%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:00:38 AM UTC 2026
% Result : Unsatisfiable 4.24s 7.51s
% Output : Refutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 490 ( 80 ~; 86 |; 0 &; 324 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(stable_decl,type,
stable: $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(appear_decl,type,
appear: $i > $i > $i ).
thf(efficient_producers_decl,type,
efficient_producers: $i ).
thf(subpopulations_decl,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
sk4 @ stable,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_11) ).
thf(17,plain,
sk4 @ stable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk3 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_9) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk3 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ sk3 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_7) ).
thf(35,plain,
! [A: $i] :
( ( A @ sk3 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( A @ sk5 @ ( sk4 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( sk4 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_12) ).
thf(18,plain,
! [A: $i] :
( ( A @ sk5 @ ( sk4 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( sk4 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ sk5 @ greater_or_equal ) )
| ~ ( sk4 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_13) ).
thf(19,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ greater_or_equal ) )
| ~ ( sk4 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ~ ( A @ sk5 @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( sk4 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_14) ).
thf(15,plain,
! [A: $i] :
( ~ ( A @ sk5 @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( sk4 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk3 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_8) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk3 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
sk4 @ environment,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_10) ).
thf(16,plain,
sk4 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[29,33,17,27,39,35,18,23,19,15,37,25,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.19/5.47 % Computer : n001.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Sat Sep 26 00:10:47 UTC 2026
% 0.19/5.48 % CPUTime :
% 0.19/5.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.05/6.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/6.26 % [INFO] Parsing done (198ms).
% 1.34/6.27 % [INFO] Running in sequential loop mode.
% 2.05/6.68 % [INFO] eprover registered as external prover.
% 2.05/6.69 % [INFO] Scanning for conjecture ...
% 2.42/6.80 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 2.42/6.84 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.42/6.88 % [INFO] Problem is propositional (TPTP CNF).
% 2.42/6.88 % [INFO] Type checking passed.
% 2.42/6.88 % [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 ...
% 4.24/7.50 % External prover 'e' found a proof!
% 4.24/7.50 % [INFO] Killing All external provers ...
% 4.24/7.51 % Time passed: 1885ms (effective reasoning time: 1228ms)
% 4.24/7.51 % Axioms used in derivation (9): l11_7, mp_first_movers_negative_growth_6, mp_first_movers_negative_growth_2, l11_8, mp_first_movers_negative_growth_3, mp_first_movers_negative_growth_4, l11_9, mp_first_movers_negative_growth_5, mp_first_movers_negative_growth_1
% 4.24/7.51 % No. of inferences in proof: 29
% 4.24/7.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1885 ms resp. 1228 ms w/o parsing
% 4.24/7.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.24/7.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------