TSTP Solution File: MGT056+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT056+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 11:35:28 EDT 2023
% Result : Theorem 3.56s 1.95s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 34 ( 1 unt; 12 typ; 0 def)
% Number of atoms : 102 ( 16 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 313 ( 9 ~; 10 |; 43 &; 224 @)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 0 ^; 55 !; 0 ?; 55 :)
% 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(greater_or_equal_type,type,
greater_or_equal: $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(has_immunity_type,type,
has_immunity: $i > $i > $o ).
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(46,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] :
( ( smaller @ A @ B )
<=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_smaller) ).
thf(41,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(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(32,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(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(23,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(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(51,plain,
! [A: $i,B: $i] :
( ( smaller @ A @ B )
| ( A = B )
| ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(68,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(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(71,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(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( organization @ A )
& ( has_endowment @ A )
& ( ( age @ A @ B )
= zero )
& ( smaller_or_equal @ ( age @ A @ C ) @ eta )
& ( greater @ ( age @ A @ D ) @ eta )
& ( greater_or_equal @ eta @ sigma )
& ( greater @ sigma @ zero ) )
=> ( ( 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_9) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( organization @ A )
& ( has_endowment @ A )
& ( ( age @ A @ B )
= zero )
& ( smaller_or_equal @ ( age @ A @ C ) @ eta )
& ( greater @ ( age @ A @ D ) @ eta )
& ( greater_or_equal @ eta @ sigma )
& ( greater @ sigma @ zero ) )
=> ( ( 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(12,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( organization @ A )
& ( has_endowment @ A )
& ( ( age @ A @ B )
= zero )
& ( smaller_or_equal @ ( age @ A @ C ) @ eta )
& ( greater @ ( age @ A @ D ) @ eta )
& ( greater_or_equal @ eta @ sigma )
& ( greater @ sigma @ zero ) )
=> ( ( 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(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(54,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(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(49,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(73,plain,
$false,
inference(e,[status(thm)],[46,41,32,23,51,68,71,12,54,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT056+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 23:40:39 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.03/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.06 % [INFO] Parsing done (148ms).
% 1.45/1.07 % [INFO] Running in sequential loop mode.
% 1.75/1.29 % [INFO] eprover registered as external prover.
% 1.75/1.29 % [INFO] cvc4 registered as external prover.
% 1.75/1.29 % [INFO] Scanning for conjecture ...
% 1.99/1.36 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 2.15/1.39 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.15/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.15/1.41 % [INFO] Type checking passed.
% 2.15/1.41 % [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 ...
% 3.56/1.95 % External prover 'e' found a proof!
% 3.56/1.95 % [INFO] Killing All external provers ...
% 3.56/1.95 % Time passed: 1415ms (effective reasoning time: 869ms)
% 3.56/1.95 % 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)>
% 3.56/1.95 % Axioms used in derivation (9): assumption_2, definition_1, assumption_3, definition_smaller_or_equal, definition_smaller, meaning_postulate_greater_comparable, meaning_postulate_greater_transitive, meaning_postulate_greater_strict, definition_greater_or_equal
% 3.56/1.95 % No. of inferences in proof: 22
% 3.56/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1415 ms resp. 869 ms w/o parsing
% 3.68/2.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.68/2.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------