%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT023+2 : 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 : n011.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 3.77s 2.42s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 2 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 213 ( 6 ~; 0 |; 29 &; 161 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 25 ( 0 ^; 19 !; 6 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(stable_decl,type,
stable: $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(critical_point_decl,type,
critical_point: $i > $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(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ( A @ critical_point @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ( A @ critical_point @ ( A @ in_environment ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ( A @ critical_point @ ( A @ in_environment ) ) ),
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 ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ( B @ ( A @ in_environment ) ) )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
& ( B @ ( A @ in_environment ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
thf(11,plain,
! [A: $i] :
( ( ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ( B @ ( A @ in_environment ) ) )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
& ( B @ ( A @ in_environment ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ greater ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ( B @ ( A @ in_environment ) )
& ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
& ( A @ environment ) )
=> ( B
= ( A @ critical_point ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ greater ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ( B @ ( A @ in_environment ) )
& ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
& ( A @ environment ) )
=> ( B
= ( A @ critical_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,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 ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ( B @ ( A @ in_environment ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
thf(28,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 ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) ) )
& ( B @ ( A @ in_environment ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[6,11,20,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.13/0.41 % Computer : n011.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 00:04:44 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.87/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.20 % [INFO] Parsing done (193ms).
% 1.41/1.22 % [INFO] Running in sequential loop mode.
% 2.08/1.62 % [INFO] eprover registered as external prover.
% 2.08/1.63 % [INFO] Scanning for conjecture ...
% 2.28/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.28/1.77 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.48/1.80 % [INFO] Problem is first-order (TPTP FOF).
% 2.48/1.81 % [INFO] Type checking passed.
% 2.48/1.81 % [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 ...
% 3.77/2.42 % External prover 'e' found a proof!
% 3.77/2.42 % [INFO] Killing All external provers ...
% 3.77/2.42 % Time passed: 1859ms (effective reasoning time: 1195ms)
% 3.77/2.42 % 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)>
% 3.77/2.42 % Axioms used in derivation (3): mp_earliest_time_growth_rate_exceeds, d1, l1
% 3.77/2.42 % No. of inferences in proof: 10
% 3.77/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1859 ms resp. 1195 ms w/o parsing
% 3.77/2.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.77/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------