TSTP Solution File: MGT027-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : MGT027-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 4.41s 2.67s
% Output   : Refutation 4.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   49 (   5 unt;  16 typ;   0 def)
%            Number of atoms       :  109 (   4 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  384 (  72   ~;  76   |;   0   &; 236   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   5 con; 0-4 aty)
%            Number of variables   :   54 (   0   ^  54   !;   0   ?;  54   :)

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

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

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

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

thf(cardinality_at_time_type,type,
    cardinality_at_time: $i > $i > $i ).

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

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

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

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

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

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

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
      | ( contracts_from @ B @ first_movers ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_26) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
      | ( contracts_from @ B @ first_movers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1,negated_conjecture,
    environment @ sk3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_37) ).

thf(17,plain,
    environment @ sk3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( greater_or_equal @ A @ B )
      | ( greater @ A @ B )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_31) ).

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ~ ( greater_or_equal @ A @ B )
      | ( greater @ A @ B )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ( in_environment @ A @ ( appear @ efficient_producers @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments_29) ).

thf(31,plain,
    ! [A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ( in_environment @ A @ ( appear @ efficient_producers @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk3 ) )
      | ~ ( contracts_from @ A @ first_movers ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_39) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ ( greater @ A @ ( appear @ efficient_producers @ sk3 ) )
      | ~ ( contracts_from @ A @ first_movers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_35) ).

thf(46,plain,
    ! [A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater @ C @ B )
      | ( in_environment @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments_28) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater @ C @ B )
      | ( in_environment @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(12,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( greater @ A @ B )
      | ( greater_or_equal @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).

thf(38,plain,
    ! [B: $i,A: $i] :
      ( ~ ( greater @ A @ B )
      | ( greater_or_equal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater @ ( cardinality_at_time @ first_movers @ ( sk1 @ B @ A ) ) @ zero )
      | ( contracts_from @ B @ first_movers ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_24) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater @ ( cardinality_at_time @ first_movers @ ( sk1 @ B @ A ) ) @ zero )
      | ( contracts_from @ B @ first_movers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( greater @ A @ B )
      | ~ ( greater @ B @ C )
      | ( greater @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_30) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( greater @ A @ B )
      | ~ ( greater @ B @ C )
      | ( greater @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater_or_equal @ B @ ( appear @ efficient_producers @ A ) )
      | ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_34) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater_or_equal @ B @ ( appear @ efficient_producers @ A ) )
      | ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
      | ~ ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero )
      | ( subpopulations @ first_movers @ efficient_producers @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_27) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( in_environment @ A @ B )
      | ~ ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
      | ~ ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero )
      | ( subpopulations @ first_movers @ efficient_producers @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( greater_or_equal @ B @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_36) ).

thf(48,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( greater_or_equal @ B @ ( sk2 @ A ) )
      | ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(2,negated_conjecture,
    stable @ sk3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_38) ).

thf(18,plain,
    stable @ sk3,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( greater_or_equal @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_33) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( greater_or_equal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
      | ( contracts_from @ B @ first_movers ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_25) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( stable @ A )
      | ~ ( in_environment @ A @ B )
      | ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
      | ( contracts_from @ B @ first_movers ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(50,plain,
    $false,
    inference(e,[status(thm)],[25,17,35,31,19,46,29,38,21,33,44,27,48,18,40,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : MGT027-1 : TPTP v8.2.0. Released v2.4.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun May 19 00:01:54 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.18/1.08  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.53/1.28  % [INFO] 	 Parsing done (194ms). 
% 1.53/1.29  % [INFO] 	 Running in sequential loop mode. 
% 2.18/1.72  % [INFO] 	 eprover registered as external prover. 
% 2.18/1.72  % [INFO] 	 cvc4 registered as external prover. 
% 2.18/1.73  % [INFO] 	 Scanning for conjecture ... 
% 2.49/1.85  % [INFO] 	 Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ... 
% 2.49/1.88  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 0 axioms). 
% 2.69/1.92  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.69/1.93  % [INFO] 	 Type checking passed. 
% 2.69/1.94  % [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 ... 
% 4.11/2.61  % External prover 'e' found a proof!
% 4.11/2.61  % [INFO] 	 Killing All external provers ... 
% 4.40/2.66  % Time passed: 2149ms (effective reasoning time: 1365ms)
% 4.41/2.67  % Axioms used in derivation (13): mp_contracts_from_25, mp_greater_or_equal_31, l10_36, mp_contracts_from_24, mp_long_stable_environments_28, l10_35, mp_non_empty_fm_and_ep_27, mp_greater_or_equal_33, mp_contracts_from_26, mp_greater_transitivity_30, mp_EP_in_stable_environments_29, t6_34, mp_greater_or_equal_32
% 4.41/2.67  % No. of inferences in proof: 33
% 4.41/2.67  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2149 ms resp. 1365 ms w/o parsing
% 4.51/2.73  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.51/2.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------