TSTP Solution File: MGT032+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 09:14:20 EDT 2023

% Result   : Theorem 0.80s 1.17s
% Output   : CNFRefutation 0.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   39 (   5 unt;   0 def)
%            Number of atoms       :  164 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  204 (  79   ~;  65   |;  46   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   77 (   0 sgn;  47   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1,X2,X3] :
      ( ( greater(growth_rate(X2,X3),growth_rate(X1,X3))
        & subpopulations(X1,X2,X0,X3)
        & environment(X0) )
     => selection_favors(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).

fof(f2,axiom,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X4] :
          ( ! [X3] :
              ( ( greater_or_equal(X3,X4)
                & subpopulations(first_movers,efficient_producers,X0,X3) )
             => greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
          & in_environment(X0,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).

fof(f3,conjecture,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X4] :
          ( ! [X3] :
              ( ( greater_or_equal(X3,X4)
                & subpopulations(first_movers,efficient_producers,X0,X3) )
             => selection_favors(efficient_producers,first_movers,X3) )
          & in_environment(X0,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1) ).

fof(f4,negated_conjecture,
    ~ ! [X0] :
        ( ( stable(X0)
          & environment(X0) )
       => ? [X4] :
            ( ! [X3] :
                ( ( greater_or_equal(X3,X4)
                  & subpopulations(first_movers,efficient_producers,X0,X3) )
               => selection_favors(efficient_producers,first_movers,X3) )
            & in_environment(X0,X4) ) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f5,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(rectify,[],[f2]) ).

fof(f6,plain,
    ~ ! [X0] :
        ( ( stable(X0)
          & environment(X0) )
       => ? [X1] :
            ( ! [X2] :
                ( ( greater_or_equal(X2,X1)
                  & subpopulations(first_movers,efficient_producers,X0,X2) )
               => selection_favors(efficient_producers,first_movers,X2) )
            & in_environment(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f7,plain,
    ! [X0,X1,X2,X3] :
      ( selection_favors(X2,X1,X3)
      | ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f8,plain,
    ! [X0,X1,X2,X3] :
      ( selection_favors(X2,X1,X3)
      | ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(flattening,[],[f7]) ).

fof(f9,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,[],[f5]) ).

fof(f10,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,[],[f9]) ).

fof(f11,plain,
    ? [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( ~ selection_favors(efficient_producers,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(f12,plain,
    ? [X0] :
      ( ! [X1] :
          ( ? [X2] :
              ( ~ selection_favors(efficient_producers,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] :
      ( ? [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,sK0(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & in_environment(X0,sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ! [X0] :
      ( ( ! [X2] :
            ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK0(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & in_environment(X0,sK0(X0)) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f13]) ).

fof(f15,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( ? [X2] :
                ( ~ selection_favors(efficient_producers,first_movers,X2)
                & greater_or_equal(X2,X1)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
            | ~ in_environment(X0,X1) )
        & stable(X0)
        & environment(X0) )
   => ( ! [X1] :
          ( ? [X2] :
              ( ~ selection_favors(efficient_producers,first_movers,X2)
              & greater_or_equal(X2,X1)
              & subpopulations(first_movers,efficient_producers,sK1,X2) )
          | ~ in_environment(sK1,X1) )
      & stable(sK1)
      & environment(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ selection_favors(efficient_producers,first_movers,X2)
          & greater_or_equal(X2,X1)
          & subpopulations(first_movers,efficient_producers,sK1,X2) )
     => ( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
        & greater_or_equal(sK2(X1),X1)
        & subpopulations(first_movers,efficient_producers,sK1,sK2(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ( ! [X1] :
        ( ( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
          & greater_or_equal(sK2(X1),X1)
          & subpopulations(first_movers,efficient_producers,sK1,sK2(X1)) )
        | ~ in_environment(sK1,X1) )
    & stable(sK1)
    & environment(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f12,f16,f15]) ).

fof(f18,plain,
    ! [X2,X3,X0,X1] :
      ( selection_favors(X2,X1,X3)
      | ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f19,plain,
    ! [X0] :
      ( in_environment(X0,sK0(X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f20,plain,
    ! [X2,X0] :
      ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
      | ~ greater_or_equal(X2,sK0(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f21,plain,
    environment(sK1),
    inference(cnf_transformation,[],[f17]) ).

fof(f22,plain,
    stable(sK1),
    inference(cnf_transformation,[],[f17]) ).

fof(f23,plain,
    ! [X1] :
      ( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
      | ~ in_environment(sK1,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f24,plain,
    ! [X1] :
      ( greater_or_equal(sK2(X1),X1)
      | ~ in_environment(sK1,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f25,plain,
    ! [X1] :
      ( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
      | ~ in_environment(sK1,X1) ),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_49,plain,
    ( ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
    | ~ subpopulations(X2,X0,X3,X1)
    | ~ environment(X3)
    | selection_favors(X0,X2,X1) ),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_50,plain,
    ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
    | ~ greater_or_equal(X1,sK0(X0))
    | ~ environment(X0)
    | ~ stable(X0)
    | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
    inference(cnf_transformation,[],[f20]) ).

cnf(c_51,plain,
    ( ~ environment(X0)
    | ~ stable(X0)
    | in_environment(X0,sK0(X0)) ),
    inference(cnf_transformation,[],[f19]) ).

cnf(c_52,negated_conjecture,
    ( ~ selection_favors(efficient_producers,first_movers,sK2(X0))
    | ~ in_environment(sK1,X0) ),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_53,negated_conjecture,
    ( ~ in_environment(sK1,X0)
    | greater_or_equal(sK2(X0),X0) ),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_54,negated_conjecture,
    ( ~ in_environment(sK1,X0)
    | subpopulations(first_movers,efficient_producers,sK1,sK2(X0)) ),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_55,negated_conjecture,
    stable(sK1),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_56,negated_conjecture,
    environment(sK1),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_60,plain,
    ( ~ environment(sK1)
    | ~ stable(sK1)
    | in_environment(sK1,sK0(sK1)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_103,plain,
    ( ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
    | ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
    | ~ in_environment(sK1,X0)
    | ~ environment(X1) ),
    inference(resolution,[status(thm)],[c_49,c_52]) ).

cnf(c_121,plain,
    ( ~ subpopulations(first_movers,efficient_producers,X0,sK2(sK0(X0)))
    | ~ in_environment(sK1,sK0(X0))
    | ~ environment(X0)
    | ~ stable(X0)
    | greater(growth_rate(efficient_producers,sK2(sK0(X0))),growth_rate(first_movers,sK2(sK0(X0)))) ),
    inference(resolution,[status(thm)],[c_50,c_53]) ).

cnf(c_133,plain,
    ( ~ subpopulations(first_movers,efficient_producers,X0,sK2(sK0(X0)))
    | ~ in_environment(sK1,sK0(X0))
    | ~ environment(X0)
    | ~ stable(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_121,c_103]) ).

cnf(c_143,plain,
    ( ~ in_environment(sK1,sK0(sK1))
    | ~ environment(sK1)
    | ~ stable(sK1) ),
    inference(resolution,[status(thm)],[c_54,c_133]) ).

cnf(c_144,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_143,c_60,c_55,c_56]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.17/0.35  % Computer : n012.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Mon Aug 28 06:30:24 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.80/1.17  % SZS status Started for theBenchmark.p
% 0.80/1.17  % SZS status Theorem for theBenchmark.p
% 0.80/1.17  
% 0.80/1.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.80/1.17  
% 0.80/1.17  ------  iProver source info
% 0.80/1.17  
% 0.80/1.17  git: date: 2023-05-31 18:12:56 +0000
% 0.80/1.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.80/1.17  git: non_committed_changes: false
% 0.80/1.17  git: last_make_outside_of_git: false
% 0.80/1.17  
% 0.80/1.17  ------ Parsing...
% 0.80/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.80/1.17  
% 0.80/1.17  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe:2:0s
% 0.80/1.17  
% 0.80/1.17  % SZS status Theorem for theBenchmark.p
% 0.80/1.17  
% 0.80/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.80/1.17  
% 0.80/1.18  
%------------------------------------------------------------------------------