TSTP Solution File: MGT023+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 11:35:16 EDT 2023

% Result   : Theorem 3.12s 1.71s
% Output   : Refutation 3.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   17 (   1 unt;   9 typ;   0 def)
%            Number of atoms       :   38 (   2 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  139 (   6   ~;   0   |;  19   &; 103   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   3 con; 0-4 aty)
%            Number of variables   :   15 (   0   ^;  13   !;   2   ?;  15   :)

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

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

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

thf(critical_point_type,type,
    critical_point: $i > $i ).

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

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

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

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

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

thf(1,conjecture,
    ! [A: $i] :
      ( ( ( environment @ A )
        & ( stable @ A ) )
     => ( in_environment @ A @ ( critical_point @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ( environment @ A )
          & ( stable @ A ) )
       => ( in_environment @ A @ ( critical_point @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ! [A: $i] :
        ( ( ( environment @ A )
          & ( stable @ A ) )
       => ( in_environment @ A @ ( critical_point @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( ( environment @ A )
        & ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
        & ( in_environment @ A @ B )
        & ! [C: $i] :
            ( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
              & ( greater @ C @ B ) )
           => ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) )
     => ( B
        = ( critical_point @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).

thf(9,plain,
    ! [A: $i,B: $i] :
      ( ( ( environment @ A )
        & ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
        & ( in_environment @ A @ B )
        & ! [C: $i] :
            ( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
              & ( greater @ C @ B ) )
           => ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) )
     => ( B
        = ( critical_point @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( ( environment @ A )
        & ( stable @ A ) )
     => ? [B: $i] :
          ( ( in_environment @ A @ B )
          & ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
          & ! [C: $i] :
              ( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
                & ( greater @ C @ B ) )
             => ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).

thf(16,plain,
    ! [A: $i] :
      ( ( ( environment @ A )
        & ( stable @ A ) )
     => ? [B: $i] :
          ( ( in_environment @ A @ B )
          & ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
          & ! [C: $i] :
              ( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
                & ( greater @ C @ B ) )
             => ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(27,plain,
    $false,
    inference(e,[status(thm)],[5,9,16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n008.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 : Thu May 18 23:42:55 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.93/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.32/1.01  % [INFO] 	 Parsing done (127ms). 
% 1.32/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.60/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.78/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.28  % [INFO] 	 Found a conjecture and 2 axioms. Running axiom selection ... 
% 1.91/1.30  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.91/1.31  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.91/1.32  % [INFO] 	 Type checking passed. 
% 1.91/1.32  % [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 ... 
% 3.12/1.71  % External prover 'e' found a proof!
% 3.12/1.71  % [INFO] 	 Killing All external provers ... 
% 3.12/1.71  % Time passed: 1186ms (effective reasoning time: 688ms)
% 3.12/1.71  % 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)>
% 3.12/1.71  % Axioms used in derivation (2): d1, l12
% 3.12/1.71  % No. of inferences in proof: 8
% 3.12/1.71  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1186 ms resp. 688 ms w/o parsing
% 3.26/1.73  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.26/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------