↑ Up

iProver---3.9.4.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:12:25 PM UTC 2026

% Result   : Theorem 1.62s 1.28s
% Output   : CNFRefutation 1.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   63 (   7 unt;   1 def)
%            Number of atoms       :  264 (   0 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  337 ( 136   ~; 131   |;  58   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :  103 (   0 sgn  82   !;  21   ?;  27   :)

% 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] :
      ( ( 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(f3,conjecture,
    ! [X0] :
      ( ( stable(X0)
        & 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',prove_l12) ).

fof(f4,negated_conjecture,
    ~ ! [X0] :
        ( ( stable(X0)
          & 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) ) ),
    inference(negated_conjecture,[status(cth)],[f3]) ).

fof(f5,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(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(ennf_transformation,[],[f5]) ).

fof(f7,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(flattening,[],[f6]) ).

fof(f8,plain,
    ! [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) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f9,plain,
    ! [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) ) ),
    inference(flattening,[],[f8]) ).

fof(f10,plain,
    ? [X0] :
      ( stable(X0)
      & 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) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f11,plain,
    ? [X0] :
      ( stable(X0)
      & 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) ) ),
    inference(flattening,[],[f10]) ).

fof(f16,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ 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) ) ),
    inference(rectify,[],[f13]) ).

fof(f17,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ environment(X0)
      | ( ! [X2] :
            ( ~ greater(X2,sK2(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2)
            | greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
        & ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
        & in_environment(X0,sK2(X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f16]) ).

fof(f18,plain,
    ! [X0] :
      ( ~ stable(X0)
      | ~ environment(X0)
      | ( ! [X2] :
            ( ~ greater_or_equal(X2,sK3(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2)
            | greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
        & in_environment(X0,sK3(X0)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f9]) ).

fof(f19,plain,
    ( stable(sK4)
    & environment(sK4)
    & ! [X1] :
        ( ( greater(sK5(X1),X1)
          & subpopulations(first_movers,efficient_producers,sK4,sK5(X1))
          & ~ greater(growth_rate(efficient_producers,sK5(X1)),growth_rate(first_movers,sK5(X1))) )
        | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
        | ~ in_environment(sK4,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X2,sK5(X1))],[f11]) ).

fof(f23,plain,
    ! [X2,X0] :
      ( sP0(X0)
      | ~ environment(X0)
      | ~ greater(X2,sK2(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f24,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ environment(X0)
      | ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0))) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f25,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ environment(X0)
      | in_environment(X0,sK2(X0)) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f26,plain,
    ! [X2,X0] :
      ( ~ stable(X0)
      | ~ environment(X0)
      | ~ greater_or_equal(X2,sK3(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f27,plain,
    ! [X0] :
      ( ~ stable(X0)
      | ~ environment(X0)
      | in_environment(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f28,plain,
    stable(sK4),
    inference(cnf_transformation,[],[f19]) ).

fof(f29,plain,
    environment(sK4),
    inference(cnf_transformation,[],[f19]) ).

fof(f30,plain,
    ! [X1] :
      ( greater(sK5(X1),X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ in_environment(sK4,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f31,plain,
    ! [X1] :
      ( subpopulations(first_movers,efficient_producers,sK4,sK5(X1))
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ in_environment(sK4,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f32,plain,
    ! [X1] :
      ( ~ greater(growth_rate(efficient_producers,sK5(X1)),growth_rate(first_movers,sK5(X1)))
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ in_environment(sK4,X1) ),
    inference(cnf_transformation,[],[f19]) ).

tcf(c_52,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | in_environment(X0,sK2(X0))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f25]) ).

tcf(c_53,plain,
    ! [X0: $i] :
      ( sP0(X0)
      | ~ environment(X0)
      | ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0))) ),
    inference(cnf_transformation,[],[f24]) ).

tcf(c_54,plain,
    ! [X0: $i,X1: $i] :
      ( sP0(X0)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0)
      | ~ greater(X1,sK2(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

tcf(c_55,plain,
    ! [X0: $i] :
      ( in_environment(X0,sK3(X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f27]) ).

tcf(c_56,plain,
    ! [X0: $i,X1: $i] :
      ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ stable(X0)
      | ~ environment(X0)
      | ~ greater_or_equal(X1,sK3(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

tcf(c_57,negated_conjecture,
    ! [X0: $i] :
      ( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | ~ in_environment(sK4,X0)
      | ~ greater(growth_rate(efficient_producers,sK5(X0)),growth_rate(first_movers,sK5(X0))) ),
    inference(cnf_transformation,[],[f32]) ).

tcf(c_58,negated_conjecture,
    ! [X0: $i] :
      ( subpopulations(first_movers,efficient_producers,sK4,sK5(X0))
      | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | ~ in_environment(sK4,X0) ),
    inference(cnf_transformation,[],[f31]) ).

tcf(c_59,negated_conjecture,
    ! [X0: $i] :
      ( greater(sK5(X0),X0)
      | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | ~ in_environment(sK4,X0) ),
    inference(cnf_transformation,[],[f30]) ).

tcf(c_60,negated_conjecture,
    environment(sK4),
    inference(cnf_transformation,[],[f29]) ).

tcf(c_61,negated_conjecture,
    stable(sK4),
    inference(cnf_transformation,[],[f28]) ).

tcf(c_191,plain,
    ( in_environment(sK4,sK3(sK4))
    | ~ environment(sK4) ),
    inference(resolution,[status(thm)],[c_55,c_61]) ).

tcf(c_201,plain,
    ! [X0: $i] :
      ( sP0(sK4)
      | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | ~ greater(X0,sK2(sK4))
      | ~ subpopulations(first_movers,efficient_producers,sK4,X0) ),
    inference(resolution,[status(thm)],[c_54,c_60]) ).

tcf(c_215,plain,
    ( sP0(sK4)
    | ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
    inference(resolution,[status(thm)],[c_53,c_60]) ).

tcf(c_222,plain,
    ( sP0(sK4)
    | in_environment(sK4,sK2(sK4)) ),
    inference(resolution,[status(thm)],[c_52,c_60]) ).

tcf(c_244,plain,
    ! [X0: $i] :
      ( sP0(sK4)
      | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | greater(growth_rate(efficient_producers,sK5(X0)),growth_rate(first_movers,sK5(X0)))
      | ~ in_environment(sK4,X0)
      | ~ greater(sK5(X0),sK2(sK4)) ),
    inference(resolution,[status(thm)],[c_58,c_201]) ).

fof(f12,definition,
    ! [X0] :
      ( ~ sP0(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) ) ),
    introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).

fof(f13,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ 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(definition_folding,[],[f7,f12]) ).

fof(f14,plain,
    ! [X0] :
      ( ~ sP0(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) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f15,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | ! [X1] :
          ( ( greater_or_equal(sK1(X0,X1),X1)
            & subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
            & ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1))) )
          | ~ in_environment(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f14]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ sP0(X0)
      | greater_or_equal(sK1(X0,X1),X1)
      | ~ in_environment(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ sP0(X0)
      | subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
      | ~ in_environment(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ sP0(X0)
      | ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
      | ~ in_environment(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

tcf(c_49,plain,
    ! [X0: $i,X1: $i] :
      ( ~ sP0(X0)
      | ~ in_environment(X0,X1)
      | ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1))) ),
    inference(cnf_transformation,[],[f22]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i] :
      ( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
      | ~ sP0(X0)
      | ~ in_environment(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i] :
      ( greater_or_equal(sK1(X0,X1),X1)
      | ~ sP0(X0)
      | ~ in_environment(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

tcf(c_151,plain,
    ! [X0: $i,X1: $i] :
      ( greater(growth_rate(efficient_producers,sK1(X1,sK3(X0))),growth_rate(first_movers,sK1(X1,sK3(X0))))
      | ~ stable(X0)
      | ~ environment(X0)
      | ~ sP0(X1)
      | ~ in_environment(X1,sK3(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK3(X0))) ),
    inference(resolution,[status(thm)],[c_51,c_56]) ).

tcf(c_165,plain,
    ! [X0: $i,X1: $i] :
      ( ~ stable(X0)
      | ~ environment(X0)
      | ~ sP0(X1)
      | ~ in_environment(X1,sK3(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK3(X0))) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_151,c_49]) ).

tcf(c_177,plain,
    ! [X0: $i] :
      ( ~ environment(sK4)
      | ~ sP0(X0)
      | ~ in_environment(X0,sK3(sK4))
      | ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4))) ),
    inference(resolution,[status(thm)],[c_165,c_61]) ).

tcf(c_179,plain,
    ! [X0: $i] :
      ( ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4)))
      | ~ in_environment(X0,sK3(sK4))
      | ~ sP0(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_177,c_60,c_177]) ).

tcf(c_180,plain,
    ! [X0: $i] :
      ( ~ sP0(X0)
      | ~ in_environment(X0,sK3(sK4))
      | ~ subpopulations(first_movers,efficient_producers,sK4,sK1(X0,sK3(sK4))) ),
    inference(renaming,[status(thm)],[c_179]) ).

tcf(c_237,plain,
    ( ~ sP0(sK4)
    | ~ in_environment(sK4,sK3(sK4)) ),
    inference(resolution,[status(thm)],[c_50,c_180]) ).

tcf(c_238,plain,
    ~ sP0(sK4),
    inference(global_subsumption_just,[status(thm)],[c_237,c_60,c_191,c_237]) ).

tcf(c_246,plain,
    ! [X0: $i] :
      ( ~ in_environment(sK4,X0)
      | ~ greater(sK5(X0),sK2(sK4))
      | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_244,c_60,c_57,c_191,c_237,c_244]) ).

tcf(c_247,plain,
    ! [X0: $i] :
      ( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | ~ in_environment(sK4,X0)
      | ~ greater(sK5(X0),sK2(sK4)) ),
    inference(renaming,[status(thm)],[c_246]) ).

tcf(c_260,plain,
    in_environment(sK4,sK2(sK4)),
    inference(backward_subsumption_resolution,[status(thm)],[c_222,c_238]) ).

tcf(c_285,plain,
    ( greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
    | ~ greater(sK5(sK2(sK4)),sK2(sK4)) ),
    inference(resolution,[status(thm)],[c_247,c_260]) ).

tcf(c_291,plain,
    ( greater(sK5(sK2(sK4)),sK2(sK4))
    | greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
    inference(resolution,[status(thm)],[c_59,c_260]) ).

tcf(c_292,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_291,c_285,c_237,c_215,c_191,c_60]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : MGT030+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37  % Computer : n011.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Thu Sep 24 01:05:27 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41  Running first-order theorem proving
% 0.14/0.41  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42  
% 0.14/0.42  % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42  
% 0.14/0.42  % Detected problem language: tptp
% 0.14/0.44  % Proving...
% 1.62/1.28  % SZS status Started for theBenchmark.p
% 1.62/1.28  % SZS status Theorem for theBenchmark.p
% 1.62/1.28  
% 1.62/1.28  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.62/1.28  
% 1.62/1.28  % ------  iProver source info
% 1.62/1.28  
% 1.62/1.28  % git: date: 2026-07-19 20:42:38 +0200
% 1.62/1.28  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.62/1.28  % git: non_committed_changes: false
% 1.62/1.28  
% 1.62/1.28  % ------ Parsing...
% 1.62/1.28  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 1.62/1.28  
% 1.62/1.28  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s% 
% 1.62/1.28  
% 1.62/1.28  % SZS status Theorem for theBenchmark.p
% 1.62/1.28  
% 1.62/1.28  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.62/1.28  
% 1.62/1.28  
%------------------------------------------------------------------------------