↑ Up

FindProof---0.1.THM-Prf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : MGT039+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:11:46 PM UTC 2026

% Result   : Theorem 16.92s 3.37s
% Output   : Proof 16.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   97 (  24 unt;   0 def)
%            Number of atoms       :  269 (  14 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  288 ( 116   ~; 131   |;  29   &)
%                                         (   1 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   85 (   0 sgn  48   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f0,axiom,
    ! [P] :
      ( ( ! [E] :
            ( ( in_environment(P,E)
              & environment(E) )
           => selection_favors(efficient_producers,first_movers,end_time(E)) )
        & propagation_strategy(efficient_producers)
        & propagation_strategy(first_movers)
        & observational_period(P) )
     => selection_favors(efficient_producers,first_movers,P) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy) ).

fof(f0_nnf,plain,
    ! [P] :
      ( selection_favors(efficient_producers,first_movers,P)
      | ? [E] :
          ( ~ selection_favors(efficient_producers,first_movers,end_time(E))
          & in_environment(P,E)
          & environment(E) )
      | ~ propagation_strategy(efficient_producers)
      | ~ propagation_strategy(first_movers)
      | ~ observational_period(P) ),
    inference(nnf_transformation,[status(thm)],[f0]) ).

fof(f0_sk,plain,
    ! [P] :
      ( selection_favors(efficient_producers,first_movers,P)
      | ( ~ selection_favors(efficient_producers,first_movers,end_time(sk0(P)))
        & in_environment(P,sk0(P))
        & environment(sk0(P)) )
      | ~ propagation_strategy(efficient_producers)
      | ~ propagation_strategy(first_movers)
      | ~ observational_period(P) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).

cnf(c2,plain,
    ( selection_favors(efficient_producers,first_movers,X0)
    | ~ selection_favors(efficient_producers,first_movers,end_time(sk0(X0)))
    | ~ propagation_strategy(efficient_producers)
    | ~ propagation_strategy(first_movers)
    | ~ observational_period(X0) ),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

fof(f11,conjecture,
    ! [P] :
      ( ( slow_change(P)
        & observational_period(P) )
     => selection_favors(efficient_producers,first_movers,P) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8) ).

fof(f11_neg,negated_conjecture,
    ~ ! [P] :
        ( ( slow_change(P)
          & observational_period(P) )
       => selection_favors(efficient_producers,first_movers,P) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f11_nnf,plain,
    ? [P] :
      ( ~ selection_favors(efficient_producers,first_movers,P)
      & slow_change(P)
      & observational_period(P) ),
    inference(nnf_transformation,[status(thm)],[f11_neg]) ).

fof(f11_sk,plain,
    ( ~ selection_favors(efficient_producers,first_movers,sk2)
    & slow_change(sk2)
    & observational_period(sk2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f11_nnf]) ).

cnf(c16,plain,
    observational_period(sk2),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(p117,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | ~ selection_favors(efficient_producers,first_movers,end_time(sk0(sk2)))
    | ~ propagation_strategy(efficient_producers)
    | ~ propagation_strategy(first_movers) ),
    inference(resolution,[status(thm)],[c2,c16]) ).

fof(f2,axiom,
    propagation_strategy(first_movers),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets1) ).

fof(f2_nnf,plain,
    propagation_strategy(first_movers),
    inference(nnf_transformation,[status(thm)],[f2]) ).

cnf(c5,plain,
    propagation_strategy(first_movers),
    inference(cnf_transformation,[status(esa)],[f2_nnf]) ).

cnf(p118,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | ~ selection_favors(efficient_producers,first_movers,end_time(sk0(sk2)))
    | ~ propagation_strategy(efficient_producers) ),
    inference(resolution,[status(thm)],[p117,c5]) ).

fof(f3,axiom,
    propagation_strategy(efficient_producers),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets2) ).

fof(f3_nnf,plain,
    propagation_strategy(efficient_producers),
    inference(nnf_transformation,[status(thm)],[f3]) ).

cnf(c6,plain,
    propagation_strategy(efficient_producers),
    inference(cnf_transformation,[status(esa)],[f3_nnf]) ).

cnf(p119,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | ~ selection_favors(efficient_producers,first_movers,end_time(sk0(sk2))) ),
    inference(resolution,[status(thm)],[p118,c6]) ).

fof(f1,axiom,
    ! [P] :
      ( ( slow_change(P)
        & observational_period(P) )
     => ! [E] :
          ( ( in_environment(P,E)
            & environment(E) )
         => ? [T] :
              ( greater(T,critical_point(E))
              & in_environment(E,T) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point) ).

fof(f1_nnf,plain,
    ! [P] :
      ( ! [E] :
          ( ? [T] :
              ( greater(T,critical_point(E))
              & in_environment(E,T) )
          | ~ in_environment(P,E)
          | ~ environment(E) )
      | ~ slow_change(P)
      | ~ observational_period(P) ),
    inference(nnf_transformation,[status(thm)],[f1]) ).

fof(f1_sk,plain,
    ! [P,E] :
      ( ( greater(sk1(P,E),critical_point(E))
        & in_environment(E,sk1(P,E)) )
      | ~ in_environment(P,E)
      | ~ environment(E)
      | ~ slow_change(P)
      | ~ observational_period(P) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).

cnf(c4,plain,
    ( greater(sk1(X0,X1),critical_point(X1))
    | ~ in_environment(X0,X1)
    | ~ environment(X1)
    | ~ slow_change(X0)
    | ~ observational_period(X0) ),
    inference(cnf_transformation,[status(esa)],[f1_sk]) ).

cnf(p63,plain,
    ( greater(sk1(sk2,X0),critical_point(X0))
    | ~ in_environment(sk2,X0)
    | ~ environment(X0)
    | ~ slow_change(sk2) ),
    inference(resolution,[status(thm)],[c4,c16]) ).

cnf(c17,plain,
    slow_change(sk2),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(p64,plain,
    ( greater(sk1(sk2,X0),critical_point(X0))
    | ~ in_environment(sk2,X0)
    | ~ environment(X0) ),
    inference(resolution,[status(thm)],[p63,c17]) ).

cnf(c0,plain,
    ( selection_favors(efficient_producers,first_movers,X0)
    | environment(sk0(X0))
    | ~ propagation_strategy(efficient_producers)
    | ~ propagation_strategy(first_movers)
    | ~ observational_period(X0) ),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

cnf(p20,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | environment(sk0(sk2))
    | ~ propagation_strategy(efficient_producers)
    | ~ propagation_strategy(first_movers) ),
    inference(resolution,[status(thm)],[c0,c16]) ).

cnf(p21,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | environment(sk0(sk2))
    | ~ propagation_strategy(efficient_producers) ),
    inference(resolution,[status(thm)],[p20,c5]) ).

cnf(p22,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | environment(sk0(sk2)) ),
    inference(resolution,[status(thm)],[p21,c6]) ).

cnf(c18,plain,
    ~ selection_favors(efficient_producers,first_movers,sk2),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(p23,plain,
    environment(sk0(sk2)),
    inference(resolution,[status(thm)],[p22,c18]) ).

cnf(p65,plain,
    ( greater(sk1(sk2,sk0(sk2)),critical_point(sk0(sk2)))
    | ~ in_environment(sk2,sk0(sk2)) ),
    inference(resolution,[status(thm)],[p64,p23]) ).

cnf(c1,plain,
    ( selection_favors(efficient_producers,first_movers,X0)
    | in_environment(X0,sk0(X0))
    | ~ propagation_strategy(efficient_producers)
    | ~ propagation_strategy(first_movers)
    | ~ observational_period(X0) ),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

cnf(p40,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | in_environment(sk2,sk0(sk2))
    | ~ propagation_strategy(efficient_producers)
    | ~ propagation_strategy(first_movers) ),
    inference(resolution,[status(thm)],[c1,c16]) ).

cnf(p41,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | in_environment(sk2,sk0(sk2))
    | ~ propagation_strategy(efficient_producers) ),
    inference(resolution,[status(thm)],[p40,c5]) ).

cnf(p42,plain,
    ( selection_favors(efficient_producers,first_movers,sk2)
    | in_environment(sk2,sk0(sk2)) ),
    inference(resolution,[status(thm)],[p41,c6]) ).

cnf(p43,plain,
    in_environment(sk2,sk0(sk2)),
    inference(resolution,[status(thm)],[p42,c18]) ).

cnf(p66,plain,
    greater(sk1(sk2,sk0(sk2)),critical_point(sk0(sk2))),
    inference(resolution,[status(thm)],[p65,p43]) ).

cnf(c3,plain,
    ( in_environment(X1,sk1(X0,X1))
    | ~ in_environment(X0,X1)
    | ~ environment(X1)
    | ~ slow_change(X0)
    | ~ observational_period(X0) ),
    inference(cnf_transformation,[status(esa)],[f1_sk]) ).

cnf(p44,plain,
    ( in_environment(X0,sk1(sk2,X0))
    | ~ in_environment(sk2,X0)
    | ~ environment(X0)
    | ~ slow_change(sk2) ),
    inference(resolution,[status(thm)],[c3,c16]) ).

cnf(p45,plain,
    ( in_environment(X0,sk1(sk2,X0))
    | ~ in_environment(sk2,X0)
    | ~ environment(X0) ),
    inference(resolution,[status(thm)],[p44,c17]) ).

cnf(p46,plain,
    ( in_environment(sk0(sk2),sk1(sk2,sk0(sk2)))
    | ~ in_environment(sk2,sk0(sk2)) ),
    inference(resolution,[status(thm)],[p45,p23]) ).

cnf(p47,plain,
    in_environment(sk0(sk2),sk1(sk2,sk0(sk2))),
    inference(resolution,[status(thm)],[p46,p43]) ).

fof(f5,axiom,
    ! [E,T] :
      ( ( in_environment(E,T)
        & environment(E) )
     => greater_or_equal(end_time(E),T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_end_point) ).

fof(f5_nnf,plain,
    ! [E,T] :
      ( greater_or_equal(end_time(E),T)
      | ~ in_environment(E,T)
      | ~ environment(E) ),
    inference(nnf_transformation,[status(thm)],[f5]) ).

fof(f5_sk,plain,
    ! [E,T] :
      ( greater_or_equal(end_time(E),T)
      | ~ in_environment(E,T)
      | ~ environment(E) ),
    inference(skolemisation,[status(esa)],[f5_nnf]) ).

cnf(c8,plain,
    ( greater_or_equal(end_time(X0),X1)
    | ~ in_environment(X0,X1)
    | ~ environment(X0) ),
    inference(cnf_transformation,[status(esa)],[f5_sk]) ).

cnf(p25,plain,
    ( greater_or_equal(end_time(sk0(sk2)),X0)
    | ~ in_environment(sk0(sk2),X0) ),
    inference(resolution,[status(thm)],[p23,c8]) ).

cnf(p48,plain,
    greater_or_equal(end_time(sk0(sk2)),sk1(sk2,sk0(sk2))),
    inference(resolution,[status(thm)],[p47,p25]) ).

fof(f8,axiom,
    ! [X,Y] :
      ( greater_or_equal(X,Y)
    <=> ( X = Y
        | greater(X,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).

fof(f8_nnf,plain,
    ! [X,Y] :
      ( ( ( X != Y
          & ~ greater(X,Y) )
        | greater_or_equal(X,Y) )
      & ( X = Y
        | greater(X,Y)
        | ~ greater_or_equal(X,Y) ) ),
    inference(nnf_transformation,[status(thm)],[f8]) ).

fof(f8_sk,plain,
    ! [X,Y] :
      ( ( ( X != Y
          & ~ greater(X,Y) )
        | greater_or_equal(X,Y) )
      & ( X = Y
        | greater(X,Y)
        | ~ greater_or_equal(X,Y) ) ),
    inference(skolemisation,[status(esa)],[f8_nnf]) ).

cnf(c11,plain,
    ( X0 = X1
    | greater(X0,X1)
    | ~ greater_or_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(p50,plain,
    ( end_time(sk0(sk2)) = sk1(sk2,sk0(sk2))
    | greater(end_time(sk0(sk2)),sk1(sk2,sk0(sk2))) ),
    inference(resolution,[status(thm)],[p48,c11]) ).

fof(f7,axiom,
    ! [X,Y,Z] :
      ( ( greater(Y,Z)
        & greater(X,Y) )
     => greater(X,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).

fof(f7_nnf,plain,
    ! [X,Y,Z] :
      ( greater(X,Z)
      | ~ greater(Y,Z)
      | ~ greater(X,Y) ),
    inference(nnf_transformation,[status(thm)],[f7]) ).

fof(f7_sk,plain,
    ! [X,Y,Z] :
      ( greater(X,Z)
      | ~ greater(Y,Z)
      | ~ greater(X,Y) ),
    inference(skolemisation,[status(esa)],[f7_nnf]) ).

cnf(c10,plain,
    ( greater(X0,X2)
    | ~ greater(X1,X2)
    | ~ greater(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

cnf(p51,plain,
    ( greater(end_time(sk0(sk2)),X0)
    | ~ greater(sk1(sk2,sk0(sk2)),X0)
    | end_time(sk0(sk2)) = sk1(sk2,sk0(sk2)) ),
    inference(resolution,[status(thm)],[p50,c10]) ).

cnf(p70,plain,
    ( greater(end_time(sk0(sk2)),critical_point(sk0(sk2)))
    | end_time(sk0(sk2)) = sk1(sk2,sk0(sk2)) ),
    inference(resolution,[status(thm)],[p66,p51]) ).

cnf(p79,plain,
    ( greater(end_time(sk0(sk2)),critical_point(sk0(sk2)))
    | greater(end_time(sk0(sk2)),critical_point(sk0(sk2))) ),
    inference(superposition,[status(thm)],[p70,p66]) ).

cnf(p91,plain,
    greater(end_time(sk0(sk2)),critical_point(sk0(sk2))),
    inference(factoring,[status(thm)],[p79]) ).

cnf(p93,plain,
    ( greater(end_time(sk0(sk2)),X0)
    | ~ greater(critical_point(sk0(sk2)),X0) ),
    inference(resolution,[status(thm)],[p91,c10]) ).

fof(f6,axiom,
    ! [E] :
      ( environment(E)
     => greater_or_equal(critical_point(E),start_time(E)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_of_critical_point) ).

fof(f6_nnf,plain,
    ! [E] :
      ( greater_or_equal(critical_point(E),start_time(E))
      | ~ environment(E) ),
    inference(nnf_transformation,[status(thm)],[f6]) ).

fof(f6_sk,plain,
    ! [E] :
      ( greater_or_equal(critical_point(E),start_time(E))
      | ~ environment(E) ),
    inference(skolemisation,[status(esa)],[f6_nnf]) ).

cnf(c9,plain,
    ( greater_or_equal(critical_point(X0),start_time(X0))
    | ~ environment(X0) ),
    inference(cnf_transformation,[status(esa)],[f6_sk]) ).

cnf(p24,plain,
    greater_or_equal(critical_point(sk0(sk2)),start_time(sk0(sk2))),
    inference(resolution,[status(thm)],[p23,c9]) ).

cnf(p28,plain,
    ( critical_point(sk0(sk2)) = start_time(sk0(sk2))
    | greater(critical_point(sk0(sk2)),start_time(sk0(sk2))) ),
    inference(resolution,[status(thm)],[p24,c11]) ).

cnf(p97,plain,
    ( critical_point(sk0(sk2)) = start_time(sk0(sk2))
    | greater(end_time(sk0(sk2)),start_time(sk0(sk2))) ),
    inference(resolution,[status(thm)],[p93,p28]) ).

cnf(c12,plain,
    ( ~ greater(X0,X1)
    | greater_or_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(p98,plain,
    ( greater_or_equal(end_time(sk0(sk2)),start_time(sk0(sk2)))
    | critical_point(sk0(sk2)) = start_time(sk0(sk2)) ),
    inference(resolution,[status(thm)],[p97,c12]) ).

fof(f4,axiom,
    ! [E,T] :
      ( ( greater_or_equal(end_time(E),T)
        & greater_or_equal(T,start_time(E))
        & environment(E) )
     => in_environment(E,T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_in_environment) ).

fof(f4_nnf,plain,
    ! [E,T] :
      ( in_environment(E,T)
      | ~ greater_or_equal(end_time(E),T)
      | ~ greater_or_equal(T,start_time(E))
      | ~ environment(E) ),
    inference(nnf_transformation,[status(thm)],[f4]) ).

fof(f4_sk,plain,
    ! [E,T] :
      ( in_environment(E,T)
      | ~ greater_or_equal(end_time(E),T)
      | ~ greater_or_equal(T,start_time(E))
      | ~ environment(E) ),
    inference(skolemisation,[status(esa)],[f4_nnf]) ).

cnf(c7,plain,
    ( in_environment(X0,X1)
    | ~ greater_or_equal(end_time(X0),X1)
    | ~ greater_or_equal(X1,start_time(X0))
    | ~ environment(X0) ),
    inference(cnf_transformation,[status(esa)],[f4_sk]) ).

cnf(p26,plain,
    ( in_environment(sk0(sk2),X0)
    | ~ greater_or_equal(end_time(sk0(sk2)),X0)
    | ~ greater_or_equal(X0,start_time(sk0(sk2))) ),
    inference(resolution,[status(thm)],[p23,c7]) ).

cnf(c13,plain,
    ( X0 != X1
    | greater_or_equal(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(p19,plain,
    greater_or_equal(X0,X0),
    inference(equality_resolution,[status(thm)],[c13]) ).

cnf(p30,plain,
    ( in_environment(sk0(sk2),start_time(sk0(sk2)))
    | ~ greater_or_equal(end_time(sk0(sk2)),start_time(sk0(sk2))) ),
    inference(resolution,[status(thm)],[p26,p19]) ).

cnf(p101,plain,
    ( in_environment(sk0(sk2),start_time(sk0(sk2)))
    | critical_point(sk0(sk2)) = start_time(sk0(sk2)) ),
    inference(resolution,[status(thm)],[p98,p30]) ).

cnf(p103,plain,
    ( in_environment(sk0(sk2),start_time(sk0(sk2)))
    | ~ greater_or_equal(end_time(sk0(sk2)),critical_point(sk0(sk2)))
    | in_environment(sk0(sk2),start_time(sk0(sk2))) ),
    inference(superposition,[status(thm)],[p101,p30]) ).

cnf(p107,plain,
    ( ~ greater_or_equal(end_time(sk0(sk2)),critical_point(sk0(sk2)))
    | in_environment(sk0(sk2),start_time(sk0(sk2))) ),
    inference(factoring,[status(thm)],[p103]) ).

cnf(p92,plain,
    greater_or_equal(end_time(sk0(sk2)),critical_point(sk0(sk2))),
    inference(resolution,[status(thm)],[p91,c12]) ).

cnf(p108,plain,
    in_environment(sk0(sk2),start_time(sk0(sk2))),
    inference(resolution,[status(thm)],[p107,p92]) ).

cnf(p109,plain,
    greater_or_equal(end_time(sk0(sk2)),start_time(sk0(sk2))),
    inference(resolution,[status(thm)],[p108,p25]) ).

cnf(p112,plain,
    ( in_environment(sk0(sk2),end_time(sk0(sk2)))
    | ~ greater_or_equal(end_time(sk0(sk2)),end_time(sk0(sk2))) ),
    inference(resolution,[status(thm)],[p109,p26]) ).

cnf(p113,plain,
    in_environment(sk0(sk2),end_time(sk0(sk2))),
    inference(resolution,[status(thm)],[p112,p19]) ).

fof(f10,hypothesis,
    ! [E,T] :
      ( ( greater(T,critical_point(E))
        & in_environment(E,T)
        & environment(E) )
     => selection_favors(efficient_producers,first_movers,T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l8) ).

fof(f10_nnf,plain,
    ! [E,T] :
      ( selection_favors(efficient_producers,first_movers,T)
      | ~ greater(T,critical_point(E))
      | ~ in_environment(E,T)
      | ~ environment(E) ),
    inference(nnf_transformation,[status(thm)],[f10]) ).

fof(f10_sk,plain,
    ! [E,T] :
      ( selection_favors(efficient_producers,first_movers,T)
      | ~ greater(T,critical_point(E))
      | ~ in_environment(E,T)
      | ~ environment(E) ),
    inference(skolemisation,[status(esa)],[f10_nnf]) ).

cnf(c15,plain,
    ( selection_favors(efficient_producers,first_movers,X1)
    | ~ greater(X1,critical_point(X0))
    | ~ in_environment(X0,X1)
    | ~ environment(X0) ),
    inference(cnf_transformation,[status(esa)],[f10_sk]) ).

cnf(p27,plain,
    ( selection_favors(efficient_producers,first_movers,X0)
    | ~ greater(X0,critical_point(sk0(sk2)))
    | ~ in_environment(sk0(sk2),X0) ),
    inference(resolution,[status(thm)],[p23,c15]) ).

cnf(p114,plain,
    ( selection_favors(efficient_producers,first_movers,end_time(sk0(sk2)))
    | ~ greater(end_time(sk0(sk2)),critical_point(sk0(sk2))) ),
    inference(resolution,[status(thm)],[p113,p27]) ).

cnf(p115,plain,
    selection_favors(efficient_producers,first_movers,end_time(sk0(sk2))),
    inference(resolution,[status(thm)],[p114,p91]) ).

cnf(p120,plain,
    selection_favors(efficient_producers,first_movers,sk2),
    inference(resolution,[status(thm)],[p119,p115]) ).

cnf(p121,plain,
    $false,
    inference(resolution,[status(thm)],[p120,c18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : MGT039+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36  % Computer : n002.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Thu Sep 24 01:12:05 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.36  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.92/3.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.92/3.37  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------