%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT027-1 : 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 6.09s 3.60s
% Output : Refutation 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 33 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 384 ( 72 ~; 76 |; 0 &; 236 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk3_decl,type,
sk3: $i ).
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(sk1_decl,type,
sk1: $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(sk2_decl,type,
sk2: $i > $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( first_movers @ ( B @ contracts_from ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_26) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( first_movers @ ( B @ contracts_from ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
sk3 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_37) ).
thf(17,plain,
sk3 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,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_31) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments_29) ).
thf(31,plain,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( first_movers @ ( A @ contracts_from ) )
| ~ ( sk3 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_39) ).
thf(19,plain,
! [A: $i] :
( ~ ( first_movers @ ( A @ contracts_from ) )
| ~ ( sk3 @ ( efficient_producers @ appear ) @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_35) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ sk2 @ greater ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ in_environment ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments_28) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ in_environment ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( first_movers @ ( B @ contracts_from ) )
| ( zero @ ( A @ ( B @ sk1 ) @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_24) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( first_movers @ ( B @ contracts_from ) )
| ( zero @ ( A @ ( B @ sk1 ) @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,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_30) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ greater ) )
| ~ ( C @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,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_34) ).
thf(44,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)],[14]) ).
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_27) ).
thf(27,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(16,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_36) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( A @ sk2 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(2,negated_conjecture,
sk3 @ stable,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_38) ).
thf(18,plain,
sk3 @ stable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_33) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( first_movers @ ( B @ contracts_from ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_25) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( first_movers @ ( B @ contracts_from ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,plain,
$false,
inference(e,[status(thm)],[25,17,35,31,19,46,29,38,21,33,44,27,48,18,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT027-1 : 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
% 0.22/0.61 % Computer : n008.cluster.edu
% 0.22/0.61 % Model : x86_64 x86_64
% 0.22/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.61 % Memory : 8046.5625MB
% 0.22/0.61 % OS : Linux 6.8.0-71-generic
% 0.22/0.61 % CPULimit : 300
% 0.22/0.61 % WCLimit : 300
% 0.22/0.61 % DateTime : Sat Sep 26 00:05:40 UTC 2026
% 0.26/0.61 % CPUTime :
% 0.26/0.61 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
% 1.38/1.46 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.91/1.75 % [INFO] Parsing done (285ms).
% 1.91/1.77 % [INFO] Running in sequential loop mode.
% 2.94/2.37 % [INFO] eprover registered as external prover.
% 2.94/2.38 % [INFO] Scanning for conjecture ...
% 3.33/2.52 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 3.33/2.57 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 3.51/2.62 % [INFO] Problem is propositional (TPTP CNF).
% 3.51/2.63 % [INFO] Type checking passed.
% 3.51/2.64 % [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 ...
% 5.66/3.59 % External prover 'e' found a proof!
% 5.66/3.60 % [INFO] Killing All external provers ...
% 5.66/3.60 % Time passed: 2775ms (effective reasoning time: 1815ms)
% 6.09/3.60 % Axioms used in derivation (13): mp_contracts_from_25, mp_greater_or_equal_31, l10_36, mp_contracts_from_24, mp_long_stable_environments_28, l10_35, mp_non_empty_fm_and_ep_27, mp_greater_or_equal_33, mp_contracts_from_26, mp_greater_transitivity_30, mp_EP_in_stable_environments_29, t6_34, mp_greater_or_equal_32
% 6.09/3.60 % No. of inferences in proof: 33
% 6.09/3.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2775 ms resp. 1815 ms w/o parsing
% 6.09/3.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.09/3.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------