%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT026-1 : 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 : n008.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 : Unsatisfiable 5.46s 3.08s
% Output : Refutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 10 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 394 ( 70 ~; 68 |; 0 &; 256 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
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(13,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_36) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_40) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ greater ) )
| ~ ( C @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_35) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ greater ) )
| ~ ( C @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_33) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ selection_favors ) ) )
| ( ( C @ ( D @ cardinality_at_time ) )
!= zero )
| ~ ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
| ~ ( C @ ( A @ ( D @ subpopulation ) ) )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members_29) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ selection_favors ) ) )
| ( ( C @ ( D @ cardinality_at_time ) )
!= zero )
| ~ ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
| ~ ( C @ ( A @ ( D @ subpopulation ) ) )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_41) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
sk1 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_42) ).
thf(19,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ selection_favors ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( D @ ( C @ growth_rate ) @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_28) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ selection_favors ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( D @ ( C @ growth_rate ) @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ critical_point @ greater_or_equal ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP_34) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ critical_point @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
sk2 @ ( sk1 @ in_environment ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_43) ).
thf(20,plain,
sk2 @ ( sk1 @ in_environment ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_38) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_30) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,negated_conjecture,
sk1 @ critical_point @ ( sk2 @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_44) ).
thf(21,plain,
sk1 @ critical_point @ ( sk2 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( first_movers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_32) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( first_movers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,negated_conjecture,
~ ( sk2 @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_45) ).
thf(22,plain,
~ ( sk2 @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_37) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_39) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist_31) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[41,54,39,35,26,58,19,24,37,20,46,29,21,33,22,44,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT026-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.20/0.48 % Computer : n008.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.48 % CPULimit : 300
% 0.20/0.48 % WCLimit : 300
% 0.20/0.48 % DateTime : Sat Sep 26 00:05:25 UTC 2026
% 0.20/0.49 % CPUTime :
% 0.20/0.49 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
% 0.97/1.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.67/1.32 % [INFO] Parsing done (259ms).
% 1.67/1.34 % [INFO] Running in sequential loop mode.
% 2.55/1.89 % [INFO] eprover registered as external prover.
% 2.78/1.90 % [INFO] Scanning for conjecture ...
% 2.78/2.05 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 3.01/2.10 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 3.22/2.16 % [INFO] Problem is propositional (TPTP CNF).
% 3.22/2.18 % [INFO] Type checking passed.
% 3.22/2.18 % [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 ...
% 5.46/3.07 % External prover 'e' found a proof!
% 5.46/3.07 % [INFO] Killing All external provers ...
% 5.46/3.07 % Time passed: 2446ms (effective reasoning time: 1722ms)
% 5.46/3.08 % Axioms used in derivation (14): mp_first_movers_exist_31, mp_greater_or_equal_38, mp_subpopulations_33, mp_non_empty_fm_and_ep_30, mp_greater_or_equal_36, mp_subpopulations_32, mp1_high_growth_rates_28, mp_greater_or_equal_37, mp2_favour_members_29, t6_41, mp_greater_transitivity_35, mp_critical_point_after_EP_34, d1_40, d1_39
% 5.46/3.08 % No. of inferences in proof: 37
% 5.46/3.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2446 ms resp. 1722 ms w/o parsing
% 5.68/3.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.68/3.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------