TSTP Solution File: MGT023+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 02:43:24 EDT 2024

% Result   : Theorem 1.20s 1.13s
% Output   : CNFRefutation 1.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  103 (  12 unt;   0 def)
%            Number of atoms       :  432 (  60 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  549 ( 220   ~; 238   |;  74   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :  151 (   0 sgn  72   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( ( ? [X1] :
            ( ! [X2] :
                ( ( greater_or_equal(X2,X1)
                  & subpopulations(first_movers,efficient_producers,X0,X2) )
               => greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
            & in_environment(X0,X1) )
        & environment(X0) )
     => ? [X1] :
          ( ! [X2] :
              ( ( greater(X2,X1)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
             => greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
          & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
          & in_environment(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( greater(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
           => greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
        & in_environment(X0,X1)
        & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
        & environment(X0) )
     => critical_point(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).

fof(f3,axiom,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X1] :
          ( ! [X2] :
              ( ( greater_or_equal(X2,X1)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
             => greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
          & in_environment(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).

fof(f4,conjecture,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => in_environment(X0,critical_point(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).

fof(f5,negated_conjecture,
    ~ ! [X0] :
        ( ( stable(X0)
          & environment(X0) )
       => in_environment(X0,critical_point(X0)) ),
    inference(negated_conjecture,[],[f4]) ).

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

fof(f7,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4))
              | ~ greater(X4,X3)
              | ~ subpopulations(first_movers,efficient_producers,X0,X4) )
          & ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
          & in_environment(X0,X3) )
      | ! [X1] :
          ( ? [X2] :
              ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
          | ~ in_environment(X0,X1) )
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f8,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4))
              | ~ greater(X4,X3)
              | ~ subpopulations(first_movers,efficient_producers,X0,X4) )
          & ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
          & in_environment(X0,X3) )
      | ! [X1] :
          ( ? [X2] :
              ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
          | ~ in_environment(X0,X1) )
      | ~ environment(X0) ),
    inference(flattening,[],[f7]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( critical_point(X0) = X1
      | ? [X2] :
          ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
          & greater(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ in_environment(X0,X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( critical_point(X0) = X1
      | ? [X2] :
          ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
          & greater(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
      | ~ in_environment(X0,X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0) ),
    inference(flattening,[],[f9]) ).

fof(f11,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),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,[],[f3]) ).

fof(f12,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),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,[],[f11]) ).

fof(f13,plain,
    ? [X0] :
      ( ~ in_environment(X0,critical_point(X0))
      & stable(X0)
      & environment(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f14,plain,
    ? [X0] :
      ( ~ in_environment(X0,critical_point(X0))
      & stable(X0)
      & environment(X0) ),
    inference(flattening,[],[f13]) ).

fof(f15,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
          | ~ in_environment(X0,X1) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f16,plain,
    ! [X0] :
      ( ? [X3] :
          ( ! [X4] :
              ( greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4))
              | ~ greater(X4,X3)
              | ~ subpopulations(first_movers,efficient_producers,X0,X4) )
          & ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
          & in_environment(X0,X3) )
      | sP0(X0)
      | ~ environment(X0) ),
    inference(definition_folding,[],[f8,f15]) ).

fof(f17,plain,
    ! [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
          | ~ in_environment(X0,X1) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
     => ( ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
        & greater_or_equal(sK1(X0,X1),X1)
        & subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
            & greater_or_equal(sK1(X0,X1),X1)
            & subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1)) )
          | ~ in_environment(X0,X1) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f17,f18]) ).

fof(f20,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              | ~ greater(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
          & in_environment(X0,X1) )
      | sP0(X0)
      | ~ environment(X0) ),
    inference(rectify,[],[f16]) ).

fof(f21,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              | ~ greater(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
          & in_environment(X0,X1) )
     => ( ! [X2] :
            ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
            | ~ greater(X2,sK2(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
        & in_environment(X0,sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0] :
      ( ( ! [X2] :
            ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
            | ~ greater(X2,sK2(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
        & in_environment(X0,sK2(X0)) )
      | sP0(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
          & greater(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2) )
     => ( ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
        & greater(sK3(X0,X1),X1)
        & subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( critical_point(X0) = X1
      | ( ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
        & greater(sK3(X0,X1),X1)
        & subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1)) )
      | ~ in_environment(X0,X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f10,f23]) ).

fof(f25,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              | ~ greater_or_equal(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & in_environment(X0,X1) )
     => ( ! [X2] :
            ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK4(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & in_environment(X0,sK4(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0] :
      ( ( ! [X2] :
            ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK4(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & in_environment(X0,sK4(X0)) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f12,f25]) ).

fof(f27,plain,
    ( ? [X0] :
        ( ~ in_environment(X0,critical_point(X0))
        & stable(X0)
        & environment(X0) )
   => ( ~ in_environment(sK5,critical_point(sK5))
      & stable(sK5)
      & environment(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ~ in_environment(sK5,critical_point(sK5))
    & stable(sK5)
    & environment(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f14,f27]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
      | ~ in_environment(X0,X1)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( greater_or_equal(sK1(X0,X1),X1)
      | ~ in_environment(X0,X1)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
      | ~ in_environment(X0,X1)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f32,plain,
    ! [X0] :
      ( in_environment(X0,sK2(X0))
      | sP0(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
      | sP0(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f34,plain,
    ! [X2,X0] :
      ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
      | ~ greater(X2,sK2(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | sP0(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( critical_point(X0) = X1
      | subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
      | ~ in_environment(X0,X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( critical_point(X0) = X1
      | greater(sK3(X0,X1),X1)
      | ~ in_environment(X0,X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( critical_point(X0) = X1
      | ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
      | ~ in_environment(X0,X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f38,plain,
    ! [X0] :
      ( in_environment(X0,sK4(X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f39,plain,
    ! [X2,X0] :
      ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
      | ~ greater_or_equal(X2,sK4(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f40,plain,
    environment(sK5),
    inference(cnf_transformation,[],[f28]) ).

fof(f41,plain,
    stable(sK5),
    inference(cnf_transformation,[],[f28]) ).

fof(f42,plain,
    ~ in_environment(sK5,critical_point(sK5)),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_49,plain,
    ( ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
    | ~ in_environment(X0,X1)
    | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f31]) ).

cnf(c_50,plain,
    ( ~ in_environment(X0,X1)
    | ~ sP0(X0)
    | greater_or_equal(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_51,plain,
    ( ~ in_environment(X0,X1)
    | ~ sP0(X0)
    | subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1)) ),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_52,plain,
    ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
    | ~ greater(X1,sK2(X0))
    | ~ environment(X0)
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
    | sP0(X0) ),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_53,plain,
    ( ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
    | ~ environment(X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_54,plain,
    ( ~ environment(X0)
    | in_environment(X0,sK2(X0))
    | sP0(X0) ),
    inference(cnf_transformation,[],[f32]) ).

cnf(c_55,plain,
    ( ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
    | ~ in_environment(X0,X1)
    | ~ environment(X0)
    | critical_point(X0) = X1
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_56,plain,
    ( ~ in_environment(X0,X1)
    | ~ environment(X0)
    | critical_point(X0) = X1
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
    | greater(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_57,plain,
    ( ~ in_environment(X0,X1)
    | ~ environment(X0)
    | critical_point(X0) = X1
    | subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_58,plain,
    ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
    | ~ greater_or_equal(X1,sK4(X0))
    | ~ environment(X0)
    | ~ stable(X0)
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_59,plain,
    ( ~ environment(X0)
    | ~ stable(X0)
    | in_environment(X0,sK4(X0)) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_60,negated_conjecture,
    ~ in_environment(sK5,critical_point(sK5)),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_61,negated_conjecture,
    stable(sK5),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_62,negated_conjecture,
    environment(sK5),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_260,plain,
    ( sK1(X0,X1) != X2
    | sK4(X3) != X1
    | ~ subpopulations(first_movers,efficient_producers,X3,X2)
    | ~ in_environment(X0,X1)
    | ~ sP0(X0)
    | ~ environment(X3)
    | ~ stable(X3)
    | greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_58]) ).

cnf(c_261,plain,
    ( ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK4(X0)))
    | ~ in_environment(X1,sK4(X0))
    | ~ sP0(X1)
    | ~ environment(X0)
    | ~ stable(X0)
    | greater(growth_rate(efficient_producers,sK1(X1,sK4(X0))),growth_rate(first_movers,sK1(X1,sK4(X0)))) ),
    inference(unflattening,[status(thm)],[c_260]) ).

cnf(c_275,plain,
    ( ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK4(X0)))
    | ~ in_environment(X1,sK4(X0))
    | ~ sP0(X1)
    | ~ environment(X0)
    | ~ stable(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_261,c_49]) ).

cnf(c_287,plain,
    ( X0 != sK5
    | ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK4(X0)))
    | ~ in_environment(X1,sK4(X0))
    | ~ sP0(X1)
    | ~ environment(X0) ),
    inference(resolution_lifted,[status(thm)],[c_275,c_61]) ).

cnf(c_288,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5)))
    | ~ in_environment(X0,sK4(sK5))
    | ~ sP0(X0)
    | ~ environment(sK5) ),
    inference(unflattening,[status(thm)],[c_287]) ).

cnf(c_290,plain,
    ( ~ sP0(X0)
    | ~ in_environment(X0,sK4(sK5))
    | ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5))) ),
    inference(global_subsumption_just,[status(thm)],[c_288,c_62,c_288]) ).

cnf(c_291,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5)))
    | ~ in_environment(X0,sK4(sK5))
    | ~ sP0(X0) ),
    inference(renaming,[status(thm)],[c_290]) ).

cnf(c_302,plain,
    ( X0 != sK5
    | ~ environment(X0)
    | in_environment(X0,sK4(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_59,c_61]) ).

cnf(c_303,plain,
    ( ~ environment(sK5)
    | in_environment(sK5,sK4(sK5)) ),
    inference(unflattening,[status(thm)],[c_302]) ).

cnf(c_304,plain,
    in_environment(sK5,sK4(sK5)),
    inference(global_subsumption_just,[status(thm)],[c_303,c_62,c_303]) ).

cnf(c_313,plain,
    ( X0 != sK5
    | ~ in_environment(X0,X1)
    | critical_point(X0) = X1
    | subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_57,c_62]) ).

cnf(c_314,plain,
    ( ~ in_environment(sK5,X0)
    | critical_point(sK5) = X0
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
    | subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,X0)) ),
    inference(unflattening,[status(thm)],[c_313]) ).

cnf(c_328,plain,
    ( X0 != sK5
    | ~ in_environment(X0,X1)
    | critical_point(X0) = X1
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
    | greater(sK3(X0,X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_56,c_62]) ).

cnf(c_329,plain,
    ( ~ in_environment(sK5,X0)
    | critical_point(sK5) = X0
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
    | greater(sK3(sK5,X0),X0) ),
    inference(unflattening,[status(thm)],[c_328]) ).

cnf(c_343,plain,
    ( X0 != sK5
    | ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
    | ~ in_environment(X0,X1)
    | critical_point(X0) = X1
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_62]) ).

cnf(c_344,plain,
    ( ~ greater(growth_rate(efficient_producers,sK3(sK5,X0)),growth_rate(first_movers,sK3(sK5,X0)))
    | ~ in_environment(sK5,X0)
    | critical_point(sK5) = X0
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
    inference(unflattening,[status(thm)],[c_343]) ).

cnf(c_358,plain,
    ( X0 != sK5
    | in_environment(X0,sK2(X0))
    | sP0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_62]) ).

cnf(c_359,plain,
    ( in_environment(sK5,sK2(sK5))
    | sP0(sK5) ),
    inference(unflattening,[status(thm)],[c_358]) ).

cnf(c_366,plain,
    ( X0 != sK5
    | ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
    | sP0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_62]) ).

cnf(c_367,plain,
    ( ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
    | sP0(sK5) ),
    inference(unflattening,[status(thm)],[c_366]) ).

cnf(c_374,plain,
    ( X0 != sK5
    | ~ subpopulations(first_movers,efficient_producers,X0,X1)
    | ~ greater(X1,sK2(X0))
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
    | sP0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_62]) ).

cnf(c_375,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK5,X0)
    | ~ greater(X0,sK2(sK5))
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
    | sP0(sK5) ),
    inference(unflattening,[status(thm)],[c_374]) ).

cnf(c_650,plain,
    ( sK4(sK5) != X1
    | X0 != sK5
    | ~ sP0(X0)
    | subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_51,c_304]) ).

cnf(c_651,plain,
    ( ~ sP0(sK5)
    | subpopulations(first_movers,efficient_producers,sK5,sK1(sK5,sK4(sK5))) ),
    inference(unflattening,[status(thm)],[c_650]) ).

cnf(c_677,plain,
    ( sK2(sK5) != critical_point(sK5)
    | sK5 != sK5
    | sP0(sK5) ),
    inference(resolution_lifted,[status(thm)],[c_60,c_359]) ).

cnf(c_687,plain,
    ( sK4(sK5) != sK4(sK5)
    | X0 != sK5
    | ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5)))
    | ~ sP0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_291,c_304]) ).

cnf(c_688,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK5,sK1(sK5,sK4(sK5)))
    | ~ sP0(sK5) ),
    inference(unflattening,[status(thm)],[c_687]) ).

cnf(c_689,plain,
    ~ sP0(sK5),
    inference(global_subsumption_just,[status(thm)],[c_688,c_651,c_688]) ).

cnf(c_694,plain,
    ( sK2(sK5) != critical_point(sK5)
    | sK5 != sK5 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_677,c_689]) ).

cnf(c_730,plain,
    ( sK2(sK5) != X0
    | sK5 != sK5
    | ~ greater(growth_rate(efficient_producers,sK3(sK5,X0)),growth_rate(first_movers,sK3(sK5,X0)))
    | critical_point(sK5) = X0
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
    | sP0(sK5) ),
    inference(resolution_lifted,[status(thm)],[c_344,c_359]) ).

cnf(c_731,plain,
    ( ~ greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
    | critical_point(sK5) = sK2(sK5)
    | greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
    | sP0(sK5) ),
    inference(unflattening,[status(thm)],[c_730]) ).

cnf(c_732,plain,
    ( ~ greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
    | critical_point(sK5) = sK2(sK5) ),
    inference(global_subsumption_just,[status(thm)],[c_731,c_367,c_651,c_688,c_731]) ).

cnf(c_740,plain,
    ( sK2(sK5) != X0
    | sK5 != sK5
    | critical_point(sK5) = X0
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
    | greater(sK3(sK5,X0),X0)
    | sP0(sK5) ),
    inference(resolution_lifted,[status(thm)],[c_329,c_359]) ).

cnf(c_741,plain,
    ( critical_point(sK5) = sK2(sK5)
    | greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
    | greater(sK3(sK5,sK2(sK5)),sK2(sK5))
    | sP0(sK5) ),
    inference(unflattening,[status(thm)],[c_740]) ).

cnf(c_742,plain,
    ( greater(sK3(sK5,sK2(sK5)),sK2(sK5))
    | critical_point(sK5) = sK2(sK5) ),
    inference(global_subsumption_just,[status(thm)],[c_741,c_367,c_651,c_688,c_741]) ).

cnf(c_743,plain,
    ( critical_point(sK5) = sK2(sK5)
    | greater(sK3(sK5,sK2(sK5)),sK2(sK5)) ),
    inference(renaming,[status(thm)],[c_742]) ).

cnf(c_750,plain,
    ( sK2(sK5) != X0
    | sK5 != sK5
    | critical_point(sK5) = X0
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
    | subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,X0))
    | sP0(sK5) ),
    inference(resolution_lifted,[status(thm)],[c_314,c_359]) ).

cnf(c_751,plain,
    ( critical_point(sK5) = sK2(sK5)
    | greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
    | subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
    | sP0(sK5) ),
    inference(unflattening,[status(thm)],[c_750]) ).

cnf(c_752,plain,
    ( subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
    | critical_point(sK5) = sK2(sK5) ),
    inference(global_subsumption_just,[status(thm)],[c_751,c_367,c_651,c_688,c_751]) ).

cnf(c_753,plain,
    ( critical_point(sK5) = sK2(sK5)
    | subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5))) ),
    inference(renaming,[status(thm)],[c_752]) ).

cnf(c_764,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK5,X0)
    | ~ greater(X0,sK2(sK5))
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_375,c_689]) ).

cnf(c_796,plain,
    ( sK3(sK5,sK2(sK5)) != X0
    | efficient_producers != efficient_producers
    | first_movers != first_movers
    | sK5 != sK5
    | ~ greater(X0,sK2(sK5))
    | sK2(sK5) = critical_point(sK5)
    | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
    inference(resolution_lifted,[status(thm)],[c_764,c_753]) ).

cnf(c_797,plain,
    ( ~ greater(sK3(sK5,sK2(sK5)),sK2(sK5))
    | sK2(sK5) = critical_point(sK5)
    | greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5)))) ),
    inference(unflattening,[status(thm)],[c_796]) ).

cnf(c_813,plain,
    sK2(sK5) != critical_point(sK5),
    inference(equality_resolution_simp,[status(thm)],[c_694]) ).

cnf(c_815,plain,
    critical_point(sK5) = sK2(sK5),
    inference(global_subsumption_just,[status(thm)],[c_743,c_732,c_743,c_797,c_813]) ).

cnf(c_850,plain,
    sK2(sK5) != sK2(sK5),
    inference(demodulation,[status(thm)],[c_813,c_815]) ).

cnf(c_851,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_850]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n023.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 23:09:54 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.20/1.13  % SZS status Started for theBenchmark.p
% 1.20/1.13  % SZS status Theorem for theBenchmark.p
% 1.20/1.13  
% 1.20/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.20/1.13  
% 1.20/1.13  ------  iProver source info
% 1.20/1.13  
% 1.20/1.13  git: date: 2024-05-02 19:28:25 +0000
% 1.20/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.20/1.13  git: non_committed_changes: false
% 1.20/1.13  
% 1.20/1.13  ------ Parsing...
% 1.20/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.20/1.13  
% 1.20/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e 
% 1.20/1.13  
% 1.20/1.13  % SZS status Theorem for theBenchmark.p
% 1.20/1.13  
% 1.20/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.20/1.13  
% 1.20/1.13  
%------------------------------------------------------------------------------