TSTP Solution File: MGT023+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 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 22:26:14 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 13 unt; 7 nHn; 25 RR)
% Number of literals : 55 ( 0 equ; 21 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
environment(skc1),
file('MGT023+1.p',unknown),
[] ).
cnf(2,axiom,
stable(skc1),
file('MGT023+1.p',unknown),
[] ).
cnf(3,axiom,
~ in_environment(skc1,critical_point(skc1)),
file('MGT023+1.p',unknown),
[] ).
cnf(4,axiom,
~ greater(growth_rate(efficient_producers,skf3(u)),growth_rate(first_movers,skf3(u))),
file('MGT023+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ stable(u)
| ~ environment(u)
| in_environment(u,skf3(u)) ),
file('MGT023+1.p',unknown),
[] ).
cnf(6,axiom,
~ greater(growth_rate(efficient_producers,skf2(u,v)),growth_rate(first_movers,skf2(u,v))),
file('MGT023+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| equal(v,critical_point(u))
| greater(skf2(v,u),v)
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT023+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ greater(v,skf3(u))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT023+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| equal(v,critical_point(u))
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v))
| subpopulations(first_movers,efficient_producers,u,skf2(v,u)) ),
file('MGT023+1.p',unknown),
[] ).
cnf(11,plain,
( ~ environment(skc1)
| in_environment(skc1,skf3(skc1)) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.1')] ).
cnf(16,plain,
in_environment(skc1,skf3(skc1)),
inference(mrr,[status(thm)],[11,1]),
[iquote('0:MRR:11.0,1.0')] ).
cnf(20,plain,
( ~ environment(skc1)
| equal(skf3(skc1),critical_point(skc1))
| greater(skf2(skf3(skc1),skc1),skf3(skc1))
| greater(growth_rate(efficient_producers,skf3(skc1)),growth_rate(first_movers,skf3(skc1))) ),
inference(res,[status(thm),theory(equality)],[16,7]),
[iquote('0:Res:16.0,7.1')] ).
cnf(22,plain,
( equal(skf3(skc1),critical_point(skc1))
| greater(skf2(skf3(skc1),skc1),skf3(skc1))
| greater(growth_rate(efficient_producers,skf3(skc1)),growth_rate(first_movers,skf3(skc1))) ),
inference(ssi,[status(thm)],[20,2,1]),
[iquote('0:SSi:20.0,2.0,1.0')] ).
cnf(23,plain,
( equal(skf3(skc1),critical_point(skc1))
| greater(skf2(skf3(skc1),skc1),skf3(skc1)) ),
inference(mrr,[status(thm)],[22,4]),
[iquote('0:MRR:22.2,4.0')] ).
cnf(26,plain,
equal(skf3(skc1),critical_point(skc1)),
inference(spt,[spt(split,[position(s1)])],[23]),
[iquote('1:Spt:23.0')] ).
cnf(27,plain,
in_environment(skc1,critical_point(skc1)),
inference(rew,[status(thm),theory(equality)],[26,16]),
[iquote('1:Rew:26.0,16.0')] ).
cnf(31,plain,
$false,
inference(mrr,[status(thm)],[27,3]),
[iquote('1:MRR:27.0,3.0')] ).
cnf(32,plain,
~ equal(skf3(skc1),critical_point(skc1)),
inference(spt,[spt(split,[position(sa)])],[31,26]),
[iquote('1:Spt:31.0,23.0,26.0')] ).
cnf(33,plain,
greater(skf2(skf3(skc1),skc1),skf3(skc1)),
inference(spt,[spt(split,[position(s2)])],[23]),
[iquote('1:Spt:31.0,23.1')] ).
cnf(39,plain,
( ~ environment(skc1)
| equal(skf3(skc1),critical_point(skc1))
| greater(growth_rate(efficient_producers,skf3(skc1)),growth_rate(first_movers,skf3(skc1)))
| subpopulations(first_movers,efficient_producers,skc1,skf2(skf3(skc1),skc1)) ),
inference(res,[status(thm),theory(equality)],[16,9]),
[iquote('0:Res:16.0,9.1')] ).
cnf(41,plain,
( equal(skf3(skc1),critical_point(skc1))
| greater(growth_rate(efficient_producers,skf3(skc1)),growth_rate(first_movers,skf3(skc1)))
| subpopulations(first_movers,efficient_producers,skc1,skf2(skf3(skc1),skc1)) ),
inference(ssi,[status(thm)],[39,2,1]),
[iquote('0:SSi:39.0,2.0,1.0')] ).
cnf(42,plain,
subpopulations(first_movers,efficient_producers,skc1,skf2(skf3(skc1),skc1)),
inference(mrr,[status(thm)],[41,32,4]),
[iquote('1:MRR:41.0,41.1,32.0,4.0')] ).
cnf(46,plain,
( ~ stable(skc1)
| ~ environment(skc1)
| ~ greater(skf2(skf3(skc1),skc1),skf3(skc1))
| greater(growth_rate(efficient_producers,skf2(skf3(skc1),skc1)),growth_rate(first_movers,skf2(skf3(skc1),skc1))) ),
inference(res,[status(thm),theory(equality)],[42,8]),
[iquote('1:Res:42.0,8.3')] ).
cnf(48,plain,
( ~ greater(skf2(skf3(skc1),skc1),skf3(skc1))
| greater(growth_rate(efficient_producers,skf2(skf3(skc1),skc1)),growth_rate(first_movers,skf2(skf3(skc1),skc1))) ),
inference(ssi,[status(thm)],[46,2,1]),
[iquote('1:SSi:46.1,46.0,2.0,1.0,2.0,1.0')] ).
cnf(49,plain,
$false,
inference(mrr,[status(thm)],[48,33,6]),
[iquote('1:MRR:48.0,48.1,33.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 09:40:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 24 clauses, backtracked 6 clauses, performed 1 splits and kept 34 clauses.
% 0.20/0.45 SPASS allocated 97643 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.00 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 3, length 25 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : prove_l5 l12 d1
% 0.20/0.45
%------------------------------------------------------------------------------