%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n006.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 : Unsatisfiable 4.51s 2.58s
% Output : Refutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 6 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 244 ( 34 ~; 40 |; 0 &; 170 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk3_decl,type,
sk3: $i ).
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(greater_decl,type,
greater: $i > $i > $o ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(efficient_producers_decl,type,
efficient_producers: $i ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(subpopulations_decl,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(1,negated_conjecture,
sk3 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_23) ).
thf(10,plain,
sk3 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_21) ).
thf(25,plain,
! [A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_17) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_19) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_18) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( B @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_22) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( B @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
~ ( sk3 @ critical_point @ ( sk3 @ in_environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_25) ).
thf(12,plain,
~ ( sk3 @ critical_point @ ( sk3 @ in_environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
sk3 @ stable,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_24) ).
thf(11,plain,
sk3 @ stable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_20) ).
thf(23,plain,
! [A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,plain,
$false,
inference(e,[status(thm)],[10,25,14,20,17,27,12,11,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.10 % 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
% 0.21/0.47 % Computer : n006.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sat Sep 26 00:04:26 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 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
% 0.97/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.14 % [INFO] Parsing done (163ms).
% 1.50/1.15 % [INFO] Running in sequential loop mode.
% 2.35/1.61 % [INFO] eprover registered as external prover.
% 2.35/1.62 % [INFO] Scanning for conjecture ...
% 2.57/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.57/1.74 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.57/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.57/1.78 % [INFO] Type checking passed.
% 2.57/1.79 % [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 ...
% 4.51/2.57 % External prover 'e' found a proof!
% 4.51/2.57 % [INFO] Killing All external provers ...
% 4.51/2.57 % Time passed: 1951ms (effective reasoning time: 1413ms)
% 4.51/2.58 % Axioms used in derivation (6): d1_19, l12_21, d1_17, l12_20, d1_18, l12_22
% 4.51/2.58 % No. of inferences in proof: 19
% 4.51/2.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1951 ms resp. 1413 ms w/o parsing
% 4.90/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.90/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------