TSTP Solution File: MGT036+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n009.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 09:14:28 EDT 2023

% Result   : Theorem 0.79s 1.19s
% Output   : CNFRefutation 0.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   37 (   9 unt;   0 def)
%            Number of atoms       :  120 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  139 (  56   ~;  47   |;  30   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   75 (   0 sgn;  44   !;  12   ?)

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

fof(f2,axiom,
    ! [X0,X1,X2,X3] :
      ( ( subpopulations(X1,X2,X0,X3)
        & environment(X0) )
     => ( ( greater(zero,growth_rate(X1,X3))
          & greater_or_equal(growth_rate(X2,X3),zero) )
      <=> outcompetes(X2,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).

fof(f3,axiom,
    ? [X0,X3] :
      ( greater(zero,growth_rate(efficient_producers,X3))
      & greater_or_equal(growth_rate(first_movers,X3),zero)
      & subpopulations(first_movers,efficient_producers,X0,X3)
      & environment(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).

fof(f4,conjecture,
    ? [X0,X3] :
      ( outcompetes(first_movers,efficient_producers,X3)
      & subpopulations(first_movers,efficient_producers,X0,X3)
      & environment(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star) ).

fof(f5,negated_conjecture,
    ~ ? [X0,X3] :
        ( outcompetes(first_movers,efficient_producers,X3)
        & subpopulations(first_movers,efficient_producers,X0,X3)
        & environment(X0) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f6,plain,
    ? [X0,X1] :
      ( greater(zero,growth_rate(efficient_producers,X1))
      & greater_or_equal(growth_rate(first_movers,X1),zero)
      & subpopulations(first_movers,efficient_producers,X0,X1)
      & environment(X0) ),
    inference(rectify,[],[f3]) ).

fof(f7,plain,
    ~ ? [X0,X1] :
        ( outcompetes(first_movers,efficient_producers,X1)
        & subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) ),
    inference(rectify,[],[f5]) ).

fof(f8,plain,
    ! [X0,X1,X2,X3] :
      ( subpopulations(X2,X1,X0,X3)
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f9,plain,
    ! [X0,X1,X2,X3] :
      ( subpopulations(X2,X1,X0,X3)
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(flattening,[],[f8]) ).

fof(f10,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( greater(zero,growth_rate(X1,X3))
          & greater_or_equal(growth_rate(X2,X3),zero) )
      <=> outcompetes(X2,X1,X3) )
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f11,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( greater(zero,growth_rate(X1,X3))
          & greater_or_equal(growth_rate(X2,X3),zero) )
      <=> outcompetes(X2,X1,X3) )
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(flattening,[],[f10]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ outcompetes(first_movers,efficient_producers,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f13,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( ( greater(zero,growth_rate(X1,X3))
            & greater_or_equal(growth_rate(X2,X3),zero) )
          | ~ outcompetes(X2,X1,X3) )
        & ( outcompetes(X2,X1,X3)
          | ~ greater(zero,growth_rate(X1,X3))
          | ~ greater_or_equal(growth_rate(X2,X3),zero) ) )
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f14,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( ( greater(zero,growth_rate(X1,X3))
            & greater_or_equal(growth_rate(X2,X3),zero) )
          | ~ outcompetes(X2,X1,X3) )
        & ( outcompetes(X2,X1,X3)
          | ~ greater(zero,growth_rate(X1,X3))
          | ~ greater_or_equal(growth_rate(X2,X3),zero) ) )
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(flattening,[],[f13]) ).

fof(f15,plain,
    ( ? [X0,X1] :
        ( greater(zero,growth_rate(efficient_producers,X1))
        & greater_or_equal(growth_rate(first_movers,X1),zero)
        & subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
   => ( greater(zero,growth_rate(efficient_producers,sK1))
      & greater_or_equal(growth_rate(first_movers,sK1),zero)
      & subpopulations(first_movers,efficient_producers,sK0,sK1)
      & environment(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ( greater(zero,growth_rate(efficient_producers,sK1))
    & greater_or_equal(growth_rate(first_movers,sK1),zero)
    & subpopulations(first_movers,efficient_producers,sK0,sK1)
    & environment(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f15]) ).

fof(f17,plain,
    ! [X2,X3,X0,X1] :
      ( subpopulations(X2,X1,X0,X3)
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f18,plain,
    ! [X2,X3,X0,X1] :
      ( outcompetes(X2,X1,X3)
      | ~ greater(zero,growth_rate(X1,X3))
      | ~ greater_or_equal(growth_rate(X2,X3),zero)
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f21,plain,
    environment(sK0),
    inference(cnf_transformation,[],[f16]) ).

fof(f22,plain,
    subpopulations(first_movers,efficient_producers,sK0,sK1),
    inference(cnf_transformation,[],[f16]) ).

fof(f23,plain,
    greater_or_equal(growth_rate(first_movers,sK1),zero),
    inference(cnf_transformation,[],[f16]) ).

fof(f24,plain,
    greater(zero,growth_rate(efficient_producers,sK1)),
    inference(cnf_transformation,[],[f16]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ outcompetes(first_movers,efficient_producers,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f12]) ).

cnf(c_49,plain,
    ( ~ subpopulations(X0,X1,X2,X3)
    | ~ environment(X2)
    | subpopulations(X1,X0,X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

cnf(c_52,plain,
    ( ~ subpopulations(X0,X1,X2,X3)
    | ~ greater(zero,growth_rate(X0,X3))
    | ~ greater_or_equal(growth_rate(X1,X3),zero)
    | ~ environment(X2)
    | outcompetes(X1,X0,X3) ),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_53,plain,
    greater(zero,growth_rate(efficient_producers,sK1)),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_54,plain,
    greater_or_equal(growth_rate(first_movers,sK1),zero),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_55,plain,
    subpopulations(first_movers,efficient_producers,sK0,sK1),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_56,plain,
    environment(sK0),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_57,negated_conjecture,
    ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
    | ~ outcompetes(first_movers,efficient_producers,X1)
    | ~ environment(X0) ),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_202,plain,
    ( ~ subpopulations(X0,X1,sK0,X2)
    | ~ greater(zero,growth_rate(X0,X2))
    | ~ greater_or_equal(growth_rate(X1,X2),zero)
    | outcompetes(X1,X0,X2) ),
    inference(resolution,[status(thm)],[c_52,c_56]) ).

cnf(c_238,plain,
    ( ~ subpopulations(X0,X1,sK0,X2)
    | subpopulations(X1,X0,sK0,X2) ),
    inference(resolution,[status(thm)],[c_49,c_56]) ).

cnf(c_245,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
    | ~ outcompetes(first_movers,efficient_producers,X0) ),
    inference(resolution,[status(thm)],[c_56,c_57]) ).

cnf(c_339,plain,
    ( ~ subpopulations(efficient_producers,first_movers,sK0,X0)
    | ~ subpopulations(first_movers,efficient_producers,sK0,X0)
    | ~ greater(zero,growth_rate(efficient_producers,X0))
    | ~ greater_or_equal(growth_rate(first_movers,X0),zero) ),
    inference(resolution,[status(thm)],[c_202,c_245]) ).

cnf(c_349,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
    | ~ greater(zero,growth_rate(efficient_producers,X0))
    | ~ greater_or_equal(growth_rate(first_movers,X0),zero) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_339,c_238]) ).

cnf(c_357,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
    | ~ greater_or_equal(growth_rate(first_movers,sK1),zero) ),
    inference(resolution,[status(thm)],[c_53,c_349]) ).

cnf(c_358,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_357,c_54,c_55]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Aug 28 06:04:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.79/1.19  % SZS status Started for theBenchmark.p
% 0.79/1.19  % SZS status Theorem for theBenchmark.p
% 0.79/1.19  
% 0.79/1.19  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.79/1.19  
% 0.79/1.19  ------  iProver source info
% 0.79/1.19  
% 0.79/1.19  git: date: 2023-05-31 18:12:56 +0000
% 0.79/1.19  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.79/1.19  git: non_committed_changes: false
% 0.79/1.19  git: last_make_outside_of_git: false
% 0.79/1.19  
% 0.79/1.19  ------ Parsing...
% 0.79/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.79/1.19  
% 0.79/1.19  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe:2:0s
% 0.79/1.19  
% 0.79/1.19  % SZS status Theorem for theBenchmark.p
% 0.79/1.19  
% 0.79/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.79/1.19  
% 0.79/1.19  
%------------------------------------------------------------------------------