TSTP Solution File: MGT023+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 : Theorem 2.94s 1.68s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 20 ( 1 unt; 10 typ; 0 def)
% Number of atoms : 56 ( 2 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 213 ( 6 ~; 0 |; 29 &; 161 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 25 ( 0 ^; 19 !; 6 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
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(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(1,conjecture,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ( in_environment @ A @ ( critical_point @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ( in_environment @ A @ ( critical_point @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ( in_environment @ A @ ( critical_point @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( ( environment @ A )
& ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
thf(10,plain,
! [A: $i] :
( ( ( environment @ A )
& ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) )
=> ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) )
=> ( B
= ( critical_point @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
thf(25,plain,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
$false,
inference(e,[status(thm)],[6,10,18,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT023+2 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n001.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 00:10:36 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.98/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (130ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 1.68/1.18 % [INFO] eprover registered as external prover.
% 1.68/1.18 % [INFO] cvc4 registered as external prover.
% 1.68/1.19 % [INFO] Scanning for conjecture ...
% 1.87/1.24 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.87/1.26 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.87/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.28 % [INFO] Type checking passed.
% 1.87/1.29 % [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 ...
% 2.94/1.68 % External prover 'e' found a proof!
% 2.94/1.68 % [INFO] Killing All external provers ...
% 2.94/1.68 % Time passed: 1179ms (effective reasoning time: 694ms)
% 2.94/1.68 % 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)>
% 2.94/1.68 % Axioms used in derivation (3): mp_earliest_time_growth_rate_exceeds, d1, l1
% 2.94/1.68 % No. of inferences in proof: 10
% 2.94/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1179 ms resp. 694 ms w/o parsing
% 3.22/1.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.22/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------