%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:19:48 AM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 31 ( 7 unt; 13 nHn; 31 RR)
% Number of literals : 112 ( 0 equ; 69 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
environment(skc1),
file('MGT023+2.p',unknown),
[] ).
cnf(2,axiom,
stable(skc1),
file('MGT023+2.p',unknown),
[] ).
cnf(3,axiom,
~ in_environment(skc1,critical_point(skc1)),
file('MGT023+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ skP0(u)
| in_environment(u,skf4(u)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(5,axiom,
~ greater(growth_rate(efficient_producers,skf4(u)),growth_rate(first_movers,skf4(u))),
file('MGT023+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ stable(u)
| ~ environment(u)
| in_environment(u,skf8(u)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(7,axiom,
~ greater(growth_rate(efficient_producers,skf5(u,v)),growth_rate(first_movers,skf5(u,v))),
file('MGT023+2.p',unknown),
[] ).
cnf(8,axiom,
~ greater(growth_rate(efficient_producers,skf6(u,v)),growth_rate(first_movers,skf6(u,v))),
file('MGT023+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| skP0(u)
| greater_or_equal(skf5(v,u),v) ),
file('MGT023+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| skP0(u)
| subpopulations(first_movers,efficient_producers,u,skf5(v,u)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ skP0(u)
| ~ greater(v,skf4(u))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| equal(v,critical_point(u))
| greater(skf6(v,u),v)
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ greater_or_equal(v,skf8(u))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(14,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,skf6(v,u)) ),
file('MGT023+2.p',unknown),
[] ).
cnf(48,plain,
( ~ skP0(u)
| ~ environment(u)
| equal(skf4(u),critical_point(u))
| greater(skf6(skf4(u),u),skf4(u))
| greater(growth_rate(efficient_producers,skf4(u)),growth_rate(first_movers,skf4(u))) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.1,12.1')] ).
cnf(51,plain,
( ~ skP0(u)
| ~ environment(u)
| equal(skf4(u),critical_point(u))
| greater(skf6(skf4(u),u),skf4(u)) ),
inference(mrr,[status(thm)],[48,5]),
[iquote('0:MRR:48.4,5.0')] ).
cnf(67,plain,
( ~ environment(u)
| ~ stable(u)
| ~ environment(u)
| ~ in_environment(u,v)
| ~ greater_or_equal(skf5(v,u),skf8(u))
| skP0(u)
| greater(growth_rate(efficient_producers,skf5(v,u)),growth_rate(first_movers,skf5(v,u))) ),
inference(res,[status(thm),theory(equality)],[10,13]),
[iquote('0:Res:10.3,13.3')] ).
cnf(68,plain,
( ~ stable(u)
| ~ environment(u)
| ~ in_environment(u,v)
| ~ greater_or_equal(skf5(v,u),skf8(u))
| skP0(u)
| greater(growth_rate(efficient_producers,skf5(v,u)),growth_rate(first_movers,skf5(v,u))) ),
inference(obv,[status(thm),theory(equality)],[67]),
[iquote('0:Obv:67.0')] ).
cnf(69,plain,
( ~ stable(u)
| ~ environment(u)
| ~ in_environment(u,v)
| ~ greater_or_equal(skf5(v,u),skf8(u))
| skP0(u) ),
inference(mrr,[status(thm)],[68,7]),
[iquote('0:MRR:68.5,7.0')] ).
cnf(71,plain,
( ~ environment(u)
| ~ stable(u)
| ~ environment(u)
| ~ in_environment(u,skf8(u))
| ~ in_environment(u,skf8(u))
| skP0(u)
| skP0(u) ),
inference(res,[status(thm),theory(equality)],[9,69]),
[iquote('0:Res:9.3,69.3')] ).
cnf(73,plain,
( ~ stable(u)
| ~ environment(u)
| ~ in_environment(u,skf8(u))
| skP0(u) ),
inference(obv,[status(thm),theory(equality)],[71]),
[iquote('0:Obv:71.5')] ).
cnf(74,plain,
( ~ stable(u)
| ~ environment(u)
| skP0(u) ),
inference(mrr,[status(thm)],[73,6]),
[iquote('0:MRR:73.2,6.2')] ).
cnf(76,plain,
( ~ skP0(u)
| ~ environment(u)
| equal(skf4(u),critical_point(u))
| greater(growth_rate(efficient_producers,skf4(u)),growth_rate(first_movers,skf4(u)))
| subpopulations(first_movers,efficient_producers,u,skf6(skf4(u),u)) ),
inference(res,[status(thm),theory(equality)],[4,14]),
[iquote('0:Res:4.1,14.1')] ).
cnf(80,plain,
( ~ skP0(u)
| ~ environment(u)
| equal(skf4(u),critical_point(u))
| subpopulations(first_movers,efficient_producers,u,skf6(skf4(u),u)) ),
inference(mrr,[status(thm)],[76,5]),
[iquote('0:MRR:76.3,5.0')] ).
cnf(83,plain,
( ~ skP0(u)
| ~ environment(u)
| ~ skP0(u)
| ~ greater(skf6(skf4(u),u),skf4(u))
| equal(skf4(u),critical_point(u))
| greater(growth_rate(efficient_producers,skf6(skf4(u),u)),growth_rate(first_movers,skf6(skf4(u),u))) ),
inference(res,[status(thm),theory(equality)],[80,11]),
[iquote('0:Res:80.3,11.2')] ).
cnf(86,plain,
( ~ environment(u)
| ~ skP0(u)
| ~ greater(skf6(skf4(u),u),skf4(u))
| equal(skf4(u),critical_point(u))
| greater(growth_rate(efficient_producers,skf6(skf4(u),u)),growth_rate(first_movers,skf6(skf4(u),u))) ),
inference(obv,[status(thm),theory(equality)],[83]),
[iquote('0:Obv:83.0')] ).
cnf(87,plain,
( ~ environment(u)
| ~ skP0(u)
| equal(skf4(u),critical_point(u)) ),
inference(mrr,[status(thm)],[86,51,8]),
[iquote('0:MRR:86.2,86.4,51.3,8.0')] ).
cnf(89,plain,
( ~ environment(u)
| ~ skP0(u)
| ~ skP0(u)
| in_environment(u,critical_point(u)) ),
inference(spr,[status(thm),theory(equality)],[87,4]),
[iquote('0:SpR:87.2,4.1')] ).
cnf(94,plain,
( ~ environment(u)
| ~ skP0(u)
| in_environment(u,critical_point(u)) ),
inference(obv,[status(thm),theory(equality)],[89]),
[iquote('0:Obv:89.1')] ).
cnf(97,plain,
( ~ environment(skc1)
| ~ skP0(skc1) ),
inference(res,[status(thm),theory(equality)],[94,3]),
[iquote('0:Res:94.2,3.0')] ).
cnf(102,plain,
$false,
inference(ssi,[status(thm)],[97,74,2,1]),
[iquote('0:SSi:97.1,97.0,74.0,2.0,1.0,2.0,1.2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 7 12:11:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.46
% 0.14/0.46 SPASS V 3.9
% 0.14/0.46 SPASS beiseite: Proof found.
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 SPASS derived 54 clauses, backtracked 18 clauses, performed 3 splits and kept 66 clauses.
% 0.14/0.46 SPASS allocated 97688 KBytes.
% 0.14/0.46 SPASS spent 0:00:00.08 on the problem.
% 0.14/0.46 0:00:00.03 for the input.
% 0.14/0.46 0:00:00.02 for the FLOTTER CNF translation.
% 0.14/0.46 0:00:00.00 for inferences.
% 0.14/0.46 0:00:00.00 for the backtracking.
% 0.14/0.46 0:00:00.00 for the reduction.
% 0.14/0.46
% 0.14/0.46
% 0.14/0.46 Here is a proof with depth 4, length 31 :
% 0.14/0.46 % SZS output start Refutation
% See solution above
% 0.14/0.46 Formulae used in the proof : prove_l5 mp_earliest_time_growth_rate_exceeds l1 d1
% 0.14/0.46
%------------------------------------------------------------------------------