TSTP Solution File: MGT028-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : MGT028-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 09:07:26 EDT 2023

% Result   : Unsatisfiable 0.19s 0.64s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   59 (  13 unt;  16 typ;   0 def)
%            Number of atoms       :  135 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  177 (  85   ~;  92   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  12   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   48 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    efficient_producers: $i ).

tff(decl_27,type,
    sk1: ( $i * $i ) > $i ).

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

tff(decl_29,type,
    sk2: $i > $i ).

tff(decl_30,type,
    appear: ( $i * $i ) > $i ).

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

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

tff(decl_33,type,
    zero: $i ).

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

tff(decl_35,type,
    sk3: $i > $i ).

tff(decl_36,type,
    sk4: $i ).

tff(decl_37,type,
    sk5: $i > $i ).

cnf(mp_first_movers_negative_growth_1,axiom,
    ( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
    | greater(sk2(X1),appear(efficient_producers,X1))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).

cnf(l11_7,hypothesis,
    ( in_environment(X1,sk3(X1))
    | ~ environment(X1)
    | ~ stable(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_7) ).

cnf(mp_first_movers_negative_growth_2,axiom,
    ( greater_or_equal(sk1(X2,X1),X2)
    | greater(sk2(X1),appear(efficient_producers,X1))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).

cnf(l11_9,hypothesis,
    ( greater(zero,growth_rate(first_movers,X2))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2)
    | ~ greater_or_equal(X2,sk3(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_9) ).

cnf(prove_l10_11,negated_conjecture,
    stable(sk4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_11) ).

cnf(prove_l10_10,negated_conjecture,
    environment(sk4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_10) ).

cnf(mp_first_movers_negative_growth_5,axiom,
    ( greater(sk2(X1),appear(efficient_producers,X1))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).

cnf(prove_l10_12,negated_conjecture,
    ( subpopulations(first_movers,efficient_producers,sk4,sk5(X1))
    | ~ greater(X1,appear(efficient_producers,sk4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_12) ).

cnf(prove_l10_14,negated_conjecture,
    ( ~ greater(X1,appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk5(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_14) ).

cnf(prove_l10_13,negated_conjecture,
    ( greater_or_equal(sk5(X1),X1)
    | ~ greater(X1,appear(efficient_producers,sk4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_13) ).

cnf(mp_first_movers_negative_growth_3,axiom,
    ( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
    | greater(zero,growth_rate(first_movers,X3))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ subpopulations(first_movers,efficient_producers,X1,X3)
    | ~ greater_or_equal(X3,sk2(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).

cnf(mp_first_movers_negative_growth_4,axiom,
    ( greater_or_equal(sk1(X2,X1),X2)
    | greater(zero,growth_rate(first_movers,X3))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ subpopulations(first_movers,efficient_producers,X1,X3)
    | ~ greater_or_equal(X3,sk2(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).

cnf(mp_first_movers_negative_growth_6,axiom,
    ( greater(zero,growth_rate(first_movers,X3))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ greater(zero,growth_rate(first_movers,sk1(X2,X1)))
    | ~ subpopulations(first_movers,efficient_producers,X1,X3)
    | ~ greater_or_equal(X3,sk2(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).

cnf(c_0_13,axiom,
    ( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
    | greater(sk2(X1),appear(efficient_producers,X1))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2) ),
    mp_first_movers_negative_growth_1 ).

cnf(c_0_14,hypothesis,
    ( in_environment(X1,sk3(X1))
    | ~ environment(X1)
    | ~ stable(X1) ),
    l11_7 ).

cnf(c_0_15,axiom,
    ( greater_or_equal(sk1(X2,X1),X2)
    | greater(sk2(X1),appear(efficient_producers,X1))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2) ),
    mp_first_movers_negative_growth_2 ).

cnf(c_0_16,hypothesis,
    ( greater(zero,growth_rate(first_movers,X2))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ subpopulations(first_movers,efficient_producers,X1,X2)
    | ~ greater_or_equal(X2,sk3(X1)) ),
    l11_9 ).

cnf(c_0_17,hypothesis,
    ( greater(sk2(X1),appear(efficient_producers,X1))
    | subpopulations(first_movers,efficient_producers,X1,sk1(sk3(X1),X1))
    | ~ stable(X1)
    | ~ environment(X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,hypothesis,
    ( greater_or_equal(sk1(sk3(X1),X1),sk3(X1))
    | greater(sk2(X1),appear(efficient_producers,X1))
    | ~ stable(X1)
    | ~ environment(X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_19,hypothesis,
    ( greater(zero,growth_rate(first_movers,sk1(sk3(X1),X1)))
    | greater(sk2(X1),appear(efficient_producers,X1))
    | ~ stable(X1)
    | ~ environment(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_20,negated_conjecture,
    stable(sk4),
    prove_l10_11 ).

cnf(c_0_21,negated_conjecture,
    environment(sk4),
    prove_l10_10 ).

cnf(c_0_22,axiom,
    ( greater(sk2(X1),appear(efficient_producers,X1))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
    mp_first_movers_negative_growth_5 ).

cnf(c_0_23,negated_conjecture,
    ( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_24,negated_conjecture,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ in_environment(sk4,sk3(sk4)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]),c_0_21])]) ).

cnf(c_0_25,negated_conjecture,
    ( subpopulations(first_movers,efficient_producers,sk4,sk5(X1))
    | ~ greater(X1,appear(efficient_producers,sk4)) ),
    prove_l10_12 ).

cnf(c_0_26,hypothesis,
    greater(sk2(sk4),appear(efficient_producers,sk4)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_14]),c_0_20]),c_0_21])]) ).

cnf(c_0_27,negated_conjecture,
    ( ~ greater(X1,appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk5(X1))) ),
    prove_l10_14 ).

cnf(c_0_28,negated_conjecture,
    ( greater_or_equal(sk5(X1),X1)
    | ~ greater(X1,appear(efficient_producers,sk4)) ),
    prove_l10_13 ).

cnf(c_0_29,axiom,
    ( subpopulations(first_movers,efficient_producers,X1,sk1(X2,X1))
    | greater(zero,growth_rate(first_movers,X3))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ subpopulations(first_movers,efficient_producers,X1,X3)
    | ~ greater_or_equal(X3,sk2(X1)) ),
    mp_first_movers_negative_growth_3 ).

cnf(c_0_30,negated_conjecture,
    subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,negated_conjecture,
    ~ greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
    inference(spm,[status(thm)],[c_0_27,c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    greater_or_equal(sk5(sk2(sk4)),sk2(sk4)),
    inference(spm,[status(thm)],[c_0_28,c_0_26]) ).

cnf(c_0_33,axiom,
    ( greater_or_equal(sk1(X2,X1),X2)
    | greater(zero,growth_rate(first_movers,X3))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ subpopulations(first_movers,efficient_producers,X1,X3)
    | ~ greater_or_equal(X3,sk2(X1)) ),
    mp_first_movers_negative_growth_4 ).

cnf(c_0_34,negated_conjecture,
    ( subpopulations(first_movers,efficient_producers,sk4,sk1(X1,sk4))
    | ~ in_environment(sk4,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_20]),c_0_21])]),c_0_31]),c_0_32])]) ).

cnf(c_0_35,negated_conjecture,
    ( greater_or_equal(sk1(X1,sk4),X1)
    | ~ in_environment(sk4,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_20]),c_0_21])]),c_0_31]),c_0_32])]) ).

cnf(c_0_36,axiom,
    ( greater(zero,growth_rate(first_movers,X3))
    | ~ environment(X1)
    | ~ stable(X1)
    | ~ in_environment(X1,X2)
    | ~ greater(zero,growth_rate(first_movers,sk1(X2,X1)))
    | ~ subpopulations(first_movers,efficient_producers,X1,X3)
    | ~ greater_or_equal(X3,sk2(X1)) ),
    mp_first_movers_negative_growth_6 ).

cnf(c_0_37,hypothesis,
    subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_20]),c_0_21])]) ).

cnf(c_0_38,hypothesis,
    greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_14]),c_0_20]),c_0_21])]) ).

cnf(c_0_39,negated_conjecture,
    ( ~ greater(zero,growth_rate(first_movers,sk1(X1,sk4)))
    | ~ in_environment(sk4,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_20]),c_0_21])]),c_0_31]),c_0_32])]) ).

cnf(c_0_40,hypothesis,
    greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_37]),c_0_38]),c_0_20]),c_0_21])]) ).

cnf(c_0_41,negated_conjecture,
    ~ in_environment(sk4,sk3(sk4)),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_42,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_14]),c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : MGT028-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 06:53:39 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.62  start to proof: theBenchmark
% 0.19/0.64  % Version  : CSE_E---1.5
% 0.19/0.64  % Problem  : theBenchmark.p
% 0.19/0.64  % Proof found
% 0.19/0.64  % SZS status Theorem for theBenchmark.p
% 0.19/0.64  % SZS output start Proof
% See solution above
% 0.19/0.64  % Total time : 0.007000 s
% 0.19/0.64  % SZS output end Proof
% 0.19/0.64  % Total time : 0.010000 s
%------------------------------------------------------------------------------