%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT026+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 : 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 08:00:38 AM UTC 2026
% Result : Theorem 6.44s 3.71s
% Output : Refutation 6.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 7 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 323 ( 4 ~; 3 |; 43 &; 247 @)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(critical_point_decl,type,
critical_point: $i > $i ).
thf(selection_favors_decl,type,
selection_favors: $i > $i > $i > $o ).
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(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(subpopulation_decl,type,
subpopulation: $i > $i > $i > $o ).
thf(cardinality_at_time_decl,type,
cardinality_at_time: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(appear_decl,type,
appear: $i > $i > $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
& ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
& ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( B
= ( A @ critical_point ) )
& ( A @ environment ) )
=> ( ! [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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( ( B
= ( A @ critical_point ) )
& ( A @ environment ) )
=> ( ! [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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ critical_point @ ( B @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ critical_point @ ( B @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ critical_point @ ( B @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
& ( B @ ( A @ ( first_movers @ subpopulation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
& ( B @ ( A @ ( first_movers @ subpopulation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ cardinality_at_time ) )
= zero )
& ( zero @ ( D @ ( B @ cardinality_at_time ) @ greater ) )
& ( D @ ( A @ ( C @ subpopulation ) ) )
& ( D @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( D @ ( C @ ( B @ selection_favors ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members) ).
thf(21,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ cardinality_at_time ) )
= zero )
& ( zero @ ( D @ ( B @ cardinality_at_time ) @ greater ) )
& ( D @ ( A @ ( C @ subpopulation ) ) )
& ( D @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( D @ ( C @ ( B @ selection_favors ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ environment )
=> ( A @ ( efficient_producers @ appear ) @ ( A @ critical_point @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
thf(32,plain,
! [A: $i] :
( ( A @ environment )
=> ( A @ ( efficient_producers @ appear ) @ ( A @ critical_point @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ greater ) ) )
=> ( B @ ( A @ greater_or_equal ) ) )
& ( ( B @ ( A @ greater_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ growth_rate ) @ ( D @ ( C @ growth_rate ) @ greater ) )
& ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( D @ ( B @ ( C @ selection_favors ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
thf(19,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ growth_rate ) @ ( D @ ( C @ growth_rate ) @ greater ) )
& ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( D @ ( B @ ( C @ selection_favors ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[24,46,13,54,26,28,21,32,34,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.13 % 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
% 0.22/0.49 % Computer : n014.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 00:04:32 UTC 2026
% 0.22/0.50 % CPUTime :
% 0.22/0.50 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
% 1.42/1.37 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.93/1.68 % [INFO] Parsing done (306ms).
% 2.26/1.70 % [INFO] Running in sequential loop mode.
% 3.26/2.33 % [INFO] eprover registered as external prover.
% 3.26/2.34 % [INFO] Scanning for conjecture ...
% 3.56/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.56/2.56 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.75/2.62 % [INFO] Problem is first-order (TPTP FOF).
% 3.75/2.63 % [INFO] Type checking passed.
% 3.75/2.63 % [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 ...
% 6.44/3.70 % External prover 'e' found a proof!
% 6.44/3.70 % [INFO] Killing All external provers ...
% 6.44/3.70 % Time passed: 2988ms (effective reasoning time: 1991ms)
% 6.44/3.70 % 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)>
% 6.44/3.70 % Axioms used in derivation (10): mp1_high_growth_rates, mp_subpopulations, t6, mp_non_empty_fm_and_ep, mp_first_movers_exist, mp_critical_point_after_EP, d1, mp_greater_transitivity, mp_greater_or_equal, mp2_favour_members
% 6.44/3.70 % No. of inferences in proof: 24
% 6.44/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2988 ms resp. 1991 ms w/o parsing
% 6.44/3.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.44/3.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------