%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n003.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 08:00:36 AM UTC 2026
% Result : Unsatisfiable 5.02s 2.99s
% Output : Refutation 5.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 2 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 264 ( 42 ~; 42 |; 0 &; 180 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
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(sk2_decl,type,
sk2: $i ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(disbanding_rate_decl,type,
disbanding_rate: $i > $i > $i ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(number_of_organizations_decl,type,
number_of_organizations: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(increases_decl,type,
increases: $i > $o ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(equilibrium_decl,type,
equilibrium: $i > $i ).
thf(resources_decl,type,
resources: $i > $i > $i ).
thf(constant_decl,type,
constant: $i > $o ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_31) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,negated_conjecture,
sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_37) ).
thf(14,plain,
sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_36) ).
thf(13,plain,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_not_empty_28) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
sk1 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_35) ).
thf(12,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ constant )
| ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_32) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ constant )
| ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_in_environment_27) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ increases )
| ~ ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_33) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ increases )
| ~ ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_30) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( B @ ( A @ resources ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_34) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( B @ ( A @ resources ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ decreases )
| ~ ( A @ increases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_increase_not_decrease_29) ).
thf(19,plain,
! [A: $i] :
( ~ ( A @ decreases )
| ~ ( A @ increases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[24,14,13,17,12,26,15,28,21,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % 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
% 0.14/0.39 % Computer : n003.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 00:06:08 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.22/1.15 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.57/1.36 % [INFO] Parsing done (208ms).
% 1.57/1.37 % [INFO] Running in sequential loop mode.
% 2.46/1.88 % [INFO] eprover registered as external prover.
% 2.46/1.89 % [INFO] Scanning for conjecture ...
% 2.66/2.04 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.95/2.09 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.95/2.13 % [INFO] Problem is propositional (TPTP CNF).
% 2.95/2.14 % [INFO] Type checking passed.
% 2.95/2.15 % [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 ...
% 5.02/2.99 % External prover 'e' found a proof!
% 5.02/2.99 % [INFO] Killing All external provers ...
% 5.02/2.99 % Time passed: 2456ms (effective reasoning time: 1612ms)
% 5.02/2.99 % Axioms used in derivation (8): mp_environment_not_empty_28, mp_time_point_in_environment_27, mp_greater_or_equal_30, a3_31, l4_34, a3_32, l4_33, mp_increase_not_decrease_29
% 5.02/2.99 % No. of inferences in proof: 23
% 5.02/2.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2456 ms resp. 1612 ms w/o parsing
% 5.55/3.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.55/3.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------