TSTP Solution File: MGT024+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT024+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 3.10s 1.70s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 21
% Syntax : Number of formulae : 30 ( 1 unt; 14 typ; 0 def)
% Number of atoms : 90 ( 10 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 336 ( 8 ~; 10 |; 41 &; 254 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% 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(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(equilibrium_type,type,
equilibrium: $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(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(number_of_organizations_type,type,
number_of_organizations: $i > $i > $i ).
thf(decreases_type,type,
decreases: $i > $o ).
thf(resources_type,type,
resources: $i > $i > $i ).
thf(constant_type,type,
constant: $i > $o ).
thf(8,axiom,
! [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/sandbox/benchmark/theBenchmark.p',l7) ).
thf(29,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)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) )
=> ~ ( greater @ ( equilibrium @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_equilibrium) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) )
=> ~ ( greater @ ( equilibrium @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) )
=> ( ( ( ( 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/sandbox/benchmark/theBenchmark.p',prove_l6) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) )
=> ( ( ( ( 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(9,plain,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) )
=> ( ( ( ( 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(3,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
thf(17,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)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( ( decreases @ ( resources @ A @ B ) )
=> ~ ( decreases @ ( number_of_organizations @ A @ B ) ) )
& ( ( constant @ ( resources @ A @ B ) )
=> ( constant @ ( number_of_organizations @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( ( decreases @ ( resources @ A @ B ) )
=> ~ ( decreases @ ( number_of_organizations @ A @ B ) ) )
& ( ( constant @ ( resources @ A @ B ) )
=> ( constant @ ( number_of_organizations @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ ( number_of_organizations @ A @ B ) @ zero ) )
=> ( ( ( greater @ ( equilibrium @ A ) @ B )
=> ( decreases @ ( resources @ A @ B ) ) )
& ( ~ ( greater @ ( equilibrium @ A ) @ B )
=> ( constant @ ( resources @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ ( number_of_organizations @ A @ B ) @ zero ) )
=> ( ( ( greater @ ( equilibrium @ A ) @ B )
=> ( decreases @ ( resources @ A @ B ) ) )
& ( ~ ( greater @ ( equilibrium @ A ) @ B )
=> ( constant @ ( resources @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[29,21,9,17,19,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT024+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri May 19 00:08:36 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.00 % [INFO] Parsing done (136ms).
% 1.32/1.01 % [INFO] Running in sequential loop mode.
% 1.62/1.21 % [INFO] eprover registered as external prover.
% 1.62/1.21 % [INFO] cvc4 registered as external prover.
% 1.62/1.21 % [INFO] Scanning for conjecture ...
% 1.94/1.28 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.94/1.30 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.94/1.32 % [INFO] Problem is first-order (TPTP FOF).
% 1.94/1.32 % [INFO] Type checking passed.
% 1.94/1.33 % [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 ...
% 3.10/1.70 % External prover 'e' found a proof!
% 3.10/1.70 % [INFO] Killing All external provers ...
% 3.10/1.70 % Time passed: 1184ms (effective reasoning time: 683ms)
% 3.10/1.70 % 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)>
% 3.10/1.70 % Axioms used in derivation (6): a6, l7, mp_equilibrium, mp_positive_number_of_organizations, mp_time_point_occur, a3
% 3.10/1.70 % No. of inferences in proof: 16
% 3.10/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1184 ms resp. 683 ms w/o parsing
% 3.28/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.28/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------