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