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 v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 2.10s 1.37s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 19 ( 1 unt; 9 typ; 0 def)
% Number of atoms : 37 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 140 ( 2 ~; 0 |; 20 &; 111 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 26 ( 0 ^; 16 !; 10 ?; 26 :)
% 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(1,conjecture,
? [A: $i,B: $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) ).
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(6,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/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
thf(9,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(4,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/sandbox/benchmark/theBenchmark.p',d2) ).
thf(11,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)],[4]) ).
thf(5,axiom,
? [A: $i,B: $i] :
( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( greater_or_equal @ ( growth_rate @ first_movers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).
thf(15,plain,
? [A: $i,B: $i] :
( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( greater_or_equal @ ( growth_rate @ first_movers @ B ) @ zero )
& ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[6,9,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.10 % Command : run_Leo-III %s %d
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Thu May 18 23:40:20 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.63/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.90/0.79 % [INFO] Parsing done (104ms).
% 0.90/0.80 % [INFO] Running in sequential loop mode.
% 1.18/0.99 % [INFO] eprover registered as external prover.
% 1.18/0.99 % [INFO] cvc4 registered as external prover.
% 1.18/1.00 % [INFO] Scanning for conjecture ...
% 1.36/1.05 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.36/1.07 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.36/1.09 % [INFO] Problem is first-order (TPTP FOF).
% 1.55/1.09 % [INFO] Type checking passed.
% 1.55/1.09 % [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 ...
% 2.10/1.37 % External prover 'e' found a proof!
% 2.10/1.37 % [INFO] Killing All external provers ...
% 2.10/1.37 % Time passed: 980ms (effective reasoning time: 573ms)
% 2.10/1.37 % 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)>
% 2.10/1.37 % Axioms used in derivation (3): mp_symmetry_of_subpopulations, d2, a13_star
% 2.10/1.37 % No. of inferences in proof: 10
% 2.10/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 980 ms resp. 573 ms w/o parsing
% 2.10/1.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.10/1.40 % [INFO] Killing All external provers ...
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