TSTP Solution File: MGT028+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 22:26:16 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 11 unt; 4 nHn; 37 RR)
% Number of literals : 93 ( 0 equ; 60 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
environment(skc1),
file('MGT028+1.p',unknown),
[] ).
cnf(2,axiom,
stable(skc1),
file('MGT028+1.p',unknown),
[] ).
cnf(3,axiom,
~ greater(zero,growth_rate(first_movers,skf4(u))),
file('MGT028+1.p',unknown),
[] ).
cnf(4,axiom,
~ greater(zero,growth_rate(first_movers,skf7(u,v))),
file('MGT028+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ skP0(u)
| greater(skf6(u),appear(efficient_producers,u)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ greater(u,appear(efficient_producers,skc1))
| greater_or_equal(skf4(u),u) ),
file('MGT028+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ stable(u)
| ~ environment(u)
| in_environment(u,skf9(u)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ greater(u,appear(efficient_producers,skc1))
| subpopulations(first_movers,efficient_producers,skc1,skf4(u)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ in_environment(u,v)
| skP0(u)
| greater_or_equal(skf7(v,u),v) ),
file('MGT028+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ skP0(u)
| ~ greater_or_equal(v,skf6(u))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(zero,growth_rate(first_movers,v)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ in_environment(u,v)
| skP0(u)
| subpopulations(first_movers,efficient_producers,u,skf7(v,u)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ greater_or_equal(v,skf9(u))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(zero,growth_rate(first_movers,v)) ),
file('MGT028+1.p',unknown),
[] ).
cnf(15,plain,
( ~ environment(skc1)
| ~ subpopulations(first_movers,efficient_producers,skc1,u)
| ~ greater_or_equal(u,skf9(skc1))
| greater(zero,growth_rate(first_movers,u)) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.1')] ).
cnf(17,plain,
( ~ environment(skc1)
| ~ in_environment(skc1,u)
| greater_or_equal(skf7(u,skc1),u)
| skP0(skc1) ),
inference(res,[status(thm),theory(equality)],[2,9]),
[iquote('0:Res:2.0,9.1')] ).
cnf(18,plain,
( ~ environment(skc1)
| in_environment(skc1,skf9(skc1)) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.1')] ).
cnf(26,plain,
in_environment(skc1,skf9(skc1)),
inference(mrr,[status(thm)],[18,1]),
[iquote('0:MRR:18.0,1.0')] ).
cnf(27,plain,
( ~ in_environment(skc1,u)
| skP0(skc1)
| greater_or_equal(skf7(u,skc1),u) ),
inference(mrr,[status(thm)],[17,1]),
[iquote('0:MRR:17.0,1.0')] ).
cnf(30,plain,
( ~ greater_or_equal(u,skf9(skc1))
| ~ subpopulations(first_movers,efficient_producers,skc1,u)
| greater(zero,growth_rate(first_movers,u)) ),
inference(mrr,[status(thm)],[15,1]),
[iquote('0:MRR:15.0,1.0')] ).
cnf(39,plain,
( ~ skP0(skc1)
| greater_or_equal(skf4(skf6(skc1)),skf6(skc1)) ),
inference(res,[status(thm),theory(equality)],[5,6]),
[iquote('0:Res:5.1,6.0')] ).
cnf(40,plain,
skP0(skc1),
inference(spt,[spt(split,[position(s1)])],[27]),
[iquote('1:Spt:27.1')] ).
cnf(41,plain,
greater_or_equal(skf4(skf6(skc1)),skf6(skc1)),
inference(mrr,[status(thm)],[39,40]),
[iquote('1:MRR:39.0,40.0')] ).
cnf(46,plain,
( ~ greater_or_equal(skf7(u,v),skf9(skc1))
| ~ subpopulations(first_movers,efficient_producers,skc1,skf7(u,v)) ),
inference(res,[status(thm),theory(equality)],[30,4]),
[iquote('0:Res:30.2,4.0')] ).
cnf(47,plain,
( ~ skP0(skc1)
| ~ greater(u,appear(efficient_producers,skc1))
| ~ greater_or_equal(skf4(u),skf6(skc1))
| greater(zero,growth_rate(first_movers,skf4(u))) ),
inference(res,[status(thm),theory(equality)],[8,10]),
[iquote('0:Res:8.1,10.2')] ).
cnf(48,plain,
( ~ greater(u,appear(efficient_producers,skc1))
| ~ greater_or_equal(skf4(u),skf6(skc1))
| greater(zero,growth_rate(first_movers,skf4(u))) ),
inference(ssi,[status(thm)],[47,2,1,40]),
[iquote('1:SSi:47.0,2.0,1.0,40.0')] ).
cnf(49,plain,
( ~ greater(u,appear(efficient_producers,skc1))
| ~ greater_or_equal(skf4(u),skf6(skc1)) ),
inference(mrr,[status(thm)],[48,3]),
[iquote('1:MRR:48.2,3.0')] ).
cnf(50,plain,
( ~ skP0(skc1)
| ~ greater_or_equal(skf4(skf6(skc1)),skf6(skc1)) ),
inference(res,[status(thm),theory(equality)],[5,49]),
[iquote('1:Res:5.1,49.0')] ).
cnf(51,plain,
~ greater_or_equal(skf4(skf6(skc1)),skf6(skc1)),
inference(ssi,[status(thm)],[50,2,1,40]),
[iquote('1:SSi:50.0,2.0,1.0,40.0')] ).
cnf(52,plain,
$false,
inference(mrr,[status(thm)],[51,41]),
[iquote('1:MRR:51.0,41.0')] ).
cnf(53,plain,
~ skP0(skc1),
inference(spt,[spt(split,[position(sa)])],[52,40]),
[iquote('1:Spt:52.0,27.1,40.0')] ).
cnf(54,plain,
( ~ in_environment(skc1,u)
| greater_or_equal(skf7(u,skc1),u) ),
inference(spt,[spt(split,[position(s2)])],[27]),
[iquote('1:Spt:52.0,27.0,27.2')] ).
cnf(57,plain,
( ~ stable(skc1)
| ~ environment(skc1)
| ~ in_environment(skc1,u)
| ~ greater_or_equal(skf7(u,skc1),skf9(skc1))
| skP0(skc1) ),
inference(res,[status(thm),theory(equality)],[11,46]),
[iquote('0:Res:11.4,46.1')] ).
cnf(59,plain,
( ~ in_environment(skc1,u)
| ~ greater_or_equal(skf7(u,skc1),skf9(skc1))
| skP0(skc1) ),
inference(ssi,[status(thm)],[57,2,1]),
[iquote('0:SSi:57.1,57.0,2.0,1.0,2.0,1.0')] ).
cnf(60,plain,
( ~ in_environment(skc1,u)
| ~ greater_or_equal(skf7(u,skc1),skf9(skc1)) ),
inference(mrr,[status(thm)],[59,53]),
[iquote('1:MRR:59.2,53.0')] ).
cnf(64,plain,
( ~ stable(skc1)
| ~ environment(skc1)
| ~ in_environment(skc1,skf9(skc1))
| ~ in_environment(skc1,skf9(skc1))
| skP0(skc1) ),
inference(res,[status(thm),theory(equality)],[9,60]),
[iquote('1:Res:9.4,60.1')] ).
cnf(68,plain,
( ~ stable(skc1)
| ~ environment(skc1)
| ~ in_environment(skc1,skf9(skc1))
| skP0(skc1) ),
inference(obv,[status(thm),theory(equality)],[64]),
[iquote('1:Obv:64.2')] ).
cnf(69,plain,
( ~ in_environment(skc1,skf9(skc1))
| skP0(skc1) ),
inference(ssi,[status(thm)],[68,2,1]),
[iquote('1:SSi:68.1,68.0,2.0,1.0,2.0,1.0')] ).
cnf(70,plain,
$false,
inference(mrr,[status(thm)],[69,26,53]),
[iquote('1:MRR:69.0,69.1,26.0,53.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.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 09:36:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 28 clauses, backtracked 6 clauses, performed 1 splits and kept 39 clauses.
% 0.18/0.43 SPASS allocated 97681 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 4, length 37 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : prove_l10 l11 mp_first_movers_negative_growth
% 0.18/0.43
%------------------------------------------------------------------------------