%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT028+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 : n013.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 : Theorem 4.95s 3.12s
% Output : Refutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 187 ( 2 ~; 0 |; 29 &; 140 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 25 ( 0 ^; 16 !; 9 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
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(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(1,conjecture,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( B @ ( A @ in_environment ) ) )
& ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
thf(12,plain,
! [A: $i] :
( ( ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( B @ ( A @ in_environment ) ) )
& ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) ) )
& ( B @ ( A @ in_environment ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11) ).
thf(20,plain,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) ) )
& ( B @ ( A @ in_environment ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[5,12,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT028+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.11 % 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
% 0.23/0.47 % Computer : n013.cluster.edu
% 0.23/0.47 % Model : x86_64 x86_64
% 0.23/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.47 % Memory : 8046.5625MB
% 0.23/0.47 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sat Sep 26 00:04:21 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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 ...
% 1.78/1.56 % [INFO] Parsing done (223ms).
% 1.78/1.57 % [INFO] Running in sequential loop mode.
% 2.49/1.98 % [INFO] eprover registered as external prover.
% 2.49/1.99 % [INFO] Scanning for conjecture ...
% 2.83/2.18 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 3.02/2.24 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 3.02/2.27 % [INFO] Problem is first-order (TPTP FOF).
% 3.02/2.28 % [INFO] Type checking passed.
% 3.02/2.29 % [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 ...
% 4.95/3.11 % External prover 'e' found a proof!
% 4.95/3.12 % [INFO] Killing All external provers ...
% 4.95/3.12 % Time passed: 2427ms (effective reasoning time: 1541ms)
% 4.95/3.12 % 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)>
% 4.95/3.12 % Axioms used in derivation (2): mp_first_movers_negative_growth, l11
% 4.95/3.12 % No. of inferences in proof: 8
% 4.95/3.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2427 ms resp. 1541 ms w/o parsing
% 5.32/3.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.32/3.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------