%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT036-3 : 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 : n014.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 08:00:41 AM UTC 2026
% Result : Unsatisfiable 3.34s 2.28s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 198 ( 30 ~; 28 |; 0 &; 140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% 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(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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( efficient_producers @ ( first_movers @ outcompetes ) ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_star_9) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( efficient_producers @ ( first_movers @ outcompetes ) ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_2) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
sk1 @ environment,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star_5) ).
thf(20,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star_6) ).
thf(21,plain,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
zero @ ( sk2 @ ( first_movers @ growth_rate ) @ greater_or_equal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star_7) ).
thf(22,plain,
zero @ ( sk2 @ ( first_movers @ growth_rate ) @ greater_or_equal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ ( C @ subpopulations ) ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ ( C @ subpopulations ) ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_4) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_3) ).
thf(16,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
sk2 @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star_8) ).
thf(23,plain,
sk2 @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,14,20,21,22,12,18,16,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-3 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n014.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 00:06:32 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.17 % [INFO] Parsing done (188ms).
% 1.25/1.19 % [INFO] Running in sequential loop mode.
% 1.82/1.59 % [INFO] eprover registered as external prover.
% 2.01/1.60 % [INFO] Scanning for conjecture ...
% 2.18/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.18/1.74 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.18/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.18/1.76 % [INFO] Type checking passed.
% 2.18/1.77 % [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 ...
% 3.34/2.28 % External prover 'e' found a proof!
% 3.34/2.28 % [INFO] Killing All external provers ...
% 3.34/2.28 % Time passed: 1741ms (effective reasoning time: 1086ms)
% 3.34/2.28 % Axioms used in derivation (8): d2_3, mp_symmetry_of_subpopulations_1, a13_star_6, a13_star_8, d2_4, a13_star_5, a13_star_7, d2_2
% 3.34/2.28 % No. of inferences in proof: 19
% 3.34/2.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1741 ms resp. 1086 ms w/o parsing
% 3.64/2.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.64/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------