TSTP Solution File: MGT028-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n010.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 : Wed Jul 27 13:06:04 EDT 2022

% Result   : Unsatisfiable 1.69s 1.89s
% Output   : Refutation 1.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   28 (   9 unt;  12 nHn;  28 RR)
%            Number of literals    :   75 (   0 equ;  36 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            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   :   21 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | ~ in_environment(A,B)
    | subpopulations(first_movers,efficient_producers,A,sk1(B,A))
    | greater(sk2(A),appear(efficient_producers,A)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | ~ in_environment(A,B)
    | greater_or_e_qual(sk1(B,A),B)
    | greater(sk2(A),appear(efficient_producers,A)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | ~ in_environment(A,B)
    | subpopulations(first_movers,efficient_producers,A,sk1(B,A))
    | ~ subpopulations(first_movers,efficient_producers,A,C)
    | ~ greater_or_e_qual(C,sk2(A))
    | greater(zero,growth_rate(first_movers,C)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | ~ in_environment(A,B)
    | greater_or_e_qual(sk1(B,A),B)
    | ~ subpopulations(first_movers,efficient_producers,A,C)
    | ~ greater_or_e_qual(C,sk2(A))
    | greater(zero,growth_rate(first_movers,C)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | ~ in_environment(A,B)
    | ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
    | greater(sk2(A),appear(efficient_producers,A)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | ~ in_environment(A,B)
    | ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
    | ~ subpopulations(first_movers,efficient_producers,A,C)
    | ~ greater_or_e_qual(C,sk2(A))
    | greater(zero,growth_rate(first_movers,C)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | in_environment(A,sk3(A)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ environment(A)
    | ~ stable(A)
    | ~ subpopulations(first_movers,efficient_producers,A,B)
    | ~ greater_or_e_qual(B,sk3(A))
    | greater(zero,growth_rate(first_movers,B)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ greater(A,appear(efficient_producers,sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk5(A)) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ greater(A,appear(efficient_producers,sk4))
    | greater_or_e_qual(sk5(A),A) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ greater(A,appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk5(A))) ),
    file('MGT028-1.p',unknown),
    [] ).

cnf(13,axiom,
    environment(sk4),
    file('MGT028-1.p',unknown),
    [] ).

cnf(14,axiom,
    stable(sk4),
    file('MGT028-1.p',unknown),
    [] ).

cnf(15,plain,
    in_environment(sk4,sk3(sk4)),
    inference(hyper,[status(thm)],[14,7,13]),
    [iquote('hyper,14,7,13')] ).

cnf(16,plain,
    ( greater_or_e_qual(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(hyper,[status(thm)],[15,2,13,14]),
    [iquote('hyper,15,2,13,14')] ).

cnf(17,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(hyper,[status(thm)],[15,1,13,14]),
    [iquote('hyper,15,1,13,14')] ).

cnf(18,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater_or_e_qual(sk5(sk2(sk4)),sk2(sk4)) ),
    inference(hyper,[status(thm)],[17,11]),
    [iquote('hyper,17,11')] ).

cnf(19,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
    inference(hyper,[status(thm)],[17,10]),
    [iquote('hyper,17,10')] ).

cnf(23,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
    inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[19,3,13,14,15,18])])]),
    [iquote('hyper,19,3,13,14,15,18,factor_simp,factor_simp')] ).

cnf(24,plain,
    subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[23,12,17])]),
    [iquote('hyper,23,12,17,factor_simp')] ).

cnf(25,plain,
    ( greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(hyper,[status(thm)],[24,9,13,14,16]),
    [iquote('hyper,24,9,13,14,16')] ).

cnf(27,plain,
    greater(sk2(sk4),appear(efficient_producers,sk4)),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[25,5,13,14,15])]),
    [iquote('hyper,25,5,13,14,15,factor_simp')] ).

cnf(30,plain,
    greater_or_e_qual(sk5(sk2(sk4)),sk2(sk4)),
    inference(hyper,[status(thm)],[27,11]),
    [iquote('hyper,27,11')] ).

cnf(31,plain,
    subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
    inference(hyper,[status(thm)],[27,10]),
    [iquote('hyper,27,10')] ).

cnf(32,plain,
    ( greater_or_e_qual(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))) ),
    inference(hyper,[status(thm)],[31,4,13,14,15,30]),
    [iquote('hyper,31,4,13,14,15,30')] ).

cnf(33,plain,
    ( greater(zero,growth_rate(first_movers,sk5(sk2(sk4))))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(hyper,[status(thm)],[32,9,13,14,24]),
    [iquote('hyper,32,9,13,14,24')] ).

cnf(36,plain,
    greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[33,6,13,14,15,31,30])]),
    [iquote('hyper,33,6,13,14,15,31,30,factor_simp')] ).

cnf(37,plain,
    $false,
    inference(hyper,[status(thm)],[36,12,27]),
    [iquote('hyper,36,12,27')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 03:54:39 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.69/1.89  ----- Otter 3.3f, August 2004 -----
% 1.69/1.89  The process was started by sandbox on n010.cluster.edu,
% 1.69/1.89  Wed Jul 27 03:54:40 2022
% 1.69/1.89  The command was "./otter".  The process ID is 22900.
% 1.69/1.89  
% 1.69/1.89  set(prolog_style_variables).
% 1.69/1.89  set(auto).
% 1.69/1.89     dependent: set(auto1).
% 1.69/1.89     dependent: set(process_input).
% 1.69/1.89     dependent: clear(print_kept).
% 1.69/1.89     dependent: clear(print_new_demod).
% 1.69/1.89     dependent: clear(print_back_demod).
% 1.69/1.89     dependent: clear(print_back_sub).
% 1.69/1.89     dependent: set(control_memory).
% 1.69/1.89     dependent: assign(max_mem, 12000).
% 1.69/1.89     dependent: assign(pick_given_ratio, 4).
% 1.69/1.89     dependent: assign(stats_level, 1).
% 1.69/1.89     dependent: assign(max_seconds, 10800).
% 1.69/1.89  clear(print_given).
% 1.69/1.89  
% 1.69/1.89  list(usable).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89  0 [] -environment(A)| -stable(A)|in_environment(A,sk3(A)).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(growth_rate(efficient_producers,B),zero).
% 1.69/1.89  0 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(zero,growth_rate(first_movers,B)).
% 1.69/1.89  0 [] environment(sk4).
% 1.69/1.89  0 [] stable(sk4).
% 1.69/1.89  0 [] -greater(A,appear(efficient_producers,sk4))|subpopulations(first_movers,efficient_producers,sk4,sk5(A)).
% 1.69/1.89  0 [] -greater(A,appear(efficient_producers,sk4))|greater_or_e_qual(sk5(A),A).
% 1.69/1.89  0 [] -greater(A,appear(efficient_producers,sk4))| -greater(zero,growth_rate(first_movers,sk5(A))).
% 1.69/1.89  end_of_list.
% 1.69/1.89  
% 1.69/1.89  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=7.
% 1.69/1.89  
% 1.69/1.89  This is a non-Horn set without equality.  The strategy will
% 1.69/1.89  be ordered hyper_res, unit deletion, and factoring, with
% 1.69/1.89  satellites in sos and with nuclei in usable.
% 1.69/1.89  
% 1.69/1.89     dependent: set(hyper_res).
% 1.69/1.89     dependent: set(factor).
% 1.69/1.89     dependent: set(unit_deletion).
% 1.69/1.89  
% 1.69/1.89  ------------> process usable:
% 1.69/1.89  ** KEPT (pick-wt=20): 1 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89  ** KEPT (pick-wt=18): 2 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89  ** KEPT (pick-wt=28): 3 [] -environment(A)| -stable(A)| -in_environment(A,B)|subpopulations(first_movers,efficient_producers,A,sk1(B,A))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89  ** KEPT (pick-wt=26): 4 [] -environment(A)| -stable(A)| -in_environment(A,B)|greater_or_e_qual(sk1(B,A),B)| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89  ** KEPT (pick-wt=20): 5 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))|greater(sk2(A),appear(efficient_producers,A)).
% 1.69/1.89  ** KEPT (pick-wt=28): 6 [] -environment(A)| -stable(A)| -in_environment(A,B)| -greater(zero,growth_rate(first_movers,sk1(B,A)))| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(C,sk2(A))|greater(zero,growth_rate(first_movers,C)).
% 1.69/1.89  ** KEPT (pick-wt=8): 7 [] -environment(A)| -stable(A)|in_environment(A,sk3(A)).
% 1.69/1.89  ** KEPT (pick-wt=18): 8 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(growth_rate(efficient_producers,B),zero).
% 1.69/1.89  ** KEPT (pick-wt=18): 9 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,sk3(A))|greater(zero,growth_rate(first_movers,B)).
% 1.69/1.89  ** KEPT (pick-wt=11): 10 [] -greater(A,appear(efficient_producers,sk4))|subpopulations(first_movers,efficient_producers,sk4,sk5(A)).
% 1.69/1.89  ** KEPT (pick-wt=9): 11 [] -greater(A,appear(efficient_producers,sk4))|greater_or_e_qual(sk5(A),A).
% 1.69/1.89  ** KEPT (pick-wt=11): 12 [] -greater(A,appear(efficient_producers,sk4))| -greater(zero,growth_rate(first_movers,sk5(A))).
% 1.69/1.89  
% 1.69/1.89  ------------> process sos:
% 1.69/1.89  ** KEPT (pick-wt=2): 13 [] environment(sk4).
% 1.69/1.89  ** KEPT (pick-wt=2): 14 [] stable(sk4).
% 1.69/1.89  
% 1.69/1.89  ======= end of input processing =======
% 1.69/1.89  
% 1.69/1.89  =========== start of search ===========
% 1.69/1.89  
% 1.69/1.89  -------- PROOF -------- 
% 1.69/1.89  
% 1.69/1.89  -----> EMPTY CLAUSE at   0.00 sec ----> 37 [hyper,36,12,27] $F.
% 1.69/1.89  
% 1.69/1.89  Length of proof is 14.  Level of proof is 11.
% 1.69/1.89  
% 1.69/1.89  ---------------- PROOF ----------------
% 1.69/1.89  % SZS status Unsatisfiable
% 1.69/1.89  % SZS output start Refutation
% See solution above
% 1.69/1.89  ------------ end of proof -------------
% 1.69/1.89  
% 1.69/1.89  
% 1.69/1.89  Search stopped by max_proofs option.
% 1.69/1.89  
% 1.69/1.89  
% 1.69/1.89  Search stopped by max_proofs option.
% 1.69/1.89  
% 1.69/1.89  ============ end of search ============
% 1.69/1.89  
% 1.69/1.89  -------------- statistics -------------
% 1.69/1.89  clauses given                 17
% 1.69/1.89  clauses generated             27
% 1.69/1.89  clauses kept                  36
% 1.69/1.89  clauses forward subsumed       4
% 1.69/1.89  clauses back subsumed         15
% 1.69/1.89  Kbytes malloced              976
% 1.69/1.89  
% 1.69/1.89  ----------- times (seconds) -----------
% 1.69/1.89  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.69/1.89  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.69/1.89  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.69/1.89  
% 1.69/1.89  That finishes the proof of the theorem.
% 1.69/1.89  
% 1.69/1.89  Process 22900 finished Wed Jul 27 03:54:41 2022
% 1.69/1.89  Otter interrupted
% 1.69/1.89  PROOF FOUND
%------------------------------------------------------------------------------