%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 06:19:52 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.49s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 8 unt; 0 nHn; 16 RR)
% Number of literals : 32 ( 0 equ; 21 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(u)
| ~ subpopulations(v,w,u,x)
| subpopulations(w,v,u,x) ),
file('MGT036-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(u)
| ~ greater(zero,growth_rate(v,w))
| ~ greater_or_equal(growth_rate(x,w),zero)
| ~ subpopulations(v,x,u,w)
| outcompetes(x,v,w) ),
file('MGT036-3.p',unknown),
[] ).
cnf(5,axiom,
environment(sk1),
file('MGT036-3.p',unknown),
[] ).
cnf(6,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('MGT036-3.p',unknown),
[] ).
cnf(7,axiom,
greater_or_equal(growth_rate(first_movers,sk2),zero),
file('MGT036-3.p',unknown),
[] ).
cnf(8,axiom,
greater(zero,growth_rate(efficient_producers,sk2)),
file('MGT036-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(u)
| ~ outcompetes(first_movers,efficient_producers,v)
| ~ subpopulations(first_movers,efficient_producers,u,v) ),
file('MGT036-3.p',unknown),
[] ).
cnf(11,plain,
( ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.0,9.1')] ).
cnf(12,plain,
~ outcompetes(first_movers,efficient_producers,sk2),
inference(mrr,[status(thm)],[11,5]),
[iquote('0:MRR:11.0,5.0')] ).
cnf(16,plain,
( ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(res,[status(thm),theory(equality)],[6,1]),
[iquote('0:Res:6.0,1.1')] ).
cnf(17,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(ssi,[status(thm)],[16,5]),
[iquote('0:SSi:16.0,5.0')] ).
cnf(25,plain,
( ~ environment(u)
| ~ greater_or_equal(growth_rate(v,sk2),zero)
| ~ subpopulations(efficient_producers,v,u,sk2)
| outcompetes(v,efficient_producers,sk2) ),
inference(res,[status(thm),theory(equality)],[8,2]),
[iquote('0:Res:8.0,2.1')] ).
cnf(27,plain,
( ~ environment(u)
| ~ subpopulations(efficient_producers,first_movers,u,sk2)
| outcompetes(first_movers,efficient_producers,sk2) ),
inference(res,[status(thm),theory(equality)],[7,25]),
[iquote('0:Res:7.0,25.1')] ).
cnf(29,plain,
( ~ environment(u)
| ~ subpopulations(efficient_producers,first_movers,u,sk2) ),
inference(mrr,[status(thm)],[27,12]),
[iquote('0:MRR:27.2,12.0')] ).
cnf(30,plain,
~ environment(sk1),
inference(res,[status(thm),theory(equality)],[17,29]),
[iquote('0:Res:17.0,29.1')] ).
cnf(31,plain,
$false,
inference(ssi,[status(thm)],[30,5]),
[iquote('0:SSi:30.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.13/0.37 % Computer : n010.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 7 12:42:40 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.22/0.49
% 0.22/0.49 SPASS V 3.9
% 0.22/0.49 SPASS beiseite: Proof found.
% 0.22/0.49 % SZS status Theorem
% 0.22/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.49 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.22/0.49 SPASS allocated 75611 KBytes.
% 0.22/0.49 SPASS spent 0:00:00.10 on the problem.
% 0.22/0.49 0:00:00.06 for the input.
% 0.22/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.49 0:00:00.00 for inferences.
% 0.22/0.49 0:00:00.00 for the backtracking.
% 0.22/0.49 0:00:00.00 for the reduction.
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 Here is a proof with depth 3, length 16 :
% 0.22/0.49 % SZS output start Refutation
% See solution above
% 0.22/0.49 Formulae used in the proof : mp_symmetry_of_subpopulations_1 d2_2 a13_star_5 a13_star_6 a13_star_7 a13_star_8 prove_t5_star_9
% 0.22/0.49
%------------------------------------------------------------------------------