TSTP Solution File: MGT036+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n023.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 09:08:32 EDT 2023

% Result   : Theorem 0.51s 0.60s
% Output   : CNFRefutation 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   32 (   7 unt;  11 typ;   0 def)
%            Number of atoms       :   65 (   0 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :   75 (  31   ~;  26   |;  15   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   6   >;   8   *;   0   +;   0  <<)
%            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   :   37 (   0 sgn;  18   !;   6   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    environment: $i > $o ).

tff(decl_23,type,
    subpopulations: ( $i * $i * $i * $i ) > $o ).

tff(decl_24,type,
    growth_rate: ( $i * $i ) > $i ).

tff(decl_25,type,
    zero: $i ).

tff(decl_26,type,
    greater_or_equal: ( $i * $i ) > $o ).

tff(decl_27,type,
    greater: ( $i * $i ) > $o ).

tff(decl_28,type,
    outcompetes: ( $i * $i * $i ) > $o ).

tff(decl_29,type,
    first_movers: $i ).

tff(decl_30,type,
    efficient_producers: $i ).

tff(decl_31,type,
    esk1_0: $i ).

tff(decl_32,type,
    esk2_0: $i ).

fof(prove_t5_star,conjecture,
    ? [X1,X4] :
      ( environment(X1)
      & subpopulations(first_movers,efficient_producers,X1,X4)
      & outcompetes(first_movers,efficient_producers,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star) ).

fof(d2,hypothesis,
    ! [X1,X2,X3,X4] :
      ( ( environment(X1)
        & subpopulations(X2,X3,X1,X4) )
     => ( ( greater_or_equal(growth_rate(X3,X4),zero)
          & greater(zero,growth_rate(X2,X4)) )
      <=> outcompetes(X3,X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).

fof(a13_star,hypothesis,
    ? [X1,X4] :
      ( environment(X1)
      & subpopulations(first_movers,efficient_producers,X1,X4)
      & greater_or_equal(growth_rate(first_movers,X4),zero)
      & greater(zero,growth_rate(efficient_producers,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).

fof(mp_symmetry_of_subpopulations,axiom,
    ! [X1,X2,X3,X4] :
      ( ( environment(X1)
        & subpopulations(X2,X3,X1,X4) )
     => subpopulations(X3,X2,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).

fof(c_0_4,negated_conjecture,
    ~ ? [X1,X4] :
        ( environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X4)
        & outcompetes(first_movers,efficient_producers,X4) ),
    inference(assume_negation,[status(cth)],[prove_t5_star]) ).

fof(c_0_5,hypothesis,
    ! [X9,X10,X11,X12] :
      ( ( ~ greater_or_equal(growth_rate(X11,X12),zero)
        | ~ greater(zero,growth_rate(X10,X12))
        | outcompetes(X11,X10,X12)
        | ~ environment(X9)
        | ~ subpopulations(X10,X11,X9,X12) )
      & ( greater_or_equal(growth_rate(X11,X12),zero)
        | ~ outcompetes(X11,X10,X12)
        | ~ environment(X9)
        | ~ subpopulations(X10,X11,X9,X12) )
      & ( greater(zero,growth_rate(X10,X12))
        | ~ outcompetes(X11,X10,X12)
        | ~ environment(X9)
        | ~ subpopulations(X10,X11,X9,X12) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2])])]) ).

fof(c_0_6,hypothesis,
    ( environment(esk1_0)
    & subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
    & greater_or_equal(growth_rate(first_movers,esk2_0),zero)
    & greater(zero,growth_rate(efficient_producers,esk2_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[a13_star])]) ).

fof(c_0_7,negated_conjecture,
    ! [X15,X16] :
      ( ~ environment(X15)
      | ~ subpopulations(first_movers,efficient_producers,X15,X16)
      | ~ outcompetes(first_movers,efficient_producers,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

cnf(c_0_8,hypothesis,
    ( outcompetes(X1,X3,X2)
    | ~ greater_or_equal(growth_rate(X1,X2),zero)
    | ~ greater(zero,growth_rate(X3,X2))
    | ~ environment(X4)
    | ~ subpopulations(X3,X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,hypothesis,
    greater(zero,growth_rate(efficient_producers,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( ~ environment(X1)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2)
    | ~ outcompetes(first_movers,efficient_producers,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,hypothesis,
    subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,hypothesis,
    environment(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_13,plain,
    ! [X5,X6,X7,X8] :
      ( ~ environment(X5)
      | ~ subpopulations(X6,X7,X5,X8)
      | subpopulations(X7,X6,X5,X8) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])]) ).

cnf(c_0_14,hypothesis,
    ( outcompetes(X1,efficient_producers,esk2_0)
    | ~ greater_or_equal(growth_rate(X1,esk2_0),zero)
    | ~ subpopulations(efficient_producers,X1,X2,esk2_0)
    | ~ environment(X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_15,hypothesis,
    greater_or_equal(growth_rate(first_movers,esk2_0),zero),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_16,negated_conjecture,
    ~ outcompetes(first_movers,efficient_producers,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).

cnf(c_0_17,plain,
    ( subpopulations(X3,X2,X1,X4)
    | ~ environment(X1)
    | ~ subpopulations(X2,X3,X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,hypothesis,
    ( ~ subpopulations(efficient_producers,first_movers,X1,esk2_0)
    | ~ environment(X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_19,hypothesis,
    subpopulations(efficient_producers,first_movers,esk1_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_12])]) ).

cnf(c_0_20,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.04/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 06:26:25 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.51/0.58  start to proof: theBenchmark
% 0.51/0.60  % Version  : CSE_E---1.5
% 0.51/0.60  % Problem  : theBenchmark.p
% 0.51/0.60  % Proof found
% 0.51/0.60  % SZS status Theorem for theBenchmark.p
% 0.51/0.60  % SZS output start Proof
% See solution above
% 0.51/0.60  % Total time : 0.006000 s
% 0.51/0.60  % SZS output end Proof
% 0.51/0.60  % Total time : 0.009000 s
%------------------------------------------------------------------------------