TSTP Solution File: MGT055+1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : MGT055+1 : TPTP v8.2.0. Released v2.4.0.
% 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 : Tue May 21 00:41:36 EDT 2024

% Result   : Theorem 25.89s 4.90s
% Output   : Refutation 25.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   47 (   1 unt;  15 typ;   0 def)
%            Number of atoms       :  161 (  20 equ;   0 cnn)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  538 (  18   ~;  10   |;  73   &; 391   @)
%                                         (   7 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   4 con; 0-3 aty)
%            Number of variables   :   86 (   0   ^  86   !;   0   ?;  86   :)

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

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

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

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

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

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

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

thf(sigma_type,type,
    sigma: $i ).

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

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

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

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

thf(dissimilar_type,type,
    dissimilar: $i > $i > $i > $o ).

thf(is_aligned_type,type,
    is_aligned: $i > $i > $o ).

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

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( greater @ A @ B )
        & ( greater @ B @ C ) )
     => ( greater @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meaning_postulate_greater_transitive) ).

thf(56,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( greater @ A @ B )
        & ( greater @ B @ C ) )
     => ( greater @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(11,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/sandbox/benchmark/theBenchmark.p',assumption_3) ).

thf(78,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)],[11]) ).

thf(9,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/sandbox/benchmark/theBenchmark.p',definition_1) ).

thf(61,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)],[9]) ).

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

thf(53,plain,
    ! [A: $i,B: $i] :
      ~ ( ( greater @ A @ B )
        & ( greater @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( ( age @ A @ B )
          = zero ) )
     => ( ( greater @ ( age @ A @ C ) @ sigma )
      <=> ( dissimilar @ A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_15) ).

thf(96,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( ( age @ A @ B )
          = zero ) )
     => ( ( ( greater @ ( age @ A @ C ) @ sigma )
         => ( dissimilar @ A @ B @ C ) )
        & ( ( dissimilar @ A @ B @ C )
         => ( greater @ ( age @ A @ C ) @ sigma ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( organization @ A )
        & ( has_endowment @ A )
        & ( ( age @ A @ B )
          = zero )
        & ( smaller_or_equal @ ( age @ A @ C ) @ eta )
        & ( greater @ ( age @ A @ D ) @ eta )
        & ( smaller_or_equal @ ( age @ A @ D ) @ sigma )
        & ( greater @ ( age @ A @ E ) @ sigma )
        & ( greater @ sigma @ eta )
        & ( greater @ eta @ zero ) )
     => ( ( 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/sandbox/benchmark/theBenchmark.p',lemma_8) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( organization @ A )
          & ( has_endowment @ A )
          & ( ( age @ A @ B )
            = zero )
          & ( smaller_or_equal @ ( age @ A @ C ) @ eta )
          & ( greater @ ( age @ A @ D ) @ eta )
          & ( smaller_or_equal @ ( age @ A @ D ) @ sigma )
          & ( greater @ ( age @ A @ E ) @ sigma )
          & ( greater @ sigma @ eta )
          & ( greater @ eta @ zero ) )
       => ( ( 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(17,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( ( organization @ A )
          & ( has_endowment @ A )
          & ( ( age @ A @ B )
            = zero )
          & ( smaller_or_equal @ ( age @ A @ C ) @ eta )
          & ( greater @ ( age @ A @ D ) @ eta )
          & ( smaller_or_equal @ ( age @ A @ D ) @ sigma )
          & ( greater @ ( age @ A @ E ) @ sigma )
          & ( greater @ sigma @ eta )
          & ( greater @ eta @ zero ) )
       => ( ( 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] :
      ( ( greater_or_equal @ A @ B )
    <=> ( ( greater @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_greater_or_equal) ).

thf(39,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)],[4]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( dissimilar @ A @ B @ C )
    <=> ( ( organization @ A )
        & ~ ( ( is_aligned @ A @ B )
          <=> ( is_aligned @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_2) ).

thf(80,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( dissimilar @ A @ B @ C )
       => ( ( organization @ A )
          & ~ ( ( ( is_aligned @ A @ B )
               => ( is_aligned @ A @ C ) )
              & ( ( is_aligned @ A @ C )
               => ( is_aligned @ A @ B ) ) ) ) )
      & ( ( ( organization @ A )
          & ~ ( ( ( is_aligned @ A @ B )
               => ( is_aligned @ A @ C ) )
              & ( ( is_aligned @ A @ C )
               => ( is_aligned @ A @ B ) ) ) )
       => ( dissimilar @ A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( smaller @ A @ B )
    <=> ( greater @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller) ).

thf(48,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)],[5]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( smaller_or_equal @ A @ B )
    <=> ( ( smaller @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller_or_equal) ).

thf(30,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)],[3]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( is_aligned @ A @ B )
        & ~ ( is_aligned @ A @ C ) )
     => ( greater @ ( capability @ A @ B ) @ ( capability @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_14) ).

thf(94,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( organization @ A )
        & ( is_aligned @ A @ B )
        & ~ ( is_aligned @ A @ C ) )
     => ( greater @ ( capability @ A @ B ) @ ( capability @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(16,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 @ ( hazard_of_mortality @ A @ B ) @ ( hazard_of_mortality @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_16) ).

thf(103,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 @ ( hazard_of_mortality @ A @ B ) @ ( hazard_of_mortality @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( ( organization @ A )
        & ( ( age @ A @ B )
          = zero ) )
     => ( is_aligned @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_13) ).

thf(91,plain,
    ! [A: $i,B: $i] :
      ( ( ( organization @ A )
        & ( ( age @ A @ B )
          = zero ) )
     => ( is_aligned @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',assumption_2) ).

thf(75,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)],[10]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( smaller @ A @ B )
      | ( A = B )
      | ( greater @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',meaning_postulate_greater_comparable) ).

thf(58,plain,
    ! [A: $i,B: $i] :
      ( ( smaller @ A @ B )
      | ( A = B )
      | ( greater @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(10020,plain,
    $false,
    inference(e,[status(thm)],[56,78,61,53,96,17,39,80,48,30,94,103,91,75,58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : MGT055+1 : TPTP v8.2.0. Released v2.4.0.
% 0.00/0.09  % Command  : run_Leo-III %s %d
% 0.08/0.27  % Computer : n032.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit : 300
% 0.08/0.27  % WCLimit  : 300
% 0.08/0.27  % DateTime : Sun May 19 00:02:23 EDT 2024
% 0.08/0.27  % CPUTime  : 
% 0.64/0.70  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 0.99/0.82  % [INFO] 	 Parsing done (117ms). 
% 0.99/0.82  % [INFO] 	 Running in sequential loop mode. 
% 1.45/1.04  % [INFO] 	 eprover registered as external prover. 
% 1.45/1.05  % [INFO] 	 cvc4 registered as external prover. 
% 1.45/1.05  % [INFO] 	 Scanning for conjecture ... 
% 1.64/1.13  % [INFO] 	 Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ... 
% 1.64/1.15  % [INFO] 	 Axiom selection finished. Selected 14 axioms (removed 0 axioms). 
% 1.64/1.18  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.64/1.18  % [INFO] 	 Type checking passed. 
% 1.90/1.19  % [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 ... 
% 25.89/4.89  % External prover 'e' found a proof!
% 25.89/4.89  % [INFO] 	 Killing All external provers ... 
% 25.89/4.89  % Time passed: 4505ms (effective reasoning time: 4066ms)
% 25.89/4.89  % 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)>
% 25.89/4.89  % Axioms used in derivation (14): assumption_16, assumption_3, definition_smaller, assumption_15, meaning_postulate_greater_comparable, meaning_postulate_greater_transitive, assumption_2, definition_2, meaning_postulate_greater_strict, definition_greater_or_equal, definition_1, assumption_13, definition_smaller_or_equal, assumption_14
% 25.89/4.89  % No. of inferences in proof: 32
% 25.89/4.90  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4505 ms resp. 4066 ms w/o parsing
% 25.89/4.92  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.89/4.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------