TSTP Solution File: MGT028-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n019.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  : 600s
% DateTime : Sun Jul 17 22:24:47 EDT 2022

% Result   : Unsatisfiable 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   25 (  11 unt;   7 nHn;  25 RR)
%            Number of literals    :   67 (   0 equ;  38 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(mp_first_movers_negative_growth_1,axiom,
    ( ~ environment(X)
    | ~ stable(X)
    | ~ in_environment(X,Y)
    | subpopulations(first_movers,efficient_producers,X,sk1(Y,X))
    | greater(sk2(X),appear(efficient_producers,X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).

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

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

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

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

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

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

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

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

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

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

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

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

cnf(15,plain,
    in_environment(sk4,sk3(sk4)),
    inference('HYPERRESOLVE',[status(thm)],[l11_7,prove_l10_10,prove_l10_11]) ).

cnf(16,plain,
    ( greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference('HYPERRESOLVE',[status(thm)],[mp_first_movers_negative_growth_2,15,prove_l10_10,prove_l10_11]) ).

cnf(17,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference('HYPERRESOLVE',[status(thm)],[mp_first_movers_negative_growth_1,15,prove_l10_10,prove_l10_11]) ).

cnf(18,plain,
    ( greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference('HYPERRESOLVE',[status(thm)],[l11_9,17,prove_l10_10,prove_l10_11,16]) ).

cnf(20,plain,
    greater(sk2(sk4),appear(efficient_producers,sk4)),
    inference('HYPERRESOLVE',[status(thm)],[mp_first_movers_negative_growth_5,18,prove_l10_10,prove_l10_11,15]) ).

cnf(21,plain,
    greater_or_equal(sk5(sk2(sk4)),sk2(sk4)),
    inference('HYPERRESOLVE',[status(thm)],[prove_l10_13,20]) ).

cnf(22,plain,
    subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))),
    inference('HYPERRESOLVE',[status(thm)],[prove_l10_12,20]) ).

cnf(23,plain,
    ~ greater(zero,growth_rate(first_movers,sk5(sk2(sk4)))),
    inference('UR-RESOLVE',[status(thm)],[prove_l10_14,20]) ).

cnf(24,plain,
    greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[mp_first_movers_negative_growth_4,22,prove_l10_10,prove_l10_11,15,21]),23]) ).

cnf(25,plain,
    subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[mp_first_movers_negative_growth_3,22,prove_l10_10,prove_l10_11,15,21]),23]) ).

cnf(27,plain,
    ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))),
    inference('UR-RESOLVE',[status(thm)],[mp_first_movers_negative_growth_6,23,prove_l10_10,prove_l10_11,15,22,21]) ).

cnf(28,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[l11_9,25,prove_l10_10,prove_l10_11,24]),27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n019.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  : 600
% 0.12/0.34  % DateTime : Thu Jun  9 10:58:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 0.19/0.47  #<PACKAGE "SNARK-USER">
% 0.19/0.47  * 
% 0.19/0.47  SNARK-TPTP-OPTIONS
% 0.19/0.47  * 
% 0.19/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47   (USE-FACTORING :POS)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47  * 
% 0.19/0.47  "."
% 0.19/0.47  * 
% 0.19/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-09T10:58:55
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-06-09T10:58:55
% 0.19/0.51  
% 0.19/0.51  
% 0.19/0.51  #||
% 0.19/0.51  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51  % SZS output start Refutation
% See solution above
% 0.19/0.51  ||#
% 0.19/0.51  
% 0.19/0.51  ; Summary of computation:
% 0.19/0.51  ;        36 formulas have been input or derived (from 26 formulas).
% 0.19/0.51  ;        28 (78%) were retained.  Of these,
% 0.19/0.51  ;            4 (14%) were simplified or subsumed later,
% 0.19/0.51  ;           24 (86%) are still being kept.
% 0.19/0.51  ; 
% 0.19/0.51  ; Run time in seconds excluding printing time:
% 0.19/0.51  ;     0.004  11%   Read assertion file          (1 call)
% 0.19/0.51  ;     0.001   3%   Assert                       (14 calls)
% 0.19/0.51  ;     0.003   8%   Process new row              (30 calls)
% 0.19/0.51  ;     0.002   6%   Resolution                   (50 calls)
% 0.19/0.51  ;     0.000   0%   Paramodulation               (25 calls)
% 0.19/0.51  ;     0.000   0%   Factoring                    (3 calls)
% 0.19/0.51  ;     0.000   0%   Condensing                   (16 calls)
% 0.19/0.51  ;     0.000   0%   Forward subsumption          (16 calls)
% 0.19/0.51  ;     0.000   0%   Backward subsumption         (16 calls)
% 0.19/0.51  ;     0.001   3%   Forward simplification       (30 calls)
% 0.19/0.51  ;     0.001   3%   Backward simplification      (28 calls)
% 0.19/0.51  ;     0.001   3%   Ordering                     (4 calls)
% 0.19/0.51  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.19/0.51  ;     0.000   0%   Purity testing               (1 call)
% 0.19/0.51  ;     0.023  64%   Other
% 0.19/0.51  ;     0.036        Total
% 0.19/0.51  ;     0.041        Real time
% 0.19/0.51  ; 
% 0.19/0.51  ; Term-hash-array has 49 terms in all.
% 0.19/0.51  ; Feature-vector-row-index has 12 entries (16 at peak, 16 added, 4 deleted).
% 0.19/0.51  ; Feature-vector-row-index has 119 nodes (173 at peak, 173 added, 54 deleted).
% 0.19/0.51  ;  Retrieved 0 possibly forward subsuming rows in 16 calls.
% 0.19/0.51  ;  Retrieved 0 possibly backward subsumed rows in 16 calls.
% 0.19/0.51  ; Path-index has 51 entries (51 at peak, 58 added, 7 deleted).
% 0.19/0.51  ; Path-index has 148 nodes (148 at peak, 161 added, 13 deleted).
% 0.19/0.51  ; Trie-index has 51 entries (51 at peak, 58 added, 7 deleted).
% 0.19/0.52  ; Trie-index has 127 nodes (127 at peak, 154 added, 27 deleted).
% 0.19/0.52  ; Retrieved 5 generalization terms in 10 calls.
% 0.19/0.52  ; Retrieved 11 instance terms in 11 calls.
% 0.19/0.52  ; Retrieved 690 unifiable terms in 563 calls.
% 0.19/0.52  ; 
% 0.19/0.52  ; The agenda of rows to process has 3 entries:
% 0.19/0.52  ;     3 with value 19
% 0.19/0.52  ; The agenda of rows to give has 1 entry:
% 0.19/0.52  ;     1 with value (4 18)
% 0.19/0.52  Evaluation took:
% 0.19/0.52    0.041 seconds of real time
% 0.19/0.52    0.034707 seconds of user run time
% 0.19/0.52    0.005942 seconds of system run time
% 0.19/0.52    0 calls to %EVAL
% 0.19/0.52    0 page faults and
% 0.19/0.52    3,979,728 bytes consed.
% 0.19/0.52  :PROOF-FOUND
% 0.19/0.52  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-09T10:58:55
% 0.19/0.52  :PROOF-FOUND
% 0.19/0.52  * 
%------------------------------------------------------------------------------