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 v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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   : Theorem 2.10s 1.37s
% Output   : Refutation 2.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   19 (   1 unt;   9 typ;   0 def)
%            Number of atoms       :   37 (   0 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  140 (   2   ~;   0   |;  20   &; 111   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   9 usr;   4 con; 0-4 aty)
%            Number of variables   :   26 (   0   ^;  16   !;  10   ?;  26   :)

% 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(1,conjecture,
    ? [A: $i,B: $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) ).

thf(2,negated_conjecture,
    ~ ? [A: $i,B: $i] :
        ( ( environment @ A )
        & ( subpopulations @ first_movers @ efficient_producers @ A @ B )
        & ( outcompetes @ first_movers @ efficient_producers @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ? [A: $i,B: $i] :
        ( ( environment @ A )
        & ( subpopulations @ first_movers @ efficient_producers @ A @ B )
        & ( outcompetes @ first_movers @ efficient_producers @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( environment @ A )
        & ( subpopulations @ B @ C @ A @ D ) )
     => ( subpopulations @ C @ B @ A @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).

thf(9,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( environment @ A )
        & ( subpopulations @ B @ C @ A @ D ) )
     => ( subpopulations @ C @ B @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $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) ).

thf(11,plain,
    ! [A: $i,B: $i,C: $i,D: $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 ) )
        & ( ( outcompetes @ C @ B @ D )
         => ( ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
            & ( greater @ zero @ ( growth_rate @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ? [A: $i,B: $i] :
      ( ( environment @ A )
      & ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      & ( greater_or_equal @ ( growth_rate @ first_movers @ B ) @ zero )
      & ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).

thf(15,plain,
    ? [A: $i,B: $i] :
      ( ( environment @ A )
      & ( subpopulations @ first_movers @ efficient_producers @ A @ B )
      & ( greater_or_equal @ ( growth_rate @ first_movers @ B ) @ zero )
      & ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(21,plain,
    $false,
    inference(e,[status(thm)],[6,9,11,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.10  % Command  : run_Leo-III %s %d
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Thu May 18 23:40:20 EDT 2023
% 0.08/0.28  % CPUTime  : 
% 0.63/0.68  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.90/0.79  % [INFO] 	 Parsing done (104ms). 
% 0.90/0.80  % [INFO] 	 Running in sequential loop mode. 
% 1.18/0.99  % [INFO] 	 eprover registered as external prover. 
% 1.18/0.99  % [INFO] 	 cvc4 registered as external prover. 
% 1.18/1.00  % [INFO] 	 Scanning for conjecture ... 
% 1.36/1.05  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.36/1.07  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.36/1.09  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.55/1.09  % [INFO] 	 Type checking passed. 
% 1.55/1.09  % [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 ... 
% 2.10/1.37  % External prover 'e' found a proof!
% 2.10/1.37  % [INFO] 	 Killing All external provers ... 
% 2.10/1.37  % Time passed: 980ms (effective reasoning time: 573ms)
% 2.10/1.37  % 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)>
% 2.10/1.37  % Axioms used in derivation (3): mp_symmetry_of_subpopulations, d2, a13_star
% 2.10/1.37  % No. of inferences in proof: 10
% 2.10/1.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 980 ms resp. 573 ms w/o parsing
% 2.10/1.40  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.10/1.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------