TSTP Solution File: MGT032-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT032-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : 600s
% DateTime : Sun Jul 17 22:26:17 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 4 unt; 0 nHn; 19 RR)
% Number of literals : 52 ( 0 equ; 41 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(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(2,axiom,
( ~ stable(u)
| ~ environment(u)
| in_environment(u,sk1(u)) ),
file('MGT032-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ greater_or_equal(v,sk1(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(4,axiom,
environment(sk2),
file('MGT032-2.p',unknown),
[] ).
cnf(5,axiom,
stable(sk2),
file('MGT032-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ in_environment(sk2,u)
| subpopulations(first_movers,efficient_producers,sk2,sk3(u)) ),
file('MGT032-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ in_environment(sk2,u)
| greater_or_equal(sk3(u),u) ),
file('MGT032-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ in_environment(sk2,u)
| ~ selection_favors(efficient_producers,first_movers,sk3(u)) ),
file('MGT032-2.p',unknown),
[] ).
cnf(11,plain,
( ~ stable(sk2)
| ~ environment(sk2)
| ~ in_environment(sk2,u)
| ~ greater_or_equal(sk3(u),sk1(sk2))
| greater(growth_rate(efficient_producers,sk3(u)),growth_rate(first_movers,sk3(u))) ),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.1,3.3')] ).
cnf(12,plain,
( ~ in_environment(sk2,u)
| ~ greater_or_equal(sk3(u),sk1(sk2))
| greater(growth_rate(efficient_producers,sk3(u)),growth_rate(first_movers,sk3(u))) ),
inference(ssi,[status(thm)],[11,5,4]),
[iquote('0:SSi:11.1,11.0,5.0,4.0,5.0,4.0')] ).
cnf(13,plain,
( ~ environment(u)
| ~ in_environment(sk2,v)
| ~ greater_or_equal(sk3(v),sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,u,sk3(v))
| selection_favors(efficient_producers,first_movers,sk3(v)) ),
inference(res,[status(thm),theory(equality)],[12,1]),
[iquote('0:Res:12.2,1.1')] ).
cnf(14,plain,
( ~ environment(u)
| ~ in_environment(sk2,v)
| ~ greater_or_equal(sk3(v),sk1(sk2))
| ~ subpopulations(first_movers,efficient_producers,u,sk3(v)) ),
inference(mrr,[status(thm)],[13,8]),
[iquote('0:MRR:13.4,8.1')] ).
cnf(15,plain,
( ~ environment(sk2)
| ~ in_environment(sk2,u)
| ~ in_environment(sk2,u)
| ~ greater_or_equal(sk3(u),sk1(sk2)) ),
inference(res,[status(thm),theory(equality)],[6,14]),
[iquote('0:Res:6.1,14.3')] ).
cnf(16,plain,
( ~ environment(sk2)
| ~ in_environment(sk2,u)
| ~ greater_or_equal(sk3(u),sk1(sk2)) ),
inference(obv,[status(thm),theory(equality)],[15]),
[iquote('0:Obv:15.1')] ).
cnf(17,plain,
( ~ in_environment(sk2,u)
| ~ greater_or_equal(sk3(u),sk1(sk2)) ),
inference(ssi,[status(thm)],[16,5,4]),
[iquote('0:SSi:16.0,5.0,4.0')] ).
cnf(18,plain,
( ~ in_environment(sk2,sk1(sk2))
| ~ in_environment(sk2,sk1(sk2)) ),
inference(res,[status(thm),theory(equality)],[7,17]),
[iquote('0:Res:7.1,17.1')] ).
cnf(19,plain,
~ in_environment(sk2,sk1(sk2)),
inference(obv,[status(thm),theory(equality)],[18]),
[iquote('0:Obv:18.0')] ).
cnf(20,plain,
( ~ stable(sk2)
| ~ environment(sk2) ),
inference(res,[status(thm),theory(equality)],[2,19]),
[iquote('0:Res:2.2,19.0')] ).
cnf(21,plain,
$false,
inference(ssi,[status(thm)],[20,5,4]),
[iquote('0:SSi:20.1,20.0,5.0,4.0,5.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT032-2 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 9 09:29:17 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.21/0.42 SPASS allocated 75603 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.42 0:00:00.04 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.00 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 5, length 19 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : mp1_high_growth_rates_1 l1_2 l1_3 prove_t1_4 prove_t1_5 prove_t1_6 prove_t1_7 prove_t1_8
% 0.21/0.42
%------------------------------------------------------------------------------