%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT023-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Unsatisfiable 0.24s 0.49s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 13 unt; 10 nHn; 30 RR)
% Number of literals : 72 ( 0 equ; 31 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(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,sk1(v,u)) ),
file('MGT023-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| equal(v,critical_point(u))
| greater(sk1(v,u),v)
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT023-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| ~ greater(growth_rate(efficient_producers,sk1(v,u)),growth_rate(first_movers,sk1(v,u)))
| equal(v,critical_point(u))
| greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
file('MGT023-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ stable(u)
| ~ environment(u)
| in_environment(u,sk2(u)) ),
file('MGT023-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ greater(growth_rate(efficient_producers,sk2(u)),growth_rate(first_movers,sk2(u))) ),
file('MGT023-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ stable(u)
| ~ environment(u)
| ~ greater(v,sk2(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(7,axiom,
environment(sk3),
file('MGT023-1.p',unknown),
[] ).
cnf(8,axiom,
stable(sk3),
file('MGT023-1.p',unknown),
[] ).
cnf(9,axiom,
~ in_environment(sk3,critical_point(sk3)),
file('MGT023-1.p',unknown),
[] ).
cnf(11,plain,
( ~ environment(sk3)
| ~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(res,[status(thm),theory(equality)],[8,5]),
[iquote('0:Res:8.0,5.1')] ).
cnf(12,plain,
( ~ environment(sk3)
| in_environment(sk3,sk2(sk3)) ),
inference(res,[status(thm),theory(equality)],[8,4]),
[iquote('0:Res:8.0,4.1')] ).
cnf(19,plain,
in_environment(sk3,sk2(sk3)),
inference(mrr,[status(thm)],[12,7]),
[iquote('0:MRR:12.0,7.0')] ).
cnf(20,plain,
~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))),
inference(mrr,[status(thm)],[11,7]),
[iquote('0:MRR:11.0,7.0')] ).
cnf(24,plain,
( ~ environment(sk3)
| equal(sk2(sk3),critical_point(sk3))
| greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(res,[status(thm),theory(equality)],[19,2]),
[iquote('0:Res:19.0,2.1')] ).
cnf(26,plain,
( equal(sk2(sk3),critical_point(sk3))
| greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(ssi,[status(thm)],[24,8,7]),
[iquote('0:SSi:24.0,8.0,7.0')] ).
cnf(27,plain,
( equal(sk2(sk3),critical_point(sk3))
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(mrr,[status(thm)],[26,20]),
[iquote('0:MRR:26.2,20.0')] ).
cnf(30,plain,
equal(sk2(sk3),critical_point(sk3)),
inference(spt,[spt(split,[position(s1)])],[27]),
[iquote('1:Spt:27.0')] ).
cnf(31,plain,
in_environment(sk3,critical_point(sk3)),
inference(rew,[status(thm),theory(equality)],[30,19]),
[iquote('1:Rew:30.0,19.0')] ).
cnf(36,plain,
$false,
inference(mrr,[status(thm)],[31,9]),
[iquote('1:MRR:31.0,9.0')] ).
cnf(38,plain,
~ equal(sk2(sk3),critical_point(sk3)),
inference(spt,[spt(split,[position(sa)])],[36,30]),
[iquote('1:Spt:36.0,27.0,30.0')] ).
cnf(39,plain,
greater(sk1(sk2(sk3),sk3),sk2(sk3)),
inference(spt,[spt(split,[position(s2)])],[27]),
[iquote('1:Spt:36.0,27.1')] ).
cnf(43,plain,
( ~ environment(sk3)
| equal(sk2(sk3),critical_point(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(res,[status(thm),theory(equality)],[19,1]),
[iquote('0:Res:19.0,1.1')] ).
cnf(45,plain,
( equal(sk2(sk3),critical_point(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(ssi,[status(thm)],[43,8,7]),
[iquote('0:SSi:43.0,8.0,7.0')] ).
cnf(46,plain,
subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)),
inference(mrr,[status(thm)],[45,38,20]),
[iquote('1:MRR:45.0,45.1,38.0,20.0')] ).
cnf(49,plain,
( ~ stable(sk3)
| ~ environment(sk3)
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(res,[status(thm),theory(equality)],[46,6]),
[iquote('1:Res:46.0,6.3')] ).
cnf(50,plain,
( ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(ssi,[status(thm)],[49,8,7]),
[iquote('1:SSi:49.1,49.0,8.0,7.0,8.0,7.0')] ).
cnf(51,plain,
greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))),
inference(mrr,[status(thm)],[50,39]),
[iquote('1:MRR:50.0,39.0')] ).
cnf(59,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| equal(sk2(sk3),critical_point(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(res,[status(thm),theory(equality)],[51,3]),
[iquote('1:Res:51.0,3.2')] ).
cnf(60,plain,
( ~ in_environment(sk3,sk2(sk3))
| equal(sk2(sk3),critical_point(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(ssi,[status(thm)],[59,8,7]),
[iquote('1:SSi:59.0,8.0,7.0')] ).
cnf(61,plain,
$false,
inference(mrr,[status(thm)],[60,19,38,20]),
[iquote('1:MRR:60.0,60.1,60.2,19.0,38.0,20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n028.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 12:08:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.24/0.49
% 0.24/0.49 SPASS V 3.9
% 0.24/0.49 SPASS beiseite: Proof found.
% 0.24/0.49 % SZS status Theorem
% 0.24/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.49 SPASS derived 31 clauses, backtracked 7 clauses, performed 1 splits and kept 40 clauses.
% 0.24/0.49 SPASS allocated 75666 KBytes.
% 0.24/0.49 SPASS spent 0:00:00.11 on the problem.
% 0.24/0.49 0:00:00.06 for the input.
% 0.24/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.24/0.49 0:00:00.00 for inferences.
% 0.24/0.49 0:00:00.00 for the backtracking.
% 0.24/0.49 0:00:00.00 for the reduction.
% 0.24/0.49
% 0.24/0.49
% 0.24/0.49 Here is a proof with depth 4, length 30 :
% 0.24/0.49 % SZS output start Refutation
% See solution above
% 0.24/0.49 Formulae used in the proof : d1_17 d1_18 d1_19 l12_20 l12_21 l12_22 prove_l5_23 prove_l5_24 prove_l5_25
% 0.24/0.49
%------------------------------------------------------------------------------