TSTP Solution File: MGT025+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT025+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:35:17 EDT 2023
% Result : Theorem 3.56s 1.83s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 33 ( 1 unt; 15 typ; 0 def)
% Number of atoms : 108 ( 20 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 358 ( 2 ~; 14 |; 51 &; 266 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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; 0-4 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(first_movers_type,type,
first_movers: $i ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(constant_type,type,
constant: $i > $o ).
thf(number_of_organizations_type,type,
number_of_organizations: $i > $i > $i ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(subpopulation_type,type,
subpopulation: $i > $i > $i > $o ).
thf(cardinality_at_time_type,type,
cardinality_at_time: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(increases_type,type,
increases: $i > $o ).
thf(decreases_type,type,
decreases: $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( constant @ ( number_of_organizations @ A @ B ) ) )
=> ( ( ( ( growth_rate @ first_movers @ B )
= zero )
& ( ( growth_rate @ efficient_producers @ B )
= zero ) )
| ( ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) ) )
| ( ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( constant @ ( number_of_organizations @ A @ B ) ) )
=> ( ( ( ( growth_rate @ first_movers @ B )
= zero )
& ( ( growth_rate @ efficient_producers @ B )
= zero ) )
| ( ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) ) )
| ( ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( constant @ ( number_of_organizations @ A @ B ) ) )
=> ( ( ( ( growth_rate @ first_movers @ B )
= zero )
& ( ( growth_rate @ efficient_producers @ B )
= zero ) )
| ( ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) ) )
| ( ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( in_environment @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( ( greater @ ( cardinality_at_time @ B @ C ) @ zero )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ) )
=> ( ( number_of_organizations @ A @ C )
= ( sum @ ( cardinality_at_time @ first_movers @ C ) @ ( cardinality_at_time @ efficient_producers @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_only_members) ).
thf(18,plain,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( ( greater @ ( cardinality_at_time @ B @ C ) @ zero )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ) )
=> ( ( number_of_organizations @ A @ C )
= ( sum @ ( cardinality_at_time @ first_movers @ C ) @ ( cardinality_at_time @ efficient_producers @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( sum @ B @ C ) )
& ( constant @ A ) )
=> ( ( ( constant @ B )
& ( constant @ C ) )
| ( ( increases @ B )
& ( decreases @ C ) )
| ( ( decreases @ B )
& ( increases @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( sum @ B @ C ) )
& ( constant @ A ) )
=> ( ( ( constant @ B )
& ( constant @ C ) )
| ( ( increases @ B )
& ( decreases @ C ) )
| ( ( decreases @ B )
& ( increases @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( greater @ ( cardinality_at_time @ B @ C ) @ zero ) )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a9) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( greater @ ( cardinality_at_time @ B @ C ) @ zero ) )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( subpopulation @ first_movers @ A @ B )
& ( subpopulation @ efficient_producers @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( subpopulation @ first_movers @ A @ B )
& ( subpopulation @ efficient_producers @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
& ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
& ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ B )
& ( in_environment @ B @ C )
& ( subpopulation @ A @ B @ C )
& ( greater @ ( cardinality_at_time @ A @ C ) @ zero ) )
=> ( ( ( constant @ ( cardinality_at_time @ A @ C ) )
=> ( ( growth_rate @ A @ C )
= zero ) )
& ( ( increases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ ( growth_rate @ A @ C ) @ zero ) )
& ( ( decreases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ zero @ ( growth_rate @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ B )
& ( in_environment @ B @ C )
& ( subpopulation @ A @ B @ C )
& ( greater @ ( cardinality_at_time @ A @ C ) @ zero ) )
=> ( ( ( constant @ ( cardinality_at_time @ A @ C ) )
=> ( ( growth_rate @ A @ C )
= zero ) )
& ( ( increases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ ( growth_rate @ A @ C ) @ zero ) )
& ( ( decreases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ zero @ ( growth_rate @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(63,plain,
$false,
inference(e,[status(thm)],[10,57,18,30,59,27,54,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT025+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n021.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Thu May 18 23:39:13 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.84/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (132ms).
% 1.21/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.20 % [INFO] eprover registered as external prover.
% 1.78/1.20 % [INFO] cvc4 registered as external prover.
% 1.78/1.21 % [INFO] Scanning for conjecture ...
% 1.90/1.28 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.90/1.31 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.90/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.90/1.33 % [INFO] Type checking passed.
% 2.21/1.34 % [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 ...
% 3.56/1.83 % External prover 'e' found a proof!
% 3.56/1.83 % [INFO] Killing All external provers ...
% 3.56/1.83 % Time passed: 1310ms (effective reasoning time: 839ms)
% 3.56/1.83 % 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)>
% 3.56/1.83 % Axioms used in derivation (7): mp_subpopulations, mp_growth_rate, a9, mp_time_point_occur, mp_only_members, mp_abc_sum_increase, mp_non_zero_producers
% 3.56/1.83 % No. of inferences in proof: 18
% 3.56/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1310 ms resp. 839 ms w/o parsing
% 3.60/1.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.60/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------