TSTP Solution File: MGT021+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : MGT021+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 : Tue Apr 30 20:28:38 EDT 2024

% Result   : Theorem 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   70 (   9 unt;   0 def)
%            Number of atoms       :  196 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  217 (  91   ~;  89   |;  17   &)
%                                         (   9 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   17 (  16 usr;  10 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   47 (  43   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [E,T] :
      ( ( environment(E)
        & subpopulations(first_movers,efficient_producers,E,T) )
     => in_environment(E,T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [E,T] :
      ( ( environment(E)
        & subpopulations(first_movers,efficient_producers,E,T) )
     => greater(number_of_organizations(E,T),zero) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X] :
      ( increases(X)
     => ~ decreases(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,hypothesis,
    ! [E,T] :
      ( ( environment(E)
        & in_environment(E,T)
        & greater(number_of_organizations(E,T),zero) )
     => ( ( greater(equilibrium(E),T)
         => decreases(resources(E,T)) )
        & ( ~ greater(equilibrium(E),T)
         => constant(resources(E,T)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,hypothesis,
    ! [E,T] :
      ( ( environment(E)
        & subpopulations(first_movers,efficient_producers,E,T) )
     => ( ( decreases(resources(E,T))
         => increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
        & ( constant(resources(E,T))
         => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,conjecture,
    ! [E,T] :
      ( ( environment(E)
        & subpopulations(first_movers,efficient_producers,E,T) )
     => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    ~ ! [E,T] :
        ( ( environment(E)
          & subpopulations(first_movers,efficient_producers,E,T) )
       => ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
    inference(negated_conjecture,[status(cth)],[f7]) ).

fof(f9,plain,
    ! [E,T] :
      ( ~ environment(E)
      | ~ subpopulations(first_movers,efficient_producers,E,T)
      | in_environment(E,T) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | in_environment(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f11,plain,
    ! [E,T] :
      ( ~ environment(E)
      | ~ subpopulations(first_movers,efficient_producers,E,T)
      | greater(number_of_organizations(E,T),zero) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | greater(number_of_organizations(X0,X1),zero) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ! [X] :
      ( ~ increases(X)
      | ~ decreases(X) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f14,plain,
    ! [X0] :
      ( ~ increases(X0)
      | ~ decreases(X0) ),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f17,plain,
    ! [E,T] :
      ( ~ environment(E)
      | ~ in_environment(E,T)
      | ~ greater(number_of_organizations(E,T),zero)
      | ( ( ~ greater(equilibrium(E),T)
          | decreases(resources(E,T)) )
        & ( greater(equilibrium(E),T)
          | constant(resources(E,T)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ in_environment(X0,X1)
      | ~ greater(number_of_organizations(X0,X1),zero)
      | ~ greater(equilibrium(X0),X1)
      | decreases(resources(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ in_environment(X0,X1)
      | ~ greater(number_of_organizations(X0,X1),zero)
      | greater(equilibrium(X0),X1)
      | constant(resources(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [E,T] :
      ( ~ environment(E)
      | ~ subpopulations(first_movers,efficient_producers,E,T)
      | ( ( ~ decreases(resources(E,T))
          | increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
        & ( ~ constant(resources(E,T))
          | ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ decreases(resources(X0,X1))
      | increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ constant(resources(X0,X1))
      | ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f23,plain,
    ? [E,T] :
      ( environment(E)
      & subpopulations(first_movers,efficient_producers,E,T)
      & decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f24,plain,
    ? [T] :
      ( ? [E] :
          ( environment(E)
          & subpopulations(first_movers,efficient_producers,E,T) )
      & decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f25,plain,
    ( environment(sk0_1)
    & subpopulations(first_movers,efficient_producers,sk0_1,sk0_0)
    & decreases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0))) ),
    inference(skolemization,[status(esa)],[f24]) ).

fof(f26,plain,
    environment(sk0_1),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    subpopulations(first_movers,efficient_producers,sk0_1,sk0_0),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f28,plain,
    decreases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0))),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ subpopulations(first_movers,efficient_producers,sk0_1,X0)
      | in_environment(sk0_1,X0) ),
    inference(resolution,[status(thm)],[f10,f26]) ).

fof(f30,plain,
    in_environment(sk0_1,sk0_0),
    inference(resolution,[status(thm)],[f29,f27]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ in_environment(X0,X1)
      | greater(equilibrium(X0),X1)
      | constant(resources(X0,X1))
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(resolution,[status(thm)],[f19,f12]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ in_environment(X0,X1)
      | greater(equilibrium(X0),X1)
      | constant(resources(X0,X1))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | greater(equilibrium(X0),X1)
      | constant(resources(X0,X1))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f32,f10]) ).

fof(f34,plain,
    ! [X0] :
      ( greater(equilibrium(sk0_1),X0)
      | constant(resources(sk0_1,X0))
      | ~ subpopulations(first_movers,efficient_producers,sk0_1,X0) ),
    inference(resolution,[status(thm)],[f33,f26]) ).

fof(f35,plain,
    ( spl0_0
  <=> greater(equilibrium(sk0_1),sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f36,plain,
    ( greater(equilibrium(sk0_1),sk0_0)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f35]) ).

fof(f38,plain,
    ( spl0_1
  <=> constant(resources(sk0_1,sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f39,plain,
    ( constant(resources(sk0_1,sk0_0))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f38]) ).

fof(f41,plain,
    ( greater(equilibrium(sk0_1),sk0_0)
    | constant(resources(sk0_1,sk0_0)) ),
    inference(resolution,[status(thm)],[f34,f27]) ).

fof(f42,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f41,f35,f38]) ).

fof(f43,plain,
    ( spl0_2
  <=> environment(sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f45,plain,
    ( ~ environment(sk0_1)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f43]) ).

fof(f46,plain,
    ( spl0_3
  <=> in_environment(sk0_1,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f48,plain,
    ( ~ in_environment(sk0_1,sk0_0)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f46]) ).

fof(f49,plain,
    ( spl0_4
  <=> greater(number_of_organizations(sk0_1,sk0_0),zero) ),
    introduced(split_symbol_definition) ).

fof(f51,plain,
    ( ~ greater(number_of_organizations(sk0_1,sk0_0),zero)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f49]) ).

fof(f52,plain,
    ( spl0_5
  <=> decreases(resources(sk0_1,sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f53,plain,
    ( decreases(resources(sk0_1,sk0_0))
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f52]) ).

fof(f55,plain,
    ( ~ environment(sk0_1)
    | ~ in_environment(sk0_1,sk0_0)
    | ~ greater(number_of_organizations(sk0_1,sk0_0),zero)
    | decreases(resources(sk0_1,sk0_0))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f36,f18]) ).

fof(f56,plain,
    ( ~ spl0_2
    | ~ spl0_3
    | ~ spl0_4
    | spl0_5
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f55,f43,f46,f49,f52,f35]) ).

fof(f57,plain,
    ( spl0_6
  <=> subpopulations(first_movers,efficient_producers,sk0_1,sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f59,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sk0_1,sk0_0)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f57]) ).

fof(f60,plain,
    ( spl0_7
  <=> decreases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0))) ),
    introduced(split_symbol_definition) ).

fof(f62,plain,
    ( ~ decreases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0)))
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f60]) ).

fof(f63,plain,
    ( ~ environment(sk0_1)
    | ~ subpopulations(first_movers,efficient_producers,sk0_1,sk0_0)
    | ~ decreases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0)))
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f39,f22]) ).

fof(f64,plain,
    ( ~ spl0_2
    | ~ spl0_6
    | ~ spl0_7
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f63,f43,f57,f60,f38]) ).

fof(f65,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f62,f28]) ).

fof(f66,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f65]) ).

fof(f67,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f59,f27]) ).

fof(f68,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f67]) ).

fof(f69,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f45,f26]) ).

fof(f70,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f69]) ).

fof(f73,plain,
    ( ~ environment(sk0_1)
    | ~ subpopulations(first_movers,efficient_producers,sk0_1,sk0_0)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f51,f12]) ).

fof(f74,plain,
    ( ~ spl0_2
    | ~ spl0_6
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f73,f43,f57,f49]) ).

fof(f75,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f48,f30]) ).

fof(f76,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f75]) ).

fof(f77,plain,
    ( spl0_8
  <=> increases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0))) ),
    introduced(split_symbol_definition) ).

fof(f78,plain,
    ( increases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0)))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f77]) ).

fof(f80,plain,
    ( ~ environment(sk0_1)
    | ~ subpopulations(first_movers,efficient_producers,sk0_1,sk0_0)
    | increases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0)))
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f53,f21]) ).

fof(f81,plain,
    ( ~ spl0_2
    | ~ spl0_6
    | spl0_8
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f80,f43,f57,f77,f52]) ).

fof(f84,plain,
    ( ~ decreases(difference(disbanding_rate(first_movers,sk0_0),disbanding_rate(efficient_producers,sk0_0)))
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f78,f14]) ).

fof(f85,plain,
    ( ~ spl0_7
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f84,f60,f77]) ).

fof(f86,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f42,f56,f64,f66,f68,f70,f74,f76,f81,f85]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : MGT021+1 : TPTP v8.1.2. Released v2.0.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n027.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 : Tue Apr 30 00:06:17 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 0.11/0.34  % Refutation found
% 0.11/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.35  % Elapsed time: 0.018828 seconds
% 0.11/0.35  % CPU time: 0.025730 seconds
% 0.11/0.35  % Total memory used: 11.057 MB
% 0.11/0.35  % Net memory used: 10.913 MB
%------------------------------------------------------------------------------