TSTP Solution File: MGT036-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT036-3 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 2.60s 1.63s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 30 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 198 ( 30 ~; 28 |; 0 &; 140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% 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(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(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star_9) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( outcompetes @ first_movers @ efficient_producers @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,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_2) ).
thf(14,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)],[3]) ).
thf(6,axiom,
environment @ sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_5) ).
thf(20,plain,
environment @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_6) ).
thf(21,plain,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
greater_or_equal @ ( growth_rate @ first_movers @ sk2 ) @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_7) ).
thf(22,plain,
greater_or_equal @ ( growth_rate @ first_movers @ sk2 ) @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,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(12,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)],[2]) ).
thf(5,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_4) ).
thf(18,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)],[5]) ).
thf(4,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_3) ).
thf(16,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)],[4]) ).
thf(9,axiom,
greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_8) ).
thf(23,plain,
greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,14,20,21,22,12,18,16,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT036-3 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.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 23:56:21 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.02 % [INFO] Parsing done (126ms).
% 1.25/1.02 % [INFO] Running in sequential loop mode.
% 1.72/1.23 % [INFO] eprover registered as external prover.
% 1.72/1.23 % [INFO] cvc4 registered as external prover.
% 1.72/1.24 % [INFO] Scanning for conjecture ...
% 1.84/1.29 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.84/1.32 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.84/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.33 % [INFO] Type checking passed.
% 1.84/1.33 % [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 ...
% 2.60/1.63 % External prover 'e' found a proof!
% 2.60/1.63 % [INFO] Killing All external provers ...
% 2.60/1.63 % Time passed: 1108ms (effective reasoning time: 605ms)
% 2.60/1.63 % 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)>
% 2.60/1.63 % Axioms used in derivation (8): d2_3, mp_symmetry_of_subpopulations_1, a13_star_6, a13_star_8, d2_4, a13_star_5, a13_star_7, d2_2
% 2.60/1.63 % No. of inferences in proof: 19
% 2.60/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1108 ms resp. 605 ms w/o parsing
% 3.00/1.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.00/1.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------