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 v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 : Theorem 2.85s 1.65s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 27 ( 3 unt; 11 typ; 0 def)
% Number of atoms : 59 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 231 ( 12 ~; 0 |; 23 &; 176 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
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(outcompetes_type,type,
outcompetes: $i > $i > $i > $o ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(resilience_type,type,
resilience: $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D ) )
=> ( subpopulations @ C @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
thf(13,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D ) )
=> ( subpopulations @ C @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D ) )
=> ( greater_or_equal @ ( growth_rate @ B @ D ) @ zero ) )
<=> ~ ( greater @ zero @ ( growth_rate @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
thf(17,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D ) )
=> ( greater_or_equal @ ( growth_rate @ B @ D ) @ zero ) )
=> ~ ( greater @ zero @ ( growth_rate @ B @ D ) ) )
& ( ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
=> ( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D ) )
=> ( greater_or_equal @ ( growth_rate @ B @ D ) @ zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ D )
& ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
& ( greater @ ( resilience @ C ) @ ( resilience @ B ) ) )
=> ~ ( greater @ zero @ ( growth_rate @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13) ).
thf(31,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ D )
& ~ ( greater @ zero @ ( growth_rate @ B @ D ) )
& ( greater @ ( resilience @ C ) @ ( resilience @ B ) ) )
=> ~ ( greater @ zero @ ( growth_rate @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $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/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(26,plain,
! [A: $i,B: $i,C: $i,D: $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 ) )
& ( ( outcompetes @ C @ B @ D )
=> ( ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
& ( greater @ zero @ ( growth_rate @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
greater @ ( resilience @ efficient_producers ) @ ( resilience @ first_movers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(30,plain,
greater @ ( resilience @ efficient_producers ) @ ( resilience @ first_movers ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
thf(15,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( in_environment @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[9,13,17,31,26,30,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT036+2 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n031.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 : Fri May 19 00:05:26 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/0.96 % [INFO] Parsing done (116ms).
% 1.29/0.96 % [INFO] Running in sequential loop mode.
% 1.61/1.17 % [INFO] eprover registered as external prover.
% 1.61/1.17 % [INFO] cvc4 registered as external prover.
% 1.61/1.18 % [INFO] Scanning for conjecture ...
% 1.77/1.23 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.77/1.26 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.95/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 1.95/1.28 % [INFO] Type checking passed.
% 1.95/1.28 % [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 ...
% 2.85/1.65 % External prover 'e' found a proof!
% 2.85/1.65 % [INFO] Killing All external provers ...
% 2.85/1.65 % Time passed: 1130ms (effective reasoning time: 678ms)
% 2.85/1.65 % 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)>
% 2.85/1.65 % Axioms used in derivation (6): a13, mp_growth_rate_relationships, d2, mp_time_point_occur, a2, mp_symmetry_of_subpopulations
% 2.85/1.65 % No. of inferences in proof: 16
% 2.85/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1130 ms resp. 678 ms w/o parsing
% 3.40/1.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.40/1.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------