TSTP Solution File: MGT021+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : MGT021+1 : 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 : 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 09:07:21 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   51 (   5 unt;  18 typ;   0 def)
%            Number of atoms       :  118 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  146 (  61   ~;  49   |;  18   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  13   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   46 (   0 sgn;  27   !;   0   ?;   0   :)

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

tff(decl_23,type,
    first_movers: $i ).

tff(decl_24,type,
    efficient_producers: $i ).

tff(decl_25,type,
    subpopulations: ( $i * $i * $i * $i ) > $o ).

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

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

tff(decl_28,type,
    zero: $i ).

tff(decl_29,type,
    greater: ( $i * $i ) > $o ).

tff(decl_30,type,
    increases: $i > $o ).

tff(decl_31,type,
    decreases: $i > $o ).

tff(decl_32,type,
    greater_or_equal: ( $i * $i ) > $o ).

tff(decl_33,type,
    equilibrium: $i > $i ).

tff(decl_34,type,
    resources: ( $i * $i ) > $i ).

tff(decl_35,type,
    constant: $i > $o ).

tff(decl_36,type,
    disbanding_rate: ( $i * $i ) > $i ).

tff(decl_37,type,
    difference: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk1_0: $i ).

tff(decl_39,type,
    esk2_0: $i ).

fof(l4,hypothesis,
    ! [X1,X2] :
      ( ( environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X2) )
     => ( ( decreases(resources(X1,X2))
         => increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
        & ( constant(resources(X1,X2))
         => ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).

fof(prove_l3,conjecture,
    ! [X1,X2] :
      ( ( environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X2) )
     => ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3) ).

fof(a3,hypothesis,
    ! [X1,X2] :
      ( ( environment(X1)
        & in_environment(X1,X2)
        & greater(number_of_organizations(X1,X2),zero) )
     => ( ( greater(equilibrium(X1),X2)
         => decreases(resources(X1,X2)) )
        & ( ~ greater(equilibrium(X1),X2)
         => constant(resources(X1,X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).

fof(mp_environment_not_empty,axiom,
    ! [X1,X2] :
      ( ( environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X2) )
     => greater(number_of_organizations(X1,X2),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_not_empty) ).

fof(mp_time_point_in_environment,axiom,
    ! [X1,X2] :
      ( ( environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X2) )
     => in_environment(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_in_environment) ).

fof(mp_increase_not_decrease,axiom,
    ! [X3] :
      ( increases(X3)
     => ~ decreases(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_increase_not_decrease) ).

fof(c_0_6,hypothesis,
    ! [X1,X2] :
      ( ( environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X2) )
     => ( ( decreases(resources(X1,X2))
         => increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
        & ( constant(resources(X1,X2))
         => ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ) ),
    inference(fof_simplification,[status(thm)],[l4]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( environment(X1)
          & subpopulations(first_movers,efficient_producers,X1,X2) )
       => ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_l3])]) ).

fof(c_0_8,hypothesis,
    ! [X1,X2] :
      ( ( environment(X1)
        & in_environment(X1,X2)
        & greater(number_of_organizations(X1,X2),zero) )
     => ( ( greater(equilibrium(X1),X2)
         => decreases(resources(X1,X2)) )
        & ( ~ greater(equilibrium(X1),X2)
         => constant(resources(X1,X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[a3]) ).

fof(c_0_9,hypothesis,
    ! [X14,X15] :
      ( ( ~ decreases(resources(X14,X15))
        | increases(difference(disbanding_rate(first_movers,X15),disbanding_rate(efficient_producers,X15)))
        | ~ environment(X14)
        | ~ subpopulations(first_movers,efficient_producers,X14,X15) )
      & ( ~ constant(resources(X14,X15))
        | ~ decreases(difference(disbanding_rate(first_movers,X15),disbanding_rate(efficient_producers,X15)))
        | ~ environment(X14)
        | ~ subpopulations(first_movers,efficient_producers,X14,X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_10,negated_conjecture,
    ( environment(esk1_0)
    & subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
    & decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_11,hypothesis,
    ! [X12,X13] :
      ( ( ~ greater(equilibrium(X12),X13)
        | decreases(resources(X12,X13))
        | ~ environment(X12)
        | ~ in_environment(X12,X13)
        | ~ greater(number_of_organizations(X12,X13),zero) )
      & ( greater(equilibrium(X12),X13)
        | constant(resources(X12,X13))
        | ~ environment(X12)
        | ~ in_environment(X12,X13)
        | ~ greater(number_of_organizations(X12,X13),zero) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_12,plain,
    ! [X7,X8] :
      ( ~ environment(X7)
      | ~ subpopulations(first_movers,efficient_producers,X7,X8)
      | greater(number_of_organizations(X7,X8),zero) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_environment_not_empty])]) ).

fof(c_0_13,plain,
    ! [X5,X6] :
      ( ~ environment(X5)
      | ~ subpopulations(first_movers,efficient_producers,X5,X6)
      | in_environment(X5,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_in_environment])]) ).

cnf(c_0_14,hypothesis,
    ( ~ constant(resources(X1,X2))
    | ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
    | ~ environment(X1)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,hypothesis,
    ( decreases(resources(X1,X2))
    | ~ greater(equilibrium(X1),X2)
    | ~ environment(X1)
    | ~ in_environment(X1,X2)
    | ~ greater(number_of_organizations(X1,X2),zero) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( greater(number_of_organizations(X1,X2),zero)
    | ~ environment(X1)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( in_environment(X1,X2)
    | ~ environment(X1)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ constant(resources(X1,esk2_0))
    | ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
    | ~ environment(X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,hypothesis,
    ( greater(equilibrium(X1),X2)
    | constant(resources(X1,X2))
    | ~ environment(X1)
    | ~ in_environment(X1,X2)
    | ~ greater(number_of_organizations(X1,X2),zero) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,hypothesis,
    ( decreases(resources(X1,X2))
    | ~ greater(equilibrium(X1),X2)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2)
    | ~ environment(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( greater(equilibrium(X1),esk2_0)
    | ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
    | ~ environment(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]),c_0_17]) ).

fof(c_0_23,plain,
    ! [X3] :
      ( increases(X3)
     => ~ decreases(X3) ),
    inference(fof_simplification,[status(thm)],[mp_increase_not_decrease]) ).

cnf(c_0_24,hypothesis,
    ( increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
    | ~ decreases(resources(X1,X2))
    | ~ environment(X1)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_25,negated_conjecture,
    ( decreases(resources(X1,esk2_0))
    | ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
    | ~ environment(X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_26,plain,
    ! [X9] :
      ( ~ increases(X9)
      | ~ decreases(X9) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).

cnf(c_0_27,hypothesis,
    ( increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
    | ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
    | ~ environment(X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_29,negated_conjecture,
    environment(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_30,plain,
    ( ~ increases(X1)
    | ~ decreases(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : MGT021+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n012.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 06:19:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.008000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.011000 s
%------------------------------------------------------------------------------