TSTP Solution File: MGT036-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT036-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 : 600s
% DateTime : Sun Jul 17 22:26:20 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 14 unt; 0 nHn; 32 RR)
% Number of literals : 64 ( 0 equ; 34 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(u)
| ~ subpopulations(v,w,u,x)
| subpopulations(w,v,u,x) ),
file('MGT036-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(u)
| ~ subpopulations(first_movers,efficient_producers,u,v)
| in_environment(u,v) ),
file('MGT036-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ greater(zero,growth_rate(u,v))
| environment(w) ),
file('MGT036-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ greater(zero,growth_rate(u,v))
| subpopulations(u,w,x,v) ),
file('MGT036-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ greater(zero,growth_rate(u,v))
| ~ greater_or_equal(growth_rate(u,v),zero) ),
file('MGT036-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ environment(u)
| ~ outcompetes(v,w,x)
| ~ subpopulations(w,v,u,x)
| greater_or_equal(growth_rate(v,x),zero) ),
file('MGT036-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(u)
| ~ outcompetes(v,w,x)
| ~ subpopulations(w,v,u,x)
| greater(zero,growth_rate(w,x)) ),
file('MGT036-2.p',unknown),
[] ).
cnf(10,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('MGT036-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| ~ greater(resilience(w),resilience(x))
| ~ greater(zero,growth_rate(w,v))
| greater(zero,growth_rate(x,v)) ),
file('MGT036-2.p',unknown),
[] ).
cnf(12,axiom,
environment(sk1),
file('MGT036-2.p',unknown),
[] ).
cnf(13,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('MGT036-2.p',unknown),
[] ).
cnf(14,axiom,
outcompetes(first_movers,efficient_producers,sk2),
file('MGT036-2.p',unknown),
[] ).
cnf(15,plain,
( ~ in_environment(u,v)
| ~ greater(zero,growth_rate(w,v))
| ~ greater(resilience(w),resilience(x))
| greater(zero,growth_rate(x,v)) ),
inference(mrr,[status(thm)],[11,3]),
[iquote('0:MRR:11.0,3.1')] ).
cnf(22,plain,
( ~ environment(u)
| ~ subpopulations(efficient_producers,first_movers,u,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(res,[status(thm),theory(equality)],[14,8]),
[iquote('0:Res:14.0,8.2')] ).
cnf(23,plain,
( ~ environment(u)
| ~ subpopulations(efficient_producers,first_movers,u,sk2)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(res,[status(thm),theory(equality)],[14,9]),
[iquote('0:Res:14.0,9.2')] ).
cnf(28,plain,
( ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(res,[status(thm),theory(equality)],[13,1]),
[iquote('0:Res:13.0,1.1')] ).
cnf(30,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(mrr,[status(thm)],[28,12]),
[iquote('0:MRR:28.0,12.0')] ).
cnf(34,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(res,[status(thm),theory(equality)],[12,23]),
[iquote('0:Res:12.0,23.0')] ).
cnf(35,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(res,[status(thm),theory(equality)],[12,22]),
[iquote('0:Res:12.0,22.0')] ).
cnf(36,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(mrr,[status(thm)],[34,30]),
[iquote('0:MRR:34.0,30.0')] ).
cnf(37,plain,
greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(mrr,[status(thm)],[35,30]),
[iquote('0:MRR:35.0,30.0')] ).
cnf(40,plain,
environment(u),
inference(res,[status(thm),theory(equality)],[36,3]),
[iquote('0:Res:36.0,3.0')] ).
cnf(41,plain,
( ~ subpopulations(first_movers,efficient_producers,u,v)
| in_environment(u,v) ),
inference(mrr,[status(thm)],[2,40]),
[iquote('0:MRR:2.0,40.0')] ).
cnf(42,plain,
( ~ subpopulations(u,v,w,x)
| subpopulations(v,u,w,x) ),
inference(mrr,[status(thm)],[1,40]),
[iquote('0:MRR:1.0,40.0')] ).
cnf(47,plain,
subpopulations(efficient_producers,u,v,sk2),
inference(res,[status(thm),theory(equality)],[36,4]),
[iquote('0:Res:36.0,4.0')] ).
cnf(50,plain,
subpopulations(u,efficient_producers,v,sk2),
inference(res,[status(thm),theory(equality)],[47,42]),
[iquote('0:Res:47.0,42.0')] ).
cnf(51,plain,
in_environment(u,sk2),
inference(res,[status(thm),theory(equality)],[50,41]),
[iquote('0:Res:50.0,41.0')] ).
cnf(55,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(res,[status(thm),theory(equality)],[37,5]),
[iquote('0:Res:37.0,5.1')] ).
cnf(105,plain,
( ~ in_environment(u,sk2)
| ~ greater(resilience(efficient_producers),resilience(v))
| greater(zero,growth_rate(v,sk2)) ),
inference(res,[status(thm),theory(equality)],[36,15]),
[iquote('0:Res:36.0,15.1')] ).
cnf(108,plain,
( ~ greater(resilience(efficient_producers),resilience(u))
| greater(zero,growth_rate(u,sk2)) ),
inference(mrr,[status(thm)],[105,51]),
[iquote('0:MRR:105.0,51.0')] ).
cnf(114,plain,
greater(zero,growth_rate(first_movers,sk2)),
inference(res,[status(thm),theory(equality)],[10,108]),
[iquote('0:Res:10.0,108.0')] ).
cnf(115,plain,
$false,
inference(mrr,[status(thm)],[114,55]),
[iquote('0:MRR:114.0,55.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT036-2 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 08:36:34 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 83 clauses, backtracked 0 clauses, performed 0 splits and kept 69 clauses.
% 0.19/0.41 SPASS allocated 75668 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 5, length 32 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : mp_symmetry_of_subpopulations_1 mp_time_point_occur_2 mp_growth_rate_relationships_3 mp_growth_rate_relationships_4 mp_growth_rate_relationships_5 d2_8 d2_9 a2_10 a13_11 prove_t5_12 prove_t5_13 prove_t5_14
% 0.19/0.41
%------------------------------------------------------------------------------