(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f17,f16]) ).

fof(f16,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( ? [X2] :
                ( subpopulations(first_movers,efficient_producers,X0,X2)
                & greater_or_equal(X2,X1)
                & ~ greater(zero,growth_rate(first_movers,X2)) )
            | ~ greater(X1,appear(efficient_producers,X0)) )
        & environment(X0)
        & stable(X0) )
   => ( ! [X1] :
          ( ? [X2] :
              ( subpopulations(first_movers,efficient_producers,sK1,X2)
              & greater_or_equal(X2,X1)
              & ~ greater(zero,growth_rate(first_movers,X2)) )
          | ~ greater(X1,appear(efficient_producers,sK1)) )
      & environment(sK1)
      & stable(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X1] :
      ( ? [X2] :
          ( subpopulations(first_movers,efficient_producers,sK1,X2)
          & greater_or_equal(X2,X1)
          & ~ greater(zero,growth_rate(first_movers,X2)) )
     => ( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
        & greater_or_equal(sK2(X1),X1)
        & ~ greater(zero,growth_rate(first_movers,sK2(X1))) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( subpopulations(first_movers,efficient_producers,X0,X2)
              & greater_or_equal(X2,X1)
              & ~ greater(zero,growth_rate(first_movers,X2)) )
          | ~ greater(X1,appear(efficient_producers,X0)) )
      & environment(X0)
      & stable(X0) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ greater(X1,appear(efficient_producers,X0))
          | ? [X2] :
              ( ~ greater(zero,growth_rate(first_movers,X2))
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) ) )
      & stable(X0)
      & environment(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,plain,
    ~ ! [X0] :
        ( ( stable(X0)
          & environment(X0) )
       => ? [X1] :
            ( greater(X1,appear(efficient_producers,X0))
            & ! [X2] :
                ( ( greater_or_equal(X2,X1)
                  & subpopulations(first_movers,efficient_producers,X0,X2) )
               => greater(zero,growth_rate(first_movers,X2)) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,negated_conjecture,
    ~ ! [X0] :
        ( ( stable(X0)
          & environment(X0) )
       => ? [X4] :
            ( greater(X4,appear(efficient_producers,X0))
            & ! [X2] :
                ( ( greater_or_equal(X2,X4)
                  & subpopulations(first_movers,efficient_producers,X0,X2) )
               => greater(zero,growth_rate(first_movers,X2)) ) ) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f3,conjecture,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X4] :
          ( greater(X4,appear(efficient_producers,X0))
          & ! [X2] :
              ( ( greater_or_equal(X2,X4)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
             => greater(zero,growth_rate(first_movers,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10) ).

fof(f106,plain,
    ( ! [X0] :
        ( ~ greater_or_equal(sK2(X0),sK3(sK1))
        | ~ greater(X0,sF5) )
    | ~ spl7_6 ),
    inference(avatar_component_clause,[],[f105]) ).

fof(f119,plain,
    ( spl7_6
    | ~ spl7_4 ),
    inference(avatar_split_clause,[],[f118,f90,f105]) ).

fof(f90,plain,
    ( spl7_4
  <=> ! [X1] :
        ( greater(zero,growth_rate(first_movers,X1))
        | ~ greater_or_equal(X1,sK3(sK1))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).

fof(f118,plain,
    ( ! [X0] :
        ( ~ greater_or_equal(sK2(X0),sK3(sK1))
        | ~ greater(X0,sF5) )
    | ~ spl7_4 ),
    inference(subsumption_resolution,[],[f117,f41]) ).

fof(f41,plain,
    ! [X1] :
      ( ~ greater(zero,sF6(X1))
      | ~ greater(X1,sF5) ),
    inference(definition_folding,[],[f28,f37,f40]) ).

fof(f40,plain,
    ! [X1] : growth_rate(first_movers,sK2(X1)) = sF6(X1),
    introduced(function_definition,[]) ).

fof(f28,plain,
    ! [X1] :
      ( ~ greater(zero,growth_rate(first_movers,sK2(X1)))
      | ~ greater(X1,appear(efficient_producers,sK1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f117,plain,
    ( ! [X0] :
        ( ~ greater(X0,sF5)
        | greater(zero,sF6(X0))
        | ~ greater_or_equal(sK2(X0),sK3(sK1)) )
    | ~ spl7_4 ),
    inference(resolution,[],[f116,f38]) ).

fof(f38,plain,
    ! [X1] :
      ( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
      | ~ greater(X1,sF5) ),
    inference(definition_folding,[],[f30,f37]) ).

fof(f30,plain,
    ! [X1] :
      ( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
      | ~ greater(X1,appear(efficient_producers,sK1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f116,plain,
    ( ! [X0] :
        ( ~ subpopulations(first_movers,efficient_producers,sK1,sK2(X0))
        | greater(zero,sF6(X0))
        | ~ greater_or_equal(sK2(X0),sK3(sK1)) )
    | ~ spl7_4 ),
    inference(superposition,[],[f91,f40]) ).

fof(f91,plain,
    ( ! [X1] :
        ( greater(zero,growth_rate(first_movers,X1))
        | ~ greater_or_equal(X1,sK3(sK1))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X1) )
    | ~ spl7_4 ),
    inference(avatar_component_clause,[],[f90]) ).

fof(f113,plain,
    ( spl7_4
    | spl7_4
    | ~ spl7_2
    | ~ spl7_5 ),
    inference(avatar_split_clause,[],[f112,f93,f51,f90,f90]) ).

fof(f112,plain,
    ( ! [X0,X1] :
        ( greater(zero,growth_rate(first_movers,X0))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X0)
        | ~ subpopulations(first_movers,efficient_producers,sK1,X1)
        | ~ greater_or_equal(X0,sK3(sK1))
        | ~ greater_or_equal(X1,sK3(sK1))
        | greater(zero,growth_rate(first_movers,X1)) )
    | ~ spl7_2
    | ~ spl7_5 ),
    inference(subsumption_resolution,[],[f111,f27]) ).

fof(f27,plain,
    environment(sK1),
    inference(cnf_transformation,[],[f18]) ).

fof(f111,plain,
    ( ! [X0,X1] :
        ( ~ greater_or_equal(X1,sK3(sK1))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X0)
        | greater(zero,growth_rate(first_movers,X1))
        | greater(zero,growth_rate(first_movers,X0))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X1)
        | ~ environment(sK1)
        | ~ greater_or_equal(X0,sK3(sK1)) )
    | ~ spl7_2
    | ~ spl7_5 ),
    inference(subsumption_resolution,[],[f110,f94]) ).

fof(f110,plain,
    ( ! [X0,X1] :
        ( greater(zero,growth_rate(first_movers,X0))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X0)
        | ~ greater_or_equal(X1,sK3(sK1))
        | greater(zero,growth_rate(first_movers,X1))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X1)
        | ~ in_environment(sK1,sK0(sK1))
        | ~ environment(sK1)
        | ~ greater_or_equal(X0,sK3(sK1)) )
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f109,f26]) ).

fof(f26,plain,
    stable(sK1),
    inference(cnf_transformation,[],[f18]) ).

fof(f109,plain,
    ( ! [X0,X1] :
        ( ~ subpopulations(first_movers,efficient_producers,sK1,X1)
        | ~ stable(sK1)
        | greater(zero,growth_rate(first_movers,X1))
        | greater(zero,growth_rate(first_movers,X0))
        | ~ greater_or_equal(X0,sK3(sK1))
        | ~ subpopulations(first_movers,efficient_producers,sK1,X0)
        | ~ in_environment(sK1,sK0(sK1))
        | ~ environment(sK1)
        | ~ greater_or_equal(X1,sK3(sK1)) )
    | ~ spl7_2 ),
    inference(duplicate_literal_removal,[],[f108]) ).

fof(f108,plain,
    ( ! [X0,X1] :
        ( ~ stable(sK1)
        | ~ subpopulations(first_movers,efficient_producers,sK1,X0)
        | ~ subpopulations(first_movers,efficient_producers,sK1,X1)
        | ~ in_environment(sK1,sK0(sK1))
        | ~ greater_or_equal(X0,sK3(sK1))
        | ~ greater_or_equal(X1,sK3(sK1))
        | ~ in_environment(sK1,sK0(sK1))
        | greater(zero,growth_rate(first_movers,X0))
        | greater(zero,growth_rate(first_movers,X1))
        | ~ environment(sK1) )
    | ~ spl7_2 ),
    inference(resolution,[],[f52,f79]) ).

fof(f79,plain,
    ! [X2,X3,X0,X1] :
      ( ~ greater_or_equal(sK4(X0,X2),sK0(X0))
      | greater(zero,growth_rate(first_movers,X3))
      | ~ environment(X0)
      | ~ greater_or_equal(X1,sK3(X0))
      | greater(zero,growth_rate(first_movers,X1))
      | ~ subpopulations(first_movers,efficient_producers,X0,X3)
      | ~ greater_or_equal(X3,sK3(X0))
      | ~ stable(X0)
      | ~ in_environment(X0,X2)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(duplicate_literal_removal,[],[f77]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1] :
      ( ~ stable(X0)
      | greater(zero,growth_rate(first_movers,X3))
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X3)
      | greater(zero,growth_rate(first_movers,X1))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ stable(X0)
      | ~ environment(X0)
      | ~ greater_or_equal(sK4(X0,X2),sK0(X0))
      | ~ environment(X0)
      | ~ greater_or_equal(X1,sK3(X0))
      | ~ greater_or_equal(X3,sK3(X0))
      | ~ in_environment(X0,X2)
      | ~ stable(X0)
      | ~ in_environment(X0,X2) ),
    inference(resolution,[],[f65,f36]) ).

fof(f36,plain,
    ! [X2,X3,X0] :
      ( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ greater_or_equal(X2,sK3(X0))
      | ~ stable(X0)
      | greater(zero,growth_rate(first_movers,X2))
      | ~ environment(X0)
      | ~ in_environment(X0,X3) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ( ! [X2] :
            ( greater(zero,growth_rate(first_movers,X2))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2)
            | ~ greater_or_equal(X2,sK3(X0)) )
        & greater(sK3(X0),appear(efficient_producers,X0)) )
      | ~ stable(X0)
      | ~ environment(X0)
      | ! [X3] :
          ( ( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
            & greater_or_equal(sK4(X0,X3),X3)
            & ~ greater(zero,growth_rate(first_movers,sK4(X0,X3))) )
          | ~ in_environment(X0,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f19,f21,f20]) ).

fof(f20,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(zero,growth_rate(first_movers,X2))
              | ~ subpopulations(first_movers,efficient_producers,X0,X2)
              | ~ greater_or_equal(X2,X1) )
          & greater(X1,appear(efficient_producers,X0)) )
     => ( ! [X2] :
            ( greater(zero,growth_rate(first_movers,X2))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2)
            | ~ greater_or_equal(X2,sK3(X0)) )
        & greater(sK3(X0),appear(efficient_producers,X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X3] :
      ( ? [X4] :
          ( subpopulations(first_movers,efficient_producers,X0,X4)
          & greater_or_equal(X4,X3)
          & ~ greater(zero,growth_rate(first_movers,X4)) )
     => ( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
        & greater_or_equal(sK4(X0,X3),X3)
        & ~ greater(zero,growth_rate(first_movers,sK4(X0,X3))) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(zero,growth_rate(first_movers,X2))
              | ~ subpopulations(first_movers,efficient_producers,X0,X2)
              | ~ greater_or_equal(X2,X1) )
          & greater(X1,appear(efficient_producers,X0)) )
      | ~ stable(X0)
      | ~ environment(X0)
      | ! [X3] :
          ( ? [X4] :
              ( subpopulations(first_movers,efficient_producers,X0,X4)
              & greater_or_equal(X4,X3)
              & ~ greater(zero,growth_rate(first_movers,X4)) )
          | ~ in_environment(X0,X3) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(zero,growth_rate(first_movers,X4))
              | ~ subpopulations(first_movers,efficient_producers,X0,X4)
              | ~ greater_or_equal(X4,X3) )
          & greater(X3,appear(efficient_producers,X0)) )
      | ~ stable(X0)
      | ~ environment(X0)
      | ! [X1] :
          ( ? [X2] :
              ( subpopulations(first_movers,efficient_producers,X0,X2)
              & greater_or_equal(X2,X1)
              & ~ greater(zero,growth_rate(first_movers,X2)) )
          | ~ in_environment(X0,X1) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(zero,growth_rate(first_movers,X4))
              | ~ subpopulations(first_movers,efficient_producers,X0,X4)
              | ~ greater_or_equal(X4,X3) )
          & greater(X3,appear(efficient_producers,X0)) )
      | ! [X1] :
          ( ? [X2] :
              ( ~ greater(zero,growth_rate(first_movers,X2))
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
          | ~ in_environment(X0,X1) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( ! [X2] :
                ( ( greater_or_equal(X2,X1)
                  & subpopulations(first_movers,efficient_producers,X0,X2) )
               => greater(zero,growth_rate(first_movers,X2)) )
            & in_environment(X0,X1) )
        & stable(X0)
        & environment(X0) )
     => ? [X3] :
          ( ! [X4] :
              ( ( subpopulations(first_movers,efficient_producers,X0,X4)
                & greater_or_equal(X4,X3) )
             => greater(zero,growth_rate(first_movers,X4)) )
          & greater(X3,appear(efficient_producers,X0)) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ( ? [X1] :
            ( ! [X2] :
                ( ( greater_or_equal(X2,X1)
                  & subpopulations(first_movers,efficient_producers,X0,X2) )
               => greater(zero,growth_rate(first_movers,X2)) )
            & in_environment(X0,X1) )
        & stable(X0)
        & environment(X0) )
     => ? [X3] :
          ( greater(X3,appear(efficient_producers,X0))
          & ! [X2] :
              ( ( subpopulations(first_movers,efficient_producers,X0,X2)
                & greater_or_equal(X2,X3) )
             => greater(zero,growth_rate(first_movers,X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).

fof(f65,plain,
    ! [X8,X6,X7,X5] :
      ( ~ subpopulations(first_movers,efficient_producers,X8,sK4(X5,X7))
      | ~ subpopulations(first_movers,efficient_producers,X5,X6)
      | ~ in_environment(X5,X7)
      | ~ greater_or_equal(sK4(X5,X7),sK0(X8))
      | ~ stable(X5)
      | ~ environment(X5)
      | ~ environment(X8)
      | greater(zero,growth_rate(first_movers,X6))
      | ~ stable(X8)
      | ~ greater_or_equal(X6,sK3(X5)) ),
    inference(resolution,[],[f34,f25]) ).

fof(f25,plain,
    ! [X2,X0] :
      ( greater(zero,growth_rate(first_movers,X2))
      | ~ environment(X0)
      | ~ stable(X0)
      | ~ greater_or_equal(X2,sK0(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ~ environment(X0)
      | ~ stable(X0)
      | ( ! [X2] :
            ( ( greater(zero,growth_rate(first_movers,X2))
              & greater(growth_rate(efficient_producers,X2),zero) )
            | ~ subpopulations(first_movers,efficient_producers,X0,X2)
            | ~ greater_or_equal(X2,sK0(X0)) )
        & in_environment(X0,sK0(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( greater(zero,growth_rate(first_movers,X2))
                & greater(growth_rate(efficient_producers,X2),zero) )
              | ~ subpopulations(first_movers,efficient_producers,X0,X2)
              | ~ greater_or_equal(X2,X1) )
          & in_environment(X0,X1) )
     => ( ! [X2] :
            ( ( greater(zero,growth_rate(first_movers,X2))
              & greater(growth_rate(efficient_producers,X2),zero) )
            | ~ subpopulations(first_movers,efficient_producers,X0,X2)
            | ~ greater_or_equal(X2,sK0(X0)) )
        & in_environment(X0,sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X0] :
      ( ~ environment(X0)
      | ~ stable(X0)
      | ? [X1] :
          ( ! [X2] :
              ( ( greater(zero,growth_rate(first_movers,X2))
                & greater(growth_rate(efficient_producers,X2),zero) )
              | ~ subpopulations(first_movers,efficient_producers,X0,X2)
              | ~ greater_or_equal(X2,X1) )
          & in_environment(X0,X1) ) ),
    inference(flattening,[],[f8]) ).

fof(f8,plain,
    ! [X0] :
      ( ? [X1] :
          ( in_environment(X0,X1)
          & ! [X2] :
              ( ( greater(zero,growth_rate(first_movers,X2))
                & greater(growth_rate(efficient_producers,X2),zero) )
              | ~ subpopulations(first_movers,efficient_producers,X0,X2)
              | ~ greater_or_equal(X2,X1) ) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X1] :
          ( in_environment(X0,X1)
          & ! [X2] :
              ( ( subpopulations(first_movers,efficient_producers,X0,X2)
                & greater_or_equal(X2,X1) )
             => ( greater(zero,growth_rate(first_movers,X2))
                & greater(growth_rate(efficient_producers,X2),zero) ) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X4] :
          ( in_environment(X0,X4)
          & ! [X2] :
              ( ( subpopulations(first_movers,efficient_producers,X0,X2)
                & greater_or_equal(X2,X4) )
             => ( greater(zero,growth_rate(first_movers,X2))
                & greater(growth_rate(efficient_producers,X2),zero) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11) ).

fof(f34,plain,
    ! [X2,X3,X0] :
      ( ~ greater(zero,growth_rate(first_movers,sK4(X0,X3)))
      | ~ stable(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ environment(X0)
      | greater(zero,growth_rate(first_movers,X2))
      | ~ in_environment(X0,X3)
      | ~ greater_or_equal(X2,sK3(X0)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f107,plain,
    ( spl7_2
    | spl7_6 ),
    inference(avatar_split_clause,[],[f103,f105,f51]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ~ greater(X0,sF5)
      | ~ greater_or_equal(sK2(X0),sK3(sK1))
      | ~ in_environment(sK1,X1)
      | greater_or_equal(sK4(sK1,X1),X1) ),
    inference(subsumption_resolution,[],[f102,f41]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(sK2(X0),sK3(sK1))
      | greater(zero,sF6(X0))
      | ~ greater(X0,sF5)
      | ~ in_environment(sK1,X1)
      | greater_or_equal(sK4(sK1,X1),X1) ),
    inference(subsumption_resolution,[],[f101,f27]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ in_environment(sK1,X1)
      | ~ environment(sK1)
      | greater_or_equal(sK4(sK1,X1),X1)
      | ~ greater_or_equal(sK2(X0),sK3(sK1))
      | greater(zero,sF6(X0))
      | ~ greater(X0,sF5) ),
    inference(subsumption_resolution,[],[f63,f26]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ greater(X0,sF5)
      | greater_or_equal(sK4(sK1,X1),X1)
      | greater(zero,sF6(X0))
      | ~ stable(sK1)
      | ~ in_environment(sK1,X1)
      | ~ greater_or_equal(sK2(X0),sK3(sK1))
      | ~ environment(sK1) ),
    inference(resolution,[],[f62,f38]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
      | greater(zero,sF6(X0))
      | ~ greater_or_equal(sK2(X0),sK3(X1))
      | ~ stable(X1)
      | greater_or_equal(sK4(X1,X2),X2)
      | ~ in_environment(X1,X2)
      | ~ environment(X1) ),
    inference(superposition,[],[f35,f40]) ).

fof(f35,plain,
    ! [X2,X3,X0] :
      ( greater(zero,growth_rate(first_movers,X2))
      | ~ stable(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | greater_or_equal(sK4(X0,X3),X3)
      | ~ greater_or_equal(X2,sK3(X0))
      | ~ environment(X0)
      | ~ in_environment(X0,X3) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f100,plain,
    spl7_5,
    inference(avatar_contradiction_clause,[],[f99]) ).

fof(f99,plain,
    ( $false
    | spl7_5 ),
    inference(subsumption_resolution,[],[f98,f26]) ).

fof(f98,plain,
    ( ~ stable(sK1)
    | spl7_5 ),
    inference(subsumption_resolution,[],[f97,f27]) ).

fof(f97,plain,
    ( ~ environment(sK1)
    | ~ stable(sK1)
    | spl7_5 ),
    inference(resolution,[],[f95,f23]) ).

fof(f23,plain,
    ! [X0] :
      ( in_environment(X0,sK0(X0))
      | ~ environment(X0)
      | ~ stable(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f95,plain,
    ( ~ in_environment(sK1,sK0(sK1))
    | spl7_5 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f76,plain,
    ( spl7_3
    | spl7_1 ),
    inference(avatar_split_clause,[],[f72,f47,f74]) ).

fof(f72,plain,
    ! [X0] :
      ( greater(sK3(sK1),sF5)
      | ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
      | ~ in_environment(sK1,X0) ),
    inference(subsumption_resolution,[],[f71,f26]) ).

fof(f71,plain,
    ! [X0] :
      ( ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
      | ~ in_environment(sK1,X0)
      | greater(sK3(sK1),sF5)
      | ~ stable(sK1) ),
    inference(subsumption_resolution,[],[f70,f27]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ environment(sK1)
      | ~ stable(sK1)
      | ~ in_environment(sK1,X0)
      | greater(sK3(sK1),sF5)
      | ~ greater_or_equal(sK4(sK1,X0),sK0(sK1)) ),
    inference(superposition,[],[f69,f37]) ).

fof(f69,plain,
    ! [X3,X4] :
      ( greater(sK3(X3),appear(efficient_producers,X3))
      | ~ stable(X3)
      | ~ greater_or_equal(sK4(X3,X4),sK0(X3))
      | ~ environment(X3)
      | ~ in_environment(X3,X4) ),
    inference(duplicate_literal_removal,[],[f67]) ).

fof(f67,plain,
    ! [X3,X4] :
      ( ~ in_environment(X3,X4)
      | greater(sK3(X3),appear(efficient_producers,X3))
      | ~ stable(X3)
      | ~ environment(X3)
      | ~ in_environment(X3,X4)
      | ~ environment(X3)
      | greater(sK3(X3),appear(efficient_producers,X3))
      | ~ stable(X3)
      | ~ greater_or_equal(sK4(X3,X4),sK0(X3))
      | ~ environment(X3)
      | ~ stable(X3) ),
    inference(resolution,[],[f60,f33]) ).

fof(f33,plain,
    ! [X3,X0] :
      ( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
      | ~ in_environment(X0,X3)
      | greater(sK3(X0),appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X2,sK4(X0,X1))
      | ~ stable(X2)
      | greater(sK3(X0),appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X2)
      | ~ environment(X0)
      | ~ greater_or_equal(sK4(X0,X1),sK0(X2))
      | ~ in_environment(X0,X1) ),
    inference(resolution,[],[f31,f25]) ).

fof(f31,plain,
    ! [X3,X0] :
      ( ~ greater(zero,growth_rate(first_movers,sK4(X0,X3)))
      | ~ environment(X0)
      | greater(sK3(X0),appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ in_environment(X0,X3) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f53,plain,
    ( spl7_1
    | spl7_2 ),
    inference(avatar_split_clause,[],[f45,f51,f47]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ in_environment(sK1,X0)
      | greater_or_equal(sK4(sK1,X0),X0)
      | greater(sK3(sK1),sF5) ),
    inference(subsumption_resolution,[],[f44,f27]) ).

fof(f44,plain,
    ! [X0] :
      ( ~ environment(sK1)
      | ~ in_environment(sK1,X0)
      | greater(sK3(sK1),sF5)
      | greater_or_equal(sK4(sK1,X0),X0) ),
    inference(subsumption_resolution,[],[f43,f26]) ).

fof(f43,plain,
    ! [X0] :
      ( ~ stable(sK1)
      | ~ in_environment(sK1,X0)
      | ~ environment(sK1)
      | greater(sK3(sK1),sF5)
      | greater_or_equal(sK4(sK1,X0),X0) ),
    inference(superposition,[],[f32,f37]) ).

fof(f32,plain,
    ! [X3,X0] :
      ( greater(sK3(X0),appear(efficient_producers,X0))
      | ~ in_environment(X0,X3)
      | ~ environment(X0)
      | greater_or_equal(sK4(X0,X3),X3)
      | ~ stable(X0) ),
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n007.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   : Tue Aug 30 03:00:15 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.21/0.49  % (14141)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.49  % (14126)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.49  % (14126)First to succeed.
% 0.21/0.50  % (14126)Refutation found. Thanks to Tanya!
% 0.21/0.50  % SZS status Theorem for theBenchmark
% 0.21/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50  % (14126)------------------------------
% 0.21/0.50  % (14126)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50  % (14126)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50  % (14126)Termination reason: Refutation
% 0.21/0.50  
% 0.21/0.50  % (14126)Memory used [KB]: 6012
% 0.21/0.50  % (14126)Time elapsed: 0.075 s
% 0.21/0.50  % (14126)Instructions burned: 5 (million)
% 0.21/0.50  % (14126)------------------------------
% 0.21/0.50  % (14126)------------------------------
% 0.21/0.50  % (14125)Success in time 0.145 s
%------------------------------------------------------------------------------