TSTP Solution File: MGT027-1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : MGT027-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:41:23 EDT 2024
% Result : Unsatisfiable 4.41s 2.67s
% Output : Refutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 49 ( 5 unt; 16 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 : 23 ( 23 >; 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_type,type,
environment: $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(stable_type,type,
stable: $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(appear_type,type,
appear: $i > $i > $i ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(contracts_from_type,type,
contracts_from: $i > $i > $o ).
thf(first_movers_type,type,
first_movers: $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(cardinality_at_time_type,type,
cardinality_at_time: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( contracts_from @ B @ first_movers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_26) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( contracts_from @ B @ first_movers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
environment @ sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_37) ).
thf(17,plain,
environment @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( greater @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_31) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( greater @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( appear @ efficient_producers @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments_29) ).
thf(31,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( appear @ efficient_producers @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk3 ) )
| ~ ( contracts_from @ A @ first_movers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_39) ).
thf(19,plain,
! [A: $i] :
( ~ ( greater @ A @ ( appear @ efficient_producers @ sk3 ) )
| ~ ( contracts_from @ A @ first_movers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_35) ).
thf(46,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( greater @ ( sk2 @ A ) @ ( appear @ efficient_producers @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ C @ B )
| ( in_environment @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments_28) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ C @ B )
| ( in_environment @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( greater_or_equal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( greater_or_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( greater @ ( cardinality_at_time @ first_movers @ ( sk1 @ B @ A ) ) @ zero )
| ( contracts_from @ B @ first_movers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_24) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( greater @ ( cardinality_at_time @ first_movers @ ( sk1 @ B @ A ) ) @ zero )
| ( contracts_from @ B @ first_movers ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ~ ( greater @ B @ C )
| ( greater @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_30) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ~ ( greater @ B @ C )
| ( greater @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater_or_equal @ B @ ( appear @ efficient_producers @ A ) )
| ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_34) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater_or_equal @ B @ ( appear @ efficient_producers @ A ) )
| ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero )
| ( subpopulations @ first_movers @ efficient_producers @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_27) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
| ~ ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero )
| ( subpopulations @ first_movers @ efficient_producers @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater_or_equal @ B @ ( sk2 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_36) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater_or_equal @ B @ ( sk2 @ A ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(2,negated_conjecture,
stable @ sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9_38) ).
thf(18,plain,
stable @ sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( greater_or_equal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_33) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( greater_or_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ( contracts_from @ B @ first_movers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from_25) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ( contracts_from @ B @ first_movers ) ),
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
% 0.02/0.11 % Problem : MGT027-1 : TPTP v8.2.0. Released v2.4.0.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 00:01:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.18/1.08 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.53/1.28 % [INFO] Parsing done (194ms).
% 1.53/1.29 % [INFO] Running in sequential loop mode.
% 2.18/1.72 % [INFO] eprover registered as external prover.
% 2.18/1.72 % [INFO] cvc4 registered as external prover.
% 2.18/1.73 % [INFO] Scanning for conjecture ...
% 2.49/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.49/1.88 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.69/1.92 % [INFO] Problem is propositional (TPTP CNF).
% 2.69/1.93 % [INFO] Type checking passed.
% 2.69/1.94 % [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 ...
% 4.11/2.61 % External prover 'e' found a proof!
% 4.11/2.61 % [INFO] Killing All external provers ...
% 4.40/2.66 % Time passed: 2149ms (effective reasoning time: 1365ms)
% 4.41/2.67 % 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
% 4.41/2.67 % No. of inferences in proof: 33
% 4.41/2.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2149 ms resp. 1365 ms w/o parsing
% 4.51/2.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.51/2.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------