TSTP Solution File: MGT036-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT036-2 : 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 11:35:21 EDT 2023
% Result : Unsatisfiable 2.89s 1.67s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 42 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 77 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 330 ( 48 ~; 48 |; 0 &; 234 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(sk1_type,type,
sk1: $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(sk2_type,type,
sk2: $i ).
thf(outcompetes_type,type,
outcompetes: $i > $i > $i > $o ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(zero_type,type,
zero: $i ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(resilience_type,type,
resilience: $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( greater @ zero @ ( growth_rate @ A @ B ) )
| ~ ( environment @ C )
| ~ ( subpopulations @ A @ D @ C @ B )
| ( greater_or_equal @ ( growth_rate @ A @ B ) @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_6) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( greater @ zero @ ( growth_rate @ A @ B ) )
| ~ ( environment @ C )
| ~ ( subpopulations @ A @ D @ C @ B )
| ( greater_or_equal @ ( growth_rate @ A @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( environment @ A )
| ~ ( greater @ zero @ ( growth_rate @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_3) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( environment @ A )
| ~ ( greater @ zero @ ( growth_rate @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ( subpopulations @ C @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ( subpopulations @ C @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_13) ).
thf(16,plain,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( greater_or_equal @ ( growth_rate @ A @ B ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( greater_or_equal @ ( growth_rate @ A @ B ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
environment @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_12) ).
thf(15,plain,
environment @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subpopulations @ A @ B @ C @ D )
| ~ ( greater @ zero @ ( growth_rate @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_4) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( subpopulations @ A @ B @ C @ D )
| ~ ( greater @ zero @ ( growth_rate @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater @ zero @ ( growth_rate @ C @ B ) )
| ~ ( greater @ ( resilience @ D ) @ ( resilience @ C ) )
| ~ ( greater @ zero @ ( growth_rate @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_11) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( greater @ zero @ ( growth_rate @ C @ B ) )
| ~ ( greater @ ( resilience @ D ) @ ( resilience @ C ) )
| ~ ( greater @ zero @ ( growth_rate @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
outcompetes @ first_movers @ efficient_producers @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_14) ).
thf(17,plain,
outcompetes @ first_movers @ efficient_producers @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_8) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater @ zero @ ( growth_rate @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_9) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( outcompetes @ C @ B @ D )
| ( greater @ zero @ ( growth_rate @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
greater @ ( resilience @ efficient_producers ) @ ( resilience @ first_movers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_10) ).
thf(36,plain,
greater @ ( resilience @ efficient_producers ) @ ( resilience @ first_movers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
| ( outcompetes @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_7) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ B @ C @ A @ D )
| ~ ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
| ( outcompetes @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,plain,
$false,
inference(e,[status(thm)],[20,28,22,18,16,26,15,24,37,17,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : MGT036-2 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 23:46:58 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.86/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (122ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.69/1.21 % [INFO] eprover registered as external prover.
% 1.69/1.21 % [INFO] cvc4 registered as external prover.
% 1.79/1.21 % [INFO] Scanning for conjecture ...
% 1.86/1.27 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.86/1.29 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.86/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.86/1.32 % [INFO] Type checking passed.
% 1.86/1.32 % [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 ...
% 2.89/1.66 % External prover 'e' found a proof!
% 2.89/1.66 % [INFO] Killing All external provers ...
% 2.89/1.67 % Time passed: 1136ms (effective reasoning time: 669ms)
% 2.89/1.67 % 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)>
% 2.89/1.67 % Axioms used in derivation (11): d2_7, mp_growth_rate_relationships_5, d2_9, mp_growth_rate_relationships_6, mp_growth_rate_relationships_3, mp_growth_rate_relationships_4, mp_symmetry_of_subpopulations_1, mp_time_point_occur_2, a13_11, d2_8, a2_10
% 2.89/1.67 % No. of inferences in proof: 29
% 2.89/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1136 ms resp. 669 ms w/o parsing
% 3.12/1.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/1.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------