TSTP Solution File: MGT032+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : MGT032+2 : TPTP v5.0.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 21:05:29 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   39 (   5 unt;   0 def)
%            Number of atoms       :  164 (   0 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  218 (  93   ~;  82   |;  36   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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   :   60 (   0 sgn  33   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1] :
      ( ( environment(X1)
        & stable(X1) )
     => ? [X2] :
          ( in_environment(X1,X2)
          & ! [X3] :
              ( ( subpopulations(first_movers,efficient_producers,X1,X3)
                & greater_or_equal(X3,X2) )
             => selection_favors(efficient_producers,first_movers,X3) ) ) ),
    file('/tmp/tmpXdORNm/sel_MGT032+2.p_1',prove_t1) ).

fof(2,axiom,
    ! [X1,X4,X5,X3] :
      ( ( environment(X1)
        & subpopulations(X4,X5,X1,X3)
        & greater(growth_rate(X5,X3),growth_rate(X4,X3)) )
     => selection_favors(X5,X4,X3) ),
    file('/tmp/tmpXdORNm/sel_MGT032+2.p_1',mp1_high_growth_rates) ).

fof(3,axiom,
    ! [X1] :
      ( ( environment(X1)
        & stable(X1) )
     => ? [X2] :
          ( in_environment(X1,X2)
          & ! [X3] :
              ( ( subpopulations(first_movers,efficient_producers,X1,X3)
                & greater_or_equal(X3,X2) )
             => greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
    file('/tmp/tmpXdORNm/sel_MGT032+2.p_1',l1) ).

fof(4,negated_conjecture,
    ~ ! [X1] :
        ( ( environment(X1)
          & stable(X1) )
       => ? [X2] :
            ( in_environment(X1,X2)
            & ! [X3] :
                ( ( subpopulations(first_movers,efficient_producers,X1,X3)
                  & greater_or_equal(X3,X2) )
               => selection_favors(efficient_producers,first_movers,X3) ) ) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(5,negated_conjecture,
    ? [X1] :
      ( environment(X1)
      & stable(X1)
      & ! [X2] :
          ( ~ in_environment(X1,X2)
          | ? [X3] :
              ( subpopulations(first_movers,efficient_producers,X1,X3)
              & greater_or_equal(X3,X2)
              & ~ selection_favors(efficient_producers,first_movers,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(6,negated_conjecture,
    ? [X4] :
      ( environment(X4)
      & stable(X4)
      & ! [X5] :
          ( ~ in_environment(X4,X5)
          | ? [X6] :
              ( subpopulations(first_movers,efficient_producers,X4,X6)
              & greater_or_equal(X6,X5)
              & ~ selection_favors(efficient_producers,first_movers,X6) ) ) ),
    inference(variable_rename,[status(thm)],[5]) ).

fof(7,negated_conjecture,
    ( environment(esk1_0)
    & stable(esk1_0)
    & ! [X5] :
        ( ~ in_environment(esk1_0,X5)
        | ( subpopulations(first_movers,efficient_producers,esk1_0,esk2_1(X5))
          & greater_or_equal(esk2_1(X5),X5)
          & ~ selection_favors(efficient_producers,first_movers,esk2_1(X5)) ) ) ),
    inference(skolemize,[status(esa)],[6]) ).

fof(8,negated_conjecture,
    ! [X5] :
      ( ( ~ in_environment(esk1_0,X5)
        | ( subpopulations(first_movers,efficient_producers,esk1_0,esk2_1(X5))
          & greater_or_equal(esk2_1(X5),X5)
          & ~ selection_favors(efficient_producers,first_movers,esk2_1(X5)) ) )
      & environment(esk1_0)
      & stable(esk1_0) ),
    inference(shift_quantors,[status(thm)],[7]) ).

fof(9,negated_conjecture,
    ! [X5] :
      ( ( subpopulations(first_movers,efficient_producers,esk1_0,esk2_1(X5))
        | ~ in_environment(esk1_0,X5) )
      & ( greater_or_equal(esk2_1(X5),X5)
        | ~ in_environment(esk1_0,X5) )
      & ( ~ selection_favors(efficient_producers,first_movers,esk2_1(X5))
        | ~ in_environment(esk1_0,X5) )
      & environment(esk1_0)
      & stable(esk1_0) ),
    inference(distribute,[status(thm)],[8]) ).

cnf(10,negated_conjecture,
    stable(esk1_0),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(11,negated_conjecture,
    environment(esk1_0),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(12,negated_conjecture,
    ( ~ in_environment(esk1_0,X1)
    | ~ selection_favors(efficient_producers,first_movers,esk2_1(X1)) ),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(13,negated_conjecture,
    ( greater_or_equal(esk2_1(X1),X1)
    | ~ in_environment(esk1_0,X1) ),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(14,negated_conjecture,
    ( subpopulations(first_movers,efficient_producers,esk1_0,esk2_1(X1))
    | ~ in_environment(esk1_0,X1) ),
    inference(split_conjunct,[status(thm)],[9]) ).

fof(15,plain,
    ! [X1,X4,X5,X3] :
      ( ~ environment(X1)
      | ~ subpopulations(X4,X5,X1,X3)
      | ~ greater(growth_rate(X5,X3),growth_rate(X4,X3))
      | selection_favors(X5,X4,X3) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(16,plain,
    ! [X6,X7,X8,X9] :
      ( ~ environment(X6)
      | ~ subpopulations(X7,X8,X6,X9)
      | ~ greater(growth_rate(X8,X9),growth_rate(X7,X9))
      | selection_favors(X8,X7,X9) ),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(17,plain,
    ( selection_favors(X1,X2,X3)
    | ~ greater(growth_rate(X1,X3),growth_rate(X2,X3))
    | ~ subpopulations(X2,X1,X4,X3)
    | ~ environment(X4) ),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,plain,
    ! [X1] :
      ( ~ environment(X1)
      | ~ stable(X1)
      | ? [X2] :
          ( in_environment(X1,X2)
          & ! [X3] :
              ( ~ subpopulations(first_movers,efficient_producers,X1,X3)
              | ~ greater_or_equal(X3,X2)
              | greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(19,plain,
    ! [X4] :
      ( ~ environment(X4)
      | ~ stable(X4)
      | ? [X5] :
          ( in_environment(X4,X5)
          & ! [X6] :
              ( ~ subpopulations(first_movers,efficient_producers,X4,X6)
              | ~ greater_or_equal(X6,X5)
              | greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6)) ) ) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,plain,
    ! [X4] :
      ( ~ environment(X4)
      | ~ stable(X4)
      | ( in_environment(X4,esk3_1(X4))
        & ! [X6] :
            ( ~ subpopulations(first_movers,efficient_producers,X4,X6)
            | ~ greater_or_equal(X6,esk3_1(X4))
            | greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6)) ) ) ),
    inference(skolemize,[status(esa)],[19]) ).

fof(21,plain,
    ! [X4,X6] :
      ( ( ( ~ subpopulations(first_movers,efficient_producers,X4,X6)
          | ~ greater_or_equal(X6,esk3_1(X4))
          | greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6)) )
        & in_environment(X4,esk3_1(X4)) )
      | ~ environment(X4)
      | ~ stable(X4) ),
    inference(shift_quantors,[status(thm)],[20]) ).

fof(22,plain,
    ! [X4,X6] :
      ( ( ~ subpopulations(first_movers,efficient_producers,X4,X6)
        | ~ greater_or_equal(X6,esk3_1(X4))
        | greater(growth_rate(efficient_producers,X6),growth_rate(first_movers,X6))
        | ~ environment(X4)
        | ~ stable(X4) )
      & ( in_environment(X4,esk3_1(X4))
        | ~ environment(X4)
        | ~ stable(X4) ) ),
    inference(distribute,[status(thm)],[21]) ).

cnf(23,plain,
    ( in_environment(X1,esk3_1(X1))
    | ~ stable(X1)
    | ~ environment(X1) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(24,plain,
    ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
    | ~ stable(X1)
    | ~ environment(X1)
    | ~ greater_or_equal(X2,esk3_1(X1))
    | ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(25,negated_conjecture,
    ( greater(growth_rate(efficient_producers,esk2_1(esk3_1(X1))),growth_rate(first_movers,esk2_1(esk3_1(X1))))
    | ~ subpopulations(first_movers,efficient_producers,X1,esk2_1(esk3_1(X1)))
    | ~ stable(X1)
    | ~ environment(X1)
    | ~ in_environment(esk1_0,esk3_1(X1)) ),
    inference(spm,[status(thm)],[24,13,theory(equality)]) ).

cnf(26,negated_conjecture,
    ( selection_favors(efficient_producers,first_movers,esk2_1(esk3_1(X1)))
    | ~ subpopulations(first_movers,efficient_producers,X2,esk2_1(esk3_1(X1)))
    | ~ environment(X2)
    | ~ subpopulations(first_movers,efficient_producers,X1,esk2_1(esk3_1(X1)))
    | ~ in_environment(esk1_0,esk3_1(X1))
    | ~ stable(X1)
    | ~ environment(X1) ),
    inference(spm,[status(thm)],[17,25,theory(equality)]) ).

cnf(27,negated_conjecture,
    ( ~ subpopulations(first_movers,efficient_producers,X2,esk2_1(esk3_1(X1)))
    | ~ subpopulations(first_movers,efficient_producers,X1,esk2_1(esk3_1(X1)))
    | ~ in_environment(esk1_0,esk3_1(X1))
    | ~ stable(X1)
    | ~ environment(X2)
    | ~ environment(X1) ),
    inference(csr,[status(thm)],[26,12]) ).

cnf(28,negated_conjecture,
    ( ~ subpopulations(first_movers,efficient_producers,X1,esk2_1(esk3_1(X1)))
    | ~ in_environment(esk1_0,esk3_1(X1))
    | ~ stable(X1)
    | ~ environment(esk1_0)
    | ~ environment(X1) ),
    inference(spm,[status(thm)],[27,14,theory(equality)]) ).

cnf(29,negated_conjecture,
    ( ~ subpopulations(first_movers,efficient_producers,X1,esk2_1(esk3_1(X1)))
    | ~ in_environment(esk1_0,esk3_1(X1))
    | ~ stable(X1)
    | $false
    | ~ environment(X1) ),
    inference(rw,[status(thm)],[28,11,theory(equality)]) ).

cnf(30,negated_conjecture,
    ( ~ subpopulations(first_movers,efficient_producers,X1,esk2_1(esk3_1(X1)))
    | ~ in_environment(esk1_0,esk3_1(X1))
    | ~ stable(X1)
    | ~ environment(X1) ),
    inference(cn,[status(thm)],[29,theory(equality)]) ).

cnf(31,negated_conjecture,
    ( ~ in_environment(esk1_0,esk3_1(esk1_0))
    | ~ stable(esk1_0)
    | ~ environment(esk1_0) ),
    inference(spm,[status(thm)],[30,14,theory(equality)]) ).

cnf(32,negated_conjecture,
    ( ~ in_environment(esk1_0,esk3_1(esk1_0))
    | $false
    | ~ environment(esk1_0) ),
    inference(rw,[status(thm)],[31,10,theory(equality)]) ).

cnf(33,negated_conjecture,
    ( ~ in_environment(esk1_0,esk3_1(esk1_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[32,11,theory(equality)]) ).

cnf(34,negated_conjecture,
    ~ in_environment(esk1_0,esk3_1(esk1_0)),
    inference(cn,[status(thm)],[33,theory(equality)]) ).

cnf(35,plain,
    ( ~ stable(esk1_0)
    | ~ environment(esk1_0) ),
    inference(spm,[status(thm)],[34,23,theory(equality)]) ).

cnf(36,plain,
    ( $false
    | ~ environment(esk1_0) ),
    inference(rw,[status(thm)],[35,10,theory(equality)]) ).

cnf(37,plain,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[36,11,theory(equality)]) ).

cnf(38,plain,
    $false,
    inference(cn,[status(thm)],[37,theory(equality)]) ).

cnf(39,plain,
    $false,
    38,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/MGT/MGT032+2.p
% --creating new selector for []
% -running prover on /tmp/tmpXdORNm/sel_MGT032+2.p_1 with time limit 29
% -prover status Theorem
% Problem MGT032+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/MGT/MGT032+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/MGT/MGT032+2.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------