TSTP Solution File: MGT032+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 22:26:17 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 5 unt; 0 nHn; 19 RR)
% Number of literals : 51 ( 0 equ; 40 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
environment(skc1),
file('MGT032+2.p',unknown),
[] ).
cnf(2,axiom,
stable(skc1),
file('MGT032+2.p',unknown),
[] ).
cnf(3,axiom,
~ selection_favors(efficient_producers,first_movers,skf2(u)),
file('MGT032+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ in_environment(skc1,u)
| greater_or_equal(skf2(u),u) ),
file('MGT032+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ in_environment(skc1,u)
| subpopulations(first_movers,efficient_producers,skc1,skf2(u)) ),
file('MGT032+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ stable(u)
| ~ environment(u)
| in_environment(u,skf4(u)) ),
file('MGT032+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(u)
| ~ greater(growth_rate(v,w),growth_rate(x,w))
| ~ subpopulations(x,v,u,w)
| selection_favors(v,x,w) ),
file('MGT032+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ greater_or_equal(v,skf4(u))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT032+2.p',unknown),
[] ).
cnf(11,plain,
( ~ stable(skc1)
| ~ environment(skc1)
| ~ in_environment(skc1,u)
| ~ greater_or_equal(skf2(u),skf4(skc1))
| greater(growth_rate(efficient_producers,skf2(u)),growth_rate(first_movers,skf2(u))) ),
inference(res,[status(thm),theory(equality)],[5,8]),
[iquote('0:Res:5.1,8.3')] ).
cnf(12,plain,
( ~ in_environment(skc1,u)
| ~ greater_or_equal(skf2(u),skf4(skc1))
| greater(growth_rate(efficient_producers,skf2(u)),growth_rate(first_movers,skf2(u))) ),
inference(ssi,[status(thm)],[11,2,1]),
[iquote('0:SSi:11.1,11.0,2.0,1.0,2.0,1.0')] ).
cnf(13,plain,
( ~ environment(u)
| ~ in_environment(skc1,v)
| ~ greater_or_equal(skf2(v),skf4(skc1))
| ~ subpopulations(first_movers,efficient_producers,u,skf2(v))
| selection_favors(efficient_producers,first_movers,skf2(v)) ),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.2,7.1')] ).
cnf(14,plain,
( ~ environment(u)
| ~ in_environment(skc1,v)
| ~ greater_or_equal(skf2(v),skf4(skc1))
| ~ subpopulations(first_movers,efficient_producers,u,skf2(v)) ),
inference(mrr,[status(thm)],[13,3]),
[iquote('0:MRR:13.4,3.0')] ).
cnf(15,plain,
( ~ environment(skc1)
| ~ in_environment(skc1,u)
| ~ in_environment(skc1,u)
| ~ greater_or_equal(skf2(u),skf4(skc1)) ),
inference(res,[status(thm),theory(equality)],[5,14]),
[iquote('0:Res:5.1,14.3')] ).
cnf(16,plain,
( ~ environment(skc1)
| ~ in_environment(skc1,u)
| ~ greater_or_equal(skf2(u),skf4(skc1)) ),
inference(obv,[status(thm),theory(equality)],[15]),
[iquote('0:Obv:15.1')] ).
cnf(17,plain,
( ~ in_environment(skc1,u)
| ~ greater_or_equal(skf2(u),skf4(skc1)) ),
inference(ssi,[status(thm)],[16,2,1]),
[iquote('0:SSi:16.0,2.0,1.0')] ).
cnf(18,plain,
( ~ in_environment(skc1,skf4(skc1))
| ~ in_environment(skc1,skf4(skc1)) ),
inference(res,[status(thm),theory(equality)],[4,17]),
[iquote('0:Res:4.1,17.1')] ).
cnf(19,plain,
~ in_environment(skc1,skf4(skc1)),
inference(obv,[status(thm),theory(equality)],[18]),
[iquote('0:Obv:18.0')] ).
cnf(20,plain,
( ~ stable(skc1)
| ~ environment(skc1) ),
inference(res,[status(thm),theory(equality)],[6,19]),
[iquote('0:Res:6.2,19.0')] ).
cnf(21,plain,
$false,
inference(ssi,[status(thm)],[20,2,1]),
[iquote('0:SSi:20.1,20.0,2.0,1.0,2.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% 0.09/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 11:26:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.18/0.42 SPASS allocated 97603 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.00 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 5, length 19 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : prove_t1 l1 mp1_high_growth_rates
% 0.18/0.42
%------------------------------------------------------------------------------