TSTP Solution File: MGT028-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : MGT028-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 : Tue May 21 00:41:23 EDT 2024

% Result   : Unsatisfiable 3.12s 1.75s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   45 (   5 unt;  16 typ;   0 def)
%            Number of atoms       :  115 (   0 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  490 (  80   ~;  86   |;   0   &; 324   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  16 usr;   5 con; 0-4 aty)
%            Number of variables   :   46 (   0   ^  46   !;   0   ?;  46   :)

% Comments : 
%------------------------------------------------------------------------------
thf(environment_type,type,
    environment: $i > $o ).

thf(sk4_type,type,
    sk4: $i ).

thf(stable_type,type,
    stable: $i > $o ).

thf(greater_type,type,
    greater: $i > $i > $o ).

thf(appear_type,type,
    appear: $i > $i > $i ).

thf(efficient_producers_type,type,
    efficient_producers: $i ).

thf(subpopulations_type,type,
    subpopulations: $i > $i > $i > $i > $o ).

thf(first_movers_type,type,
    first_movers: $i ).

thf(sk5_type,type,
    sk5: $i > $i ).

thf(greater_or_equal_type,type,
    greater_or_equal: $i > $i > $o ).

thf(zero_type,type,
    zero: $i ).

thf(growth_rate_type,type,
    growth_rate: $i > $i > $i ).

thf(in_environment_type,type,
    in_environment: $i > $i > $o ).

thf(sk1_type,type,
    sk1: $i > $i > $i ).

thf(sk2_type,type,
    sk2: $i > $i ).

thf(sk3_type,type,
    sk3: $i > $i ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
      | ~ ( greater_or_equal @ C @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
      | ~ ( greater_or_equal @ C @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( 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_equal @ C @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( 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_equal @ C @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(2,negated_conjecture,
    stable @ sk4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_11) ).

thf(17,plain,
    stable @ sk4,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( 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_equal @ C @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( 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_equal @ C @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( greater_or_equal @ B @ ( sk3 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_9) ).

thf(39,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( greater_or_equal @ B @ ( sk3 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ( in_environment @ A @ ( sk3 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_7) ).

thf(35,plain,
    ! [A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ( in_environment @ A @ ( sk3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk4 ) )
      | ( subpopulations @ first_movers @ efficient_producers @ sk4 @ ( sk5 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_12) ).

thf(18,plain,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk4 ) )
      | ( subpopulations @ first_movers @ efficient_producers @ sk4 @ ( sk5 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
      | ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,negated_conjecture,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk4 ) )
      | ( greater_or_equal @ ( sk5 @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_13) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk4 ) )
      | ( greater_or_equal @ ( sk5 @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,negated_conjecture,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk4 ) )
      | ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk5 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_14) ).

thf(15,plain,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk4 ) )
      | ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk5 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( greater_or_equal @ B @ ( sk3 @ A ) )
      | ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_8) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( greater_or_equal @ B @ ( sk3 @ A ) )
      | ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
      | ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
      | ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,negated_conjecture,
    environment @ sk4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_10) ).

thf(16,plain,
    environment @ sk4,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( 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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
      | ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(41,plain,
    $false,
    inference(e,[status(thm)],[29,33,17,27,39,35,18,23,19,15,37,25,16,31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : MGT028-1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n018.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 00:07:08 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.97/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.98  % [INFO] 	 Parsing done (135ms). 
% 1.31/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.76/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.76/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ... 
% 2.01/1.35  % [INFO] 	 Axiom selection finished. Selected 9 axioms (removed 0 axioms). 
% 2.09/1.38  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.09/1.38  % [INFO] 	 Type checking passed. 
% 2.09/1.38  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 3.12/1.75  % External prover 'e' found a proof!
% 3.12/1.75  % [INFO] 	 Killing All external provers ... 
% 3.12/1.75  % Time passed: 1242ms (effective reasoning time: 752ms)
% 3.12/1.75  % Axioms used in derivation (9): l11_7, mp_first_movers_negative_growth_6, mp_first_movers_negative_growth_2, l11_8, mp_first_movers_negative_growth_3, mp_first_movers_negative_growth_4, l11_9, mp_first_movers_negative_growth_5, mp_first_movers_negative_growth_1
% 3.12/1.75  % No. of inferences in proof: 29
% 3.12/1.75  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1242 ms resp. 752 ms w/o parsing
% 3.33/1.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------