%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:00:37 AM UTC 2026
% Result : Theorem 5.59s 3.45s
% Output : Refutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 1 unt; 0 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 : 0 ( 0 >; 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_decl,type,
environment: $i > $o ).
thf(subpopulations_decl,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(efficient_producers_decl,type,
efficient_producers: $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(equilibrium_decl,type,
equilibrium: $i > $i ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(number_of_organizations_decl,type,
number_of_organizations: $i > $i > $i ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(resources_decl,type,
resources: $i > $i > $i ).
thf(constant_decl,type,
constant: $i > $o ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ~ ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ constant ) )
& ( ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ decreases ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ~ ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ constant ) )
& ( ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ decreases ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ( B @ ( A @ resources ) @ constant )
=> ( B @ ( A @ number_of_organizations ) @ constant ) )
& ( ( B @ ( A @ resources ) @ decreases )
=> ~ ( B @ ( A @ number_of_organizations ) @ decreases ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ( B @ ( A @ resources ) @ constant )
=> ( B @ ( A @ number_of_organizations ) @ constant ) )
& ( ( B @ ( A @ resources ) @ decreases )
=> ~ ( B @ ( A @ number_of_organizations ) @ decreases ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ equilibrium @ ( B @ greater_or_equal ) )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ equilibrium @ ( B @ greater_or_equal ) )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ equilibrium @ ( B @ greater_or_equal ) )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ number_of_organizations ) @ constant )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ number_of_organizations ) @ constant )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ equilibrium @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ~ ( B @ ( A @ equilibrium @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_equilibrium) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( ( A @ equilibrium @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ~ ( B @ ( A @ equilibrium @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[24,20,28,9,32,22,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.22/0.47 % Computer : n014.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sat Sep 26 00:04:17 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.46/1.33 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.80/1.59 % [INFO] Parsing done (261ms).
% 2.04/1.61 % [INFO] Running in sequential loop mode.
% 3.00/2.21 % [INFO] eprover registered as external prover.
% 3.00/2.23 % [INFO] Scanning for conjecture ...
% 3.19/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 3.33/2.46 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 3.33/2.49 % [INFO] Problem is first-order (TPTP FOF).
% 3.54/2.50 % [INFO] Type checking passed.
% 3.54/2.51 % [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 ...
% 5.59/3.45 % External prover 'e' found a proof!
% 5.59/3.45 % [INFO] Killing All external provers ...
% 5.59/3.45 % Time passed: 2766ms (effective reasoning time: 1827ms)
% 5.59/3.45 % 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)>
% 5.59/3.45 % Axioms used in derivation (6): a6, l7, mp_equilibrium, mp_positive_number_of_organizations, mp_time_point_occur, a3
% 5.59/3.45 % No. of inferences in proof: 16
% 5.59/3.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2766 ms resp. 1827 ms w/o parsing
% 5.90/3.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.90/3.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------