%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT027+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n019.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 4.18s 7.52s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 3 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 262 ( 2 ~; 3 |; 41 &; 192 @)
% ( 1 <=>; 23 =>; 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 : 15 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 44 ( 0 ^; 39 !; 5 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(stable_decl,type,
stable: $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(appear_decl,type,
appear: $i > $i > $i ).
thf(efficient_producers_decl,type,
efficient_producers: $i ).
thf(contracts_from_decl,type,
contracts_from: $i > $i > $o ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(in_environment_decl,type,
in_environment: $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(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(subpopulations_decl,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(6,axiom,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ( A @ ( efficient_producers @ appear ) @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
thf(25,plain,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ( A @ ( efficient_producers @ appear ) @ ( A @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater_or_equal ) )
<=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
thf(29,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)],[8]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
thf(21,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)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10) ).
thf(41,plain,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',t6) ).
thf(39,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)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( zero @ ( C @ ( first_movers @ cardinality_at_time ) @ greater ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( B @ ( A @ in_environment ) )
& ( A @ stable )
& ( A @ environment ) )
=> ( first_movers @ ( B @ contracts_from ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ greater_or_equal ) )
& ( zero @ ( C @ ( first_movers @ cardinality_at_time ) @ greater ) ) )
=> ( C @ ( first_movers @ growth_rate ) @ ( zero @ greater ) ) )
& ( B @ ( A @ in_environment ) )
& ( A @ stable )
& ( A @ environment ) )
=> ( first_movers @ ( B @ contracts_from ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ( first_movers @ ( B @ contracts_from ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ( first_movers @ ( B @ contracts_from ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i] :
( ( ( A @ stable )
& ( A @ environment ) )
=> ? [B: $i] :
( ( first_movers @ ( B @ contracts_from ) )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ stable )
& ( A @ environment ) )
=> ( C @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments) ).
thf(23,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ stable )
& ( A @ environment ) )
=> ( C @ ( A @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(45,plain,
$false,
inference(e,[status(thm)],[25,29,21,41,27,39,16,11,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT027+1 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.14/5.41 % Computer : n019.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 00:05:09 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 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
% 0.19/6.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/6.21 % [INFO] Parsing done (198ms).
% 1.38/6.22 % [INFO] Running in sequential loop mode.
% 2.05/6.63 % [INFO] eprover registered as external prover.
% 2.05/6.64 % [INFO] Scanning for conjecture ...
% 2.28/6.74 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.28/6.78 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.44/6.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.44/6.83 % [INFO] Type checking passed.
% 2.44/6.83 % [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 ...
% 4.18/7.52 % External prover 'e' found a proof!
% 4.18/7.52 % [INFO] Killing All external provers ...
% 4.18/7.52 % Time passed: 1959ms (effective reasoning time: 1292ms)
% 4.18/7.52 % 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)>
% 4.18/7.52 % Axioms used in derivation (8): t6, mp_contracts_from, mp_EP_in_stable_environments, l10, mp_greater_transitivity, mp_greater_or_equal, mp_long_stable_environments, mp_non_empty_fm_and_ep
% 4.18/7.52 % No. of inferences in proof: 20
% 4.18/7.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1959 ms resp. 1292 ms w/o parsing
% 4.18/7.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.18/7.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------