%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT036+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 : n016.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 08:00:40 AM UTC 2026
% Result : Theorem 2.61s 1.49s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 231 ( 12 ~; 0 |; 23 &; 176 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 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 : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% 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(outcompetes_decl,type,
outcompetes: $i > $i > $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
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(resilience_decl,type,
resilience: $i > $i ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( A @ ( first_movers @ ( efficient_producers @ subpopulations ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( A @ ( first_movers @ ( efficient_producers @ subpopulations ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ~ ( B @ ( efficient_producers @ ( first_movers @ outcompetes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ~ ( B @ ( efficient_producers @ ( first_movers @ outcompetes ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ~ ( B @ ( efficient_producers @ ( first_movers @ outcompetes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(35,plain,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( zero @ ( D @ ( B @ growth_rate ) @ greater_or_equal ) ) )
<=> ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
thf(18,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
=> ( ( ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( zero @ ( D @ ( B @ growth_rate ) @ greater_or_equal ) ) ) )
& ( ( ( ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( zero @ ( D @ ( B @ growth_rate ) @ greater_or_equal ) ) )
=> ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,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(16,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)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) ) )
<=> ( D @ ( B @ ( C @ outcompetes ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(28,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( D @ ( B @ ( C @ outcompetes ) ) )
=> ( ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) ) ) )
& ( ( ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) ) )
=> ( D @ ( B @ ( C @ outcompetes ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ resilience @ ( C @ resilience @ greater ) )
& ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
& ( D @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ~ ( D @ ( C @ growth_rate ) @ ( zero @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
thf(33,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ resilience @ ( C @ resilience @ greater ) )
& ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
& ( D @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ~ ( D @ ( C @ growth_rate ) @ ( zero @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(39,plain,
$false,
inference(e,[status(thm)],[14,9,35,18,16,28,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % 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
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 00:10:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.72/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.98/0.80 % [INFO] Parsing done (99ms).
% 0.98/0.81 % [INFO] Running in sequential loop mode.
% 1.22/1.01 % [INFO] eprover registered as external prover.
% 1.22/1.01 % [INFO] Scanning for conjecture ...
% 1.51/1.06 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.51/1.08 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.51/1.10 % [INFO] Problem is first-order (TPTP FOF).
% 1.51/1.10 % [INFO] Type checking passed.
% 1.51/1.10 % [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 ...
% 2.61/1.48 % External prover 'e' found a proof!
% 2.61/1.48 % [INFO] Killing All external provers ...
% 2.61/1.48 % Time passed: 1003ms (effective reasoning time: 676ms)
% 2.61/1.49 % 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)>
% 2.61/1.49 % Axioms used in derivation (6): mp_symmetry_of_FM_and_EP, mp_growth_rate_relationships, d2, mp_time_point_occur, a12, a2
% 2.61/1.49 % No. of inferences in proof: 16
% 2.61/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1003 ms resp. 676 ms w/o parsing
% 3.02/1.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.02/1.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------