TSTP Solution File: MGT023-2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT023-2 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Fri May 19 11:35:16 EDT 2023
% Result : Unsatisfiable 3.07s 1.77s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 50 ( 7 unt; 15 typ; 0 def)
% Number of atoms : 137 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 658 ( 88 ~; 102 |; 0 &; 468 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(sk5_type,type,
sk5: $i ).
thf(stable_type,type,
stable: $i > $o ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(critical_point_type,type,
critical_point: $i > $i ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(first_movers_type,type,
first_movers: $i ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ( in_environment @ A @ ( sk2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_20) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ( in_environment @ A @ ( sk2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ( in_environment @ A @ ( sk2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_19) ).
thf(22,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ( in_environment @ A @ ( sk2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( sk4 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_31) ).
thf(49,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( sk4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
environment @ sk5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_33) ).
thf(18,plain,
environment @ sk5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( greater @ ( sk3 @ B @ A ) @ B )
| ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_29) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( greater @ ( sk3 @ B @ A ) @ B )
| ( B
= ( critical_point @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
~ ( in_environment @ sk5 @ ( critical_point @ sk5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_35) ).
thf(20,plain,
~ ( in_environment @ sk5 @ ( critical_point @ sk5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk3 @ B @ A ) ) )
| ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_30) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk3 @ B @ A ) ) )
| ( B
= ( critical_point @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater @ C @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_22) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater @ C @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater @ C @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_27) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater @ C @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater @ C @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_24) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ C )
| ~ ( greater @ C @ ( sk2 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( in_environment @ A @ ( sk2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_25) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ( in_environment @ A @ ( sk2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk3 @ B @ A ) )
| ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_28) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk3 @ B @ A ) )
| ( B
= ( critical_point @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_21) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk1 @ B @ A ) )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_26) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk1 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk1 @ B @ A ) ) )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_23) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater_or_equal @ ( sk1 @ B @ A ) @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater_or_equal @ B @ ( sk4 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_32) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater_or_equal @ B @ ( sk4 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,negated_conjecture,
stable @ sk5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_34) ).
thf(19,plain,
stable @ sk5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[24,22,49,18,43,20,46,28,38,32,34,40,26,36,30,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT023-2 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 23:48:00 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.05 % [INFO] Parsing done (138ms).
% 1.29/1.06 % [INFO] Running in sequential loop mode.
% 1.77/1.25 % [INFO] eprover registered as external prover.
% 1.77/1.25 % [INFO] cvc4 registered as external prover.
% 1.77/1.26 % [INFO] Scanning for conjecture ...
% 1.97/1.32 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.97/1.33 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.97/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/1.37 % [INFO] Type checking passed.
% 2.21/1.37 % [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 ...
% 3.07/1.77 % External prover 'e' found a proof!
% 3.07/1.77 % [INFO] Killing All external provers ...
% 3.07/1.77 % Time passed: 1242ms (effective reasoning time: 705ms)
% 3.07/1.77 % 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)>
% 3.07/1.77 % Axioms used in derivation (14): mp_earliest_time_growth_rate_exceeds_25, l1_32, l1_31, mp_earliest_time_growth_rate_exceeds_24, d1_28, mp_earliest_time_growth_rate_exceeds_19, d1_29, mp_earliest_time_growth_rate_exceeds_23, mp_earliest_time_growth_rate_exceeds_21, mp_earliest_time_growth_rate_exceeds_26, d1_30, mp_earliest_time_growth_rate_exceeds_22, mp_earliest_time_growth_rate_exceeds_27, mp_earliest_time_growth_rate_exceeds_20
% 3.07/1.77 % No. of inferences in proof: 35
% 3.07/1.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1242 ms resp. 705 ms w/o parsing
% 3.53/1.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.53/1.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------