TSTP Solution File: MGT028+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : MGT028+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 : Sun May  5 07:57:09 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   81 (  15 unt;   0 def)
%            Number of atoms       :  321 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  377 ( 137   ~; 128   |;  91   &)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :  142 ( 108   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f94,plain,
    $false,
    inference(subsumption_resolution,[],[f93,f87]) ).

fof(f87,plain,
    greater_or_equal(sK6(sK5(sK4),sK4),sK5(sK4)),
    inference(resolution,[],[f84,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ sP2(X0,X1)
      | greater_or_equal(sK6(X0,X1),X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( ~ greater(zero,growth_rate(first_movers,sK6(X0,X1)))
        & greater_or_equal(sK6(X0,X1),X0)
        & subpopulations(first_movers,efficient_producers,X1,sK6(X0,X1)) )
      | ~ sP2(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X0)
          & subpopulations(first_movers,efficient_producers,X1,X2) )
     => ( ~ greater(zero,growth_rate(first_movers,sK6(X0,X1)))
        & greater_or_equal(sK6(X0,X1),X0)
        & subpopulations(first_movers,efficient_producers,X1,sK6(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X0)
          & subpopulations(first_movers,efficient_producers,X1,X2) )
      | ~ sP2(X0,X1) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ sP2(X1,X0) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ sP2(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f84,plain,
    sP2(sK5(sK4),sK4),
    inference(resolution,[],[f82,f53]) ).

fof(f53,plain,
    in_environment(sK4,sK5(sK4)),
    inference(subsumption_resolution,[],[f52,f40]) ).

fof(f40,plain,
    environment(sK4),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( ! [X1] :
        ( sP0(X1,sK4)
        | ~ greater(X1,appear(efficient_producers,sK4)) )
    & stable(sK4)
    & environment(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f15,f24]) ).

fof(f24,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( sP0(X1,X0)
            | ~ greater(X1,appear(efficient_producers,X0)) )
        & stable(X0)
        & environment(X0) )
   => ( ! [X1] :
          ( sP0(X1,sK4)
          | ~ greater(X1,appear(efficient_producers,sK4)) )
      & stable(sK4)
      & environment(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0] :
      ( ! [X1] :
          ( sP0(X1,X0)
          | ~ greater(X1,appear(efficient_producers,X0)) )
      & stable(X0)
      & environment(X0) ),
    inference(definition_folding,[],[f9,f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ sP0(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

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

fof(f8,plain,
    ? [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( ~ greater(zero,growth_rate(first_movers,X2))
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
          | ~ greater(X1,appear(efficient_producers,X0)) )
      & stable(X0)
      & environment(X0) ),
    inference(ennf_transformation,[],[f5]) ).

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

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

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

fof(f52,plain,
    ( in_environment(sK4,sK5(sK4))
    | ~ environment(sK4) ),
    inference(resolution,[],[f45,f41]) ).

fof(f41,plain,
    stable(sK4),
    inference(cnf_transformation,[],[f25]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ stable(X0)
      | in_environment(X0,sK5(X0))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ( sP1(sK5(X0),X0)
        & in_environment(X0,sK5(X0)) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f17,f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ? [X1] :
          ( sP1(X1,X0)
          & in_environment(X0,X1) )
     => ( sP1(sK5(X0),X0)
        & in_environment(X0,sK5(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0] :
      ( ? [X1] :
          ( sP1(X1,X0)
          & in_environment(X0,X1) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(definition_folding,[],[f11,f16]) ).

fof(f16,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( greater(zero,growth_rate(first_movers,X2))
            & greater(growth_rate(efficient_producers,X2),zero) )
          | ~ greater_or_equal(X2,X1)
          | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ sP1(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

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

fof(f10,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( greater(zero,growth_rate(first_movers,X2))
                & greater(growth_rate(efficient_producers,X2),zero) )
              | ~ 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] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X1] :
          ( ! [X2] :
              ( ( greater_or_equal(X2,X1)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
             => ( greater(zero,growth_rate(first_movers,X2))
                & greater(growth_rate(efficient_producers,X2),zero) ) )
          & in_environment(X0,X1) ) ),
    inference(rectify,[],[f2]) ).

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

fof(f82,plain,
    ! [X0] :
      ( ~ in_environment(sK4,X0)
      | sP2(X0,sK4) ),
    inference(subsumption_resolution,[],[f81,f40]) ).

fof(f81,plain,
    ! [X0] :
      ( sP2(X0,sK4)
      | ~ in_environment(sK4,X0)
      | ~ environment(sK4) ),
    inference(subsumption_resolution,[],[f80,f41]) ).

fof(f80,plain,
    ! [X0] :
      ( sP2(X0,sK4)
      | ~ in_environment(sK4,X0)
      | ~ stable(sK4)
      | ~ environment(sK4) ),
    inference(subsumption_resolution,[],[f79,f73]) ).

fof(f73,plain,
    ~ greater(zero,growth_rate(first_movers,sK3(sK7(sK4),sK4))),
    inference(resolution,[],[f72,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ greater(zero,growth_rate(first_movers,sK3(X0,X1))) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ~ greater(zero,growth_rate(first_movers,sK3(X0,X1)))
        & greater_or_equal(sK3(X0,X1),X0)
        & subpopulations(first_movers,efficient_producers,X1,sK3(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X0)
          & subpopulations(first_movers,efficient_producers,X1,X2) )
     => ( ~ greater(zero,growth_rate(first_movers,sK3(X0,X1)))
        & greater_or_equal(sK3(X0,X1),X0)
        & subpopulations(first_movers,efficient_producers,X1,sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X0)
          & subpopulations(first_movers,efficient_producers,X1,X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ sP0(X1,X0) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f72,plain,
    sP0(sK7(sK4),sK4),
    inference(resolution,[],[f71,f42]) ).

fof(f42,plain,
    ! [X1] :
      ( ~ greater(X1,appear(efficient_producers,sK4))
      | sP0(X1,sK4) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f71,plain,
    greater(sK7(sK4),appear(efficient_producers,sK4)),
    inference(subsumption_resolution,[],[f70,f61]) ).

fof(f61,plain,
    ( greater(sK7(sK4),appear(efficient_producers,sK4))
    | greater_or_equal(sK6(sK5(sK4),sK4),sK5(sK4)) ),
    inference(resolution,[],[f58,f48]) ).

fof(f58,plain,
    ( sP2(sK5(sK4),sK4)
    | greater(sK7(sK4),appear(efficient_producers,sK4)) ),
    inference(subsumption_resolution,[],[f57,f40]) ).

fof(f57,plain,
    ( sP2(sK5(sK4),sK4)
    | greater(sK7(sK4),appear(efficient_producers,sK4))
    | ~ environment(sK4) ),
    inference(subsumption_resolution,[],[f56,f41]) ).

fof(f56,plain,
    ( sP2(sK5(sK4),sK4)
    | greater(sK7(sK4),appear(efficient_producers,sK4))
    | ~ stable(sK4)
    | ~ environment(sK4) ),
    inference(resolution,[],[f50,f53]) ).

fof(f50,plain,
    ! [X3,X0] :
      ( ~ in_environment(X0,X3)
      | sP2(X3,X0)
      | greater(sK7(X0),appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ( ! [X2] :
            ( greater(zero,growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK7(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & greater(sK7(X0),appear(efficient_producers,X0)) )
      | ! [X3] :
          ( sP2(X3,X0)
          | ~ in_environment(X0,X3) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f34,f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(zero,growth_rate(first_movers,X2))
              | ~ greater_or_equal(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & greater(X1,appear(efficient_producers,X0)) )
     => ( ! [X2] :
            ( greater(zero,growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK7(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & greater(sK7(X0),appear(efficient_producers,X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(zero,growth_rate(first_movers,X2))
              | ~ greater_or_equal(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & greater(X1,appear(efficient_producers,X0)) )
      | ! [X3] :
          ( sP2(X3,X0)
          | ~ in_environment(X0,X3) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(zero,growth_rate(first_movers,X4))
              | ~ greater_or_equal(X4,X3)
              | ~ subpopulations(first_movers,efficient_producers,X0,X4) )
          & greater(X3,appear(efficient_producers,X0)) )
      | ! [X1] :
          ( sP2(X1,X0)
          | ~ in_environment(X0,X1) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(definition_folding,[],[f13,f18]) ).

fof(f13,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(zero,growth_rate(first_movers,X4))
              | ~ greater_or_equal(X4,X3)
              | ~ subpopulations(first_movers,efficient_producers,X0,X4) )
          & 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(flattening,[],[f12]) ).

fof(f12,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(zero,growth_rate(first_movers,X4))
              | ~ greater_or_equal(X4,X3)
              | ~ subpopulations(first_movers,efficient_producers,X0,X4) )
          & 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,[],[f7]) ).

fof(f7,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] :
              ( ( greater_or_equal(X4,X3)
                & subpopulations(first_movers,efficient_producers,X0,X4) )
             => 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] :
          ( ! [X2] :
              ( ( greater_or_equal(X2,X3)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
             => greater(zero,growth_rate(first_movers,X2)) )
          & greater(X3,appear(efficient_producers,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).

fof(f70,plain,
    ( ~ greater_or_equal(sK6(sK5(sK4),sK4),sK5(sK4))
    | greater(sK7(sK4),appear(efficient_producers,sK4)) ),
    inference(resolution,[],[f68,f55]) ).

fof(f55,plain,
    sP1(sK5(sK4),sK4),
    inference(subsumption_resolution,[],[f54,f40]) ).

fof(f54,plain,
    ( sP1(sK5(sK4),sK4)
    | ~ environment(sK4) ),
    inference(resolution,[],[f46,f41]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ stable(X0)
      | sP1(sK5(X0),X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ sP1(X0,sK4)
      | ~ greater_or_equal(sK6(sK5(sK4),sK4),X0)
      | greater(sK7(sK4),appear(efficient_producers,sK4)) ),
    inference(subsumption_resolution,[],[f66,f59]) ).

fof(f59,plain,
    ( ~ greater(zero,growth_rate(first_movers,sK6(sK5(sK4),sK4)))
    | greater(sK7(sK4),appear(efficient_producers,sK4)) ),
    inference(resolution,[],[f58,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ sP2(X0,X1)
      | ~ greater(zero,growth_rate(first_movers,sK6(X0,X1))) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f66,plain,
    ! [X0] :
      ( greater(sK7(sK4),appear(efficient_producers,sK4))
      | ~ greater_or_equal(sK6(sK5(sK4),sK4),X0)
      | greater(zero,growth_rate(first_movers,sK6(sK5(sK4),sK4)))
      | ~ sP1(X0,sK4) ),
    inference(resolution,[],[f60,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X1,X2)
      | ~ greater_or_equal(X2,X0)
      | greater(zero,growth_rate(first_movers,X2))
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( greater(zero,growth_rate(first_movers,X2))
            & greater(growth_rate(efficient_producers,X2),zero) )
          | ~ greater_or_equal(X2,X0)
          | ~ subpopulations(first_movers,efficient_producers,X1,X2) )
      | ~ sP1(X0,X1) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( greater(zero,growth_rate(first_movers,X2))
            & greater(growth_rate(efficient_producers,X2),zero) )
          | ~ greater_or_equal(X2,X1)
          | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ sP1(X1,X0) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f60,plain,
    ( subpopulations(first_movers,efficient_producers,sK4,sK6(sK5(sK4),sK4))
    | greater(sK7(sK4),appear(efficient_producers,sK4)) ),
    inference(resolution,[],[f58,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ sP2(X0,X1)
      | subpopulations(first_movers,efficient_producers,X1,sK6(X0,X1)) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f79,plain,
    ! [X0] :
      ( greater(zero,growth_rate(first_movers,sK3(sK7(sK4),sK4)))
      | sP2(X0,sK4)
      | ~ in_environment(sK4,X0)
      | ~ stable(sK4)
      | ~ environment(sK4) ),
    inference(subsumption_resolution,[],[f76,f75]) ).

fof(f75,plain,
    greater_or_equal(sK3(sK7(sK4),sK4),sK7(sK4)),
    inference(resolution,[],[f72,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | greater_or_equal(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f76,plain,
    ! [X0] :
      ( ~ greater_or_equal(sK3(sK7(sK4),sK4),sK7(sK4))
      | greater(zero,growth_rate(first_movers,sK3(sK7(sK4),sK4)))
      | sP2(X0,sK4)
      | ~ in_environment(sK4,X0)
      | ~ stable(sK4)
      | ~ environment(sK4) ),
    inference(resolution,[],[f74,f51]) ).

fof(f51,plain,
    ! [X2,X3,X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ greater_or_equal(X2,sK7(X0))
      | greater(zero,growth_rate(first_movers,X2))
      | sP2(X3,X0)
      | ~ in_environment(X0,X3)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f74,plain,
    subpopulations(first_movers,efficient_producers,sK4,sK3(sK7(sK4),sK4)),
    inference(resolution,[],[f72,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | subpopulations(first_movers,efficient_producers,X1,sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f93,plain,
    ~ greater_or_equal(sK6(sK5(sK4),sK4),sK5(sK4)),
    inference(resolution,[],[f91,f55]) ).

fof(f91,plain,
    ! [X0] :
      ( ~ sP1(X0,sK4)
      | ~ greater_or_equal(sK6(sK5(sK4),sK4),X0) ),
    inference(subsumption_resolution,[],[f89,f85]) ).

fof(f85,plain,
    ~ greater(zero,growth_rate(first_movers,sK6(sK5(sK4),sK4))),
    inference(resolution,[],[f84,f49]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ greater_or_equal(sK6(sK5(sK4),sK4),X0)
      | greater(zero,growth_rate(first_movers,sK6(sK5(sK4),sK4)))
      | ~ sP1(X0,sK4) ),
    inference(resolution,[],[f86,f44]) ).

fof(f86,plain,
    subpopulations(first_movers,efficient_producers,sK4,sK6(sK5(sK4),sK4)),
    inference(resolution,[],[f84,f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : MGT028+1 : TPTP v8.1.2. Released v2.0.0.
% 0.13/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n008.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 20:03:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (14835)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (14838)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  % (14840)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.38  % (14839)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (14842)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (14841)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38  % (14844)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  % (14843)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  % (14842)First to succeed.
% 0.14/0.39  TRYING [1]
% 0.14/0.39  Detected minimum model sizes of [1,1,1,1,1,1]
% 0.14/0.39  Detected maximum model sizes of [1,1,max,max,max,1]
% 0.14/0.39  TRYING [1,1,1,1,1,1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [1,1,1,2,1,1]
% 0.14/0.39  % (14843)Also succeeded, but the first one will report.
% 0.14/0.39  TRYING [1,1,2,2,1,1]
% 0.14/0.39  Detected minimum model sizes of [1,1,1,1,1,1]
% 0.14/0.39  Detected maximum model sizes of [1,1,max,max,max,1]
% 0.14/0.39  TRYING [1,1,1,1,1,1]
% 0.14/0.39  % (14842)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14835"
% 0.14/0.39  TRYING [1,1,1,3,1,1]
% 0.14/0.39  % (14840)Also succeeded, but the first one will report.
% 0.14/0.39  TRYING [1,1,1,2,1,1]
% 0.14/0.39  % (14842)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (14842)------------------------------
% 0.14/0.39  % (14842)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (14842)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (14842)Memory used [KB]: 758
% 0.14/0.39  % (14842)Time elapsed: 0.005 s
% 0.14/0.39  % (14842)Instructions burned: 7 (million)
% 0.14/0.39  % (14835)Success in time 0.02 s
%------------------------------------------------------------------------------