TSTP Solution File: MGT051+1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : MGT051+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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  7 07:57:35 EDT 2024

% Result   : Theorem 4.25s 1.99s
% Output   : Refutation 4.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   31
% Syntax   : Number of formulae    :   49 (   1 unt;  15 typ;   0 def)
%            Number of atoms       :  170 (  33 equ;   0 cnn)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  701 (  13   ~;  10   |;  71   &; 552   @)
%                                         (   4 <=>;  51  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   2 con; 0-2 aty)
%            Number of variables   :   94 (   0   ^  94   !;   0   ?;  94   :)

% Comments : 
%------------------------------------------------------------------------------
thf(organization_type,type,
    organization: $i > $o ).

thf(has_endowment_type,type,
    has_endowment: $i > $o ).

thf(smaller_or_equal_type,type,
    smaller_or_equal: $i > $i > $o ).

thf(age_type,type,
    age: $i > $i > $i ).

thf(eta_type,type,
    eta: $i ).

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

thf(hazard_of_mortality_type,type,
    hazard_of_mortality: $i > $i > $i ).

thf(stock_of_knowledge_type,type,
    stock_of_knowledge: $i > $i > $i ).

thf(has_immunity_type,type,
    has_immunity: $i > $i > $o ).

thf(capability_type,type,
    capability: $i > $i > $i ).

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

thf(position_type,type,
    position: $i > $i > $i ).

thf(smaller_type,type,
    smaller: $i > $i > $o ).

thf(external_ties_type,type,
    external_ties: $i > $i > $i ).

thf(internal_friction_type,type,
    internal_friction: $i > $i > $i ).

thf(8,axiom,
    ! [A: $i] :
      ( ( has_endowment @ A )
    <=> ! [B: $i] :
          ( ( organization @ A )
          & ( ( smaller_or_equal @ ( age @ A @ B ) @ eta )
           => ( has_immunity @ A @ B ) )
          & ( ( greater @ ( age @ A @ B ) @ eta )
           => ~ ( has_immunity @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_1) ).

thf(46,plain,
    ! [A: $i] :
      ( ( ( has_endowment @ A )
       => ! [B: $i] :
            ( ( organization @ A )
            & ( ( smaller_or_equal @ ( age @ A @ B ) @ eta )
             => ( has_immunity @ A @ B ) )
            & ( ( greater @ ( age @ A @ B ) @ eta )
             => ~ ( has_immunity @ A @ B ) ) ) )
      & ( ! [B: $i] :
            ( ( organization @ A )
            & ( ( smaller_or_equal @ ( age @ A @ B ) @ eta )
             => ( has_immunity @ A @ B ) )
            & ( ( greater @ ( age @ A @ B ) @ eta )
             => ~ ( has_immunity @ A @ B ) ) )
       => ( has_endowment @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( ( greater @ ( external_ties @ A @ C ) @ ( external_ties @ A @ B ) )
         => ( greater @ ( position @ A @ C ) @ ( position @ A @ B ) ) )
        & ( ( ( external_ties @ A @ C )
            = ( external_ties @ A @ B ) )
         => ( ( position @ A @ C )
            = ( position @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_6) ).

thf(70,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( ( greater @ ( external_ties @ A @ C ) @ ( external_ties @ A @ B ) )
         => ( greater @ ( position @ A @ C ) @ ( position @ A @ B ) ) )
        & ( ( ( external_ties @ A @ C )
            = ( external_ties @ A @ B ) )
         => ( ( position @ A @ C )
            = ( position @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( stock_of_knowledge @ A @ C )
        = ( stock_of_knowledge @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_10) ).

thf(27,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( stock_of_knowledge @ A @ C )
        = ( stock_of_knowledge @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( smaller_or_equal @ A @ B )
    <=> ( ( smaller @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller_or_equal) ).

thf(76,plain,
    ! [A: $i,B: $i] :
      ( ( ( smaller_or_equal @ A @ B )
       => ( ( smaller @ A @ B )
          | ( A = B ) ) )
      & ( ( ( smaller @ A @ B )
          | ( A = B ) )
       => ( smaller_or_equal @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( organization @ A )
        & ( has_endowment @ A )
        & ( smaller_or_equal @ ( age @ A @ B ) @ ( age @ A @ C ) )
        & ( smaller_or_equal @ ( age @ A @ C ) @ eta )
        & ( greater @ ( age @ A @ D ) @ eta )
        & ( greater @ ( age @ A @ E ) @ ( age @ A @ D ) ) )
     => ( ( greater @ ( hazard_of_mortality @ A @ E ) @ ( hazard_of_mortality @ A @ D ) )
        & ( greater @ ( hazard_of_mortality @ A @ D ) @ ( hazard_of_mortality @ A @ C ) )
        & ( ( hazard_of_mortality @ A @ C )
          = ( hazard_of_mortality @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_4) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( organization @ A )
          & ( has_endowment @ A )
          & ( smaller_or_equal @ ( age @ A @ B ) @ ( age @ A @ C ) )
          & ( smaller_or_equal @ ( age @ A @ C ) @ eta )
          & ( greater @ ( age @ A @ D ) @ eta )
          & ( greater @ ( age @ A @ E ) @ ( age @ A @ D ) ) )
       => ( ( greater @ ( hazard_of_mortality @ A @ E ) @ ( hazard_of_mortality @ A @ D ) )
          & ( greater @ ( hazard_of_mortality @ A @ D ) @ ( hazard_of_mortality @ A @ C ) )
          & ( ( hazard_of_mortality @ A @ C )
            = ( hazard_of_mortality @ A @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(18,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( organization @ A )
          & ( has_endowment @ A )
          & ( smaller_or_equal @ ( age @ A @ B ) @ ( age @ A @ C ) )
          & ( smaller_or_equal @ ( age @ A @ C ) @ eta )
          & ( greater @ ( age @ A @ D ) @ eta )
          & ( greater @ ( age @ A @ E ) @ ( age @ A @ D ) ) )
       => ( ( greater @ ( hazard_of_mortality @ A @ E ) @ ( hazard_of_mortality @ A @ D ) )
          & ( greater @ ( hazard_of_mortality @ A @ D ) @ ( hazard_of_mortality @ A @ C ) )
          & ( ( hazard_of_mortality @ A @ C )
            = ( hazard_of_mortality @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ~ ( has_immunity @ A @ B )
        & ~ ( has_immunity @ A @ C ) )
     => ( ( ( ( greater @ ( capability @ A @ C ) @ ( capability @ A @ B ) )
            & ( greater_or_equal @ ( position @ A @ C ) @ ( position @ A @ B ) ) )
         => ( smaller @ ( hazard_of_mortality @ A @ C ) @ ( hazard_of_mortality @ A @ B ) ) )
        & ( ( ( greater_or_equal @ ( capability @ A @ C ) @ ( capability @ A @ B ) )
            & ( greater @ ( position @ A @ C ) @ ( position @ A @ B ) ) )
         => ( smaller @ ( hazard_of_mortality @ A @ C ) @ ( hazard_of_mortality @ A @ B ) ) )
        & ( ( ( ( capability @ A @ C )
              = ( capability @ A @ B ) )
            & ( ( position @ A @ C )
              = ( position @ A @ B ) ) )
         => ( ( hazard_of_mortality @ A @ C )
            = ( hazard_of_mortality @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_4) ).

thf(31,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ~ ( has_immunity @ A @ B )
        & ~ ( has_immunity @ A @ C ) )
     => ( ( ( ( greater @ ( capability @ A @ C ) @ ( capability @ A @ B ) )
            & ( greater_or_equal @ ( position @ A @ C ) @ ( position @ A @ B ) ) )
         => ( smaller @ ( hazard_of_mortality @ A @ C ) @ ( hazard_of_mortality @ A @ B ) ) )
        & ( ( ( greater_or_equal @ ( capability @ A @ C ) @ ( capability @ A @ B ) )
            & ( greater @ ( position @ A @ C ) @ ( position @ A @ B ) ) )
         => ( smaller @ ( hazard_of_mortality @ A @ C ) @ ( hazard_of_mortality @ A @ B ) ) )
        & ( ( ( ( capability @ A @ C )
              = ( capability @ A @ B ) )
            & ( ( position @ A @ C )
              = ( position @ A @ B ) ) )
         => ( ( hazard_of_mortality @ A @ C )
            = ( hazard_of_mortality @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( has_immunity @ A @ B )
        & ( has_immunity @ A @ C ) )
     => ( ( hazard_of_mortality @ A @ B )
        = ( hazard_of_mortality @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2) ).

thf(43,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( has_immunity @ A @ B )
        & ( has_immunity @ A @ C ) )
     => ( ( hazard_of_mortality @ A @ B )
        = ( hazard_of_mortality @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( smaller @ A @ B )
    <=> ( greater @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_smaller) ).

thf(87,plain,
    ! [A: $i,B: $i] :
      ( ( ( smaller @ A @ B )
       => ( greater @ B @ A ) )
      & ( ( greater @ B @ A )
       => ( smaller @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

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

thf(40,plain,
    ! [A: $i,B: $i] :
      ~ ( ( greater @ A @ B )
        & ( greater @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( external_ties @ A @ C )
        = ( external_ties @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_11) ).

thf(36,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( external_ties @ A @ C )
        = ( external_ties @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( smaller @ A @ B )
      | ( A = B )
      | ( greater @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_comparable) ).

thf(94,plain,
    ! [A: $i,B: $i] :
      ( ( smaller @ A @ B )
      | ( A = B )
      | ( greater @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( ( ( greater @ ( stock_of_knowledge @ A @ C ) @ ( stock_of_knowledge @ A @ B ) )
            & ( smaller_or_equal @ ( internal_friction @ A @ C ) @ ( internal_friction @ A @ B ) ) )
         => ( greater @ ( capability @ A @ C ) @ ( capability @ A @ B ) ) )
        & ( ( ( smaller_or_equal @ ( stock_of_knowledge @ A @ C ) @ ( stock_of_knowledge @ A @ B ) )
            & ( greater @ ( internal_friction @ A @ C ) @ ( internal_friction @ A @ B ) ) )
         => ( smaller @ ( capability @ A @ C ) @ ( capability @ A @ B ) ) )
        & ( ( ( ( stock_of_knowledge @ A @ C )
              = ( stock_of_knowledge @ A @ B ) )
            & ( ( internal_friction @ A @ C )
              = ( internal_friction @ A @ B ) ) )
         => ( ( capability @ A @ C )
            = ( capability @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_5) ).

thf(62,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( organization @ A )
     => ( ( ( ( greater @ ( stock_of_knowledge @ A @ C ) @ ( stock_of_knowledge @ A @ B ) )
            & ( smaller_or_equal @ ( internal_friction @ A @ C ) @ ( internal_friction @ A @ B ) ) )
         => ( greater @ ( capability @ A @ C ) @ ( capability @ A @ B ) ) )
        & ( ( ( smaller_or_equal @ ( stock_of_knowledge @ A @ C ) @ ( stock_of_knowledge @ A @ B ) )
            & ( greater @ ( internal_friction @ A @ C ) @ ( internal_friction @ A @ B ) ) )
         => ( smaller @ ( capability @ A @ C ) @ ( capability @ A @ B ) ) )
        & ( ( ( ( stock_of_knowledge @ A @ C )
              = ( stock_of_knowledge @ A @ B ) )
            & ( ( internal_friction @ A @ C )
              = ( internal_friction @ A @ B ) ) )
         => ( ( capability @ A @ C )
            = ( capability @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( greater @ ( age @ A @ C ) @ ( age @ A @ B ) ) )
     => ( greater @ ( internal_friction @ A @ C ) @ ( internal_friction @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_12) ).

thf(60,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( greater @ ( age @ A @ C ) @ ( age @ A @ B ) ) )
     => ( greater @ ( internal_friction @ A @ C ) @ ( internal_friction @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( has_immunity @ A @ B )
        & ~ ( has_immunity @ A @ C ) )
     => ( greater @ ( hazard_of_mortality @ A @ C ) @ ( hazard_of_mortality @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_3) ).

thf(85,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( has_immunity @ A @ B )
        & ~ ( has_immunity @ A @ C ) )
     => ( greater @ ( hazard_of_mortality @ A @ C ) @ ( hazard_of_mortality @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( greater @ A @ B )
        & ( greater @ B @ C ) )
     => ( greater @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meaning_postulate_greater_transitive) ).

thf(92,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( greater @ A @ B )
        & ( greater @ B @ C ) )
     => ( greater @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( greater_or_equal @ A @ B )
    <=> ( ( greater @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_greater_or_equal) ).

thf(97,plain,
    ! [A: $i,B: $i] :
      ( ( ( greater_or_equal @ A @ B )
       => ( ( greater @ A @ B )
          | ( A = B ) ) )
      & ( ( ( greater @ A @ B )
          | ( A = B ) )
       => ( greater_or_equal @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(150,plain,
    $false,
    inference(cvc4,[status(thm)],[46,70,27,76,18,31,43,87,40,36,94,62,60,85,92,97]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : MGT051+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon May  6 15:29:09 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.87/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.11/1.03  % [INFO] 	 Parsing done (119ms). 
% 1.11/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.45/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.45/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.45/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.29  % [INFO] 	 Found a conjecture and 15 axioms. Running axiom selection ... 
% 1.73/1.34  % [INFO] 	 Axiom selection finished. Selected 15 axioms (removed 0 axioms). 
% 2.04/1.37  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.04/1.37  % [INFO] 	 Type checking passed. 
% 2.04/1.38  % [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 ... 
% 4.25/1.98  % External prover 'cvc4' found a proof!
% 4.25/1.98  % [INFO] 	 Killing All external provers ... 
% 4.25/1.98  % Time passed: 1512ms (effective reasoning time: 945ms)
% 4.25/1.98  % 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)>
% 4.25/1.98  % Axioms used in derivation (15): assumption_5, definition_1, assumption_3, definition_smaller_or_equal, assumption_10, definition_smaller, assumption_4, assumption_6, assumption_11, meaning_postulate_greater_comparable, meaning_postulate_greater_transitive, assumption_2, assumption_12, meaning_postulate_greater_strict, definition_greater_or_equal
% 4.25/1.98  % No. of inferences in proof: 34
% 4.25/1.99  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1512 ms resp. 945 ms w/o parsing
% 4.25/2.02  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.25/2.02  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------