TSTP Solution File: MGT036-3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : MGT036-3 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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 : Fri May 19 11:35:21 EDT 2023

% Result   : Unsatisfiable 2.60s 1.63s
% Output   : Refutation 3.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   30 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :   47 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  198 (  30   ~;  28   |;   0   &; 140   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  11 usr;   6 con; 0-4 aty)
%            Number of variables   :   36 (   0   ^;  36   !;   0   ?;  36   :)

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

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

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

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

thf(outcompetes_type,type,
    outcompetes: $i > $i > $i > $o ).

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

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

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

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

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

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

thf(1,negated_conjecture,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star_9) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      | ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(3,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ~ ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
      | ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
      | ( outcompetes @ C @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_2) ).

thf(14,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ~ ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
      | ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
      | ( outcompetes @ C @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    environment @ sk1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_5) ).

thf(20,plain,
    environment @ sk1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(7,axiom,
    subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_6) ).

thf(21,plain,
    subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    greater_or_equal @ ( growth_rate @ first_movers @ sk2 ) @ zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_7) ).

thf(22,plain,
    greater_or_equal @ ( growth_rate @ first_movers @ sk2 ) @ zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ( subpopulations @ C @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).

thf(12,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ( subpopulations @ C @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ~ ( outcompetes @ C @ B @ D )
      | ( greater @ zero @ ( growth_rate @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_4) ).

thf(18,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ~ ( outcompetes @ C @ B @ D )
      | ( greater @ zero @ ( growth_rate @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ~ ( outcompetes @ C @ B @ D )
      | ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_3) ).

thf(16,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( environment @ A )
      | ~ ( subpopulations @ B @ C @ A @ D )
      | ~ ( outcompetes @ C @ B @ D )
      | ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(9,axiom,
    greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_8) ).

thf(23,plain,
    greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(24,plain,
    $false,
    inference(e,[status(thm)],[10,14,20,21,22,12,18,16,23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : MGT036-3 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n026.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 23:56:21 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.92/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.02  % [INFO] 	 Parsing done (126ms). 
% 1.25/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.29  % [INFO] 	 Found a conjecture and 8 axioms. Running axiom selection ... 
% 1.84/1.32  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.84/1.33  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.84/1.33  % [INFO] 	 Type checking passed. 
% 1.84/1.33  % [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 ... 
% 2.60/1.63  % External prover 'e' found a proof!
% 2.60/1.63  % [INFO] 	 Killing All external provers ... 
% 2.60/1.63  % Time passed: 1108ms (effective reasoning time: 605ms)
% 2.60/1.63  % Solved by 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)>
% 2.60/1.63  % Axioms used in derivation (8): d2_3, mp_symmetry_of_subpopulations_1, a13_star_6, a13_star_8, d2_4, a13_star_5, a13_star_7, d2_2
% 2.60/1.63  % No. of inferences in proof: 19
% 2.60/1.63  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1108 ms resp. 605 ms w/o parsing
% 3.00/1.66  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.00/1.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------