%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 : Theorem 0.23s 0.52s
% Output : Refutation 0.23s
% 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(skc3),
file('MGT036+3.p',unknown),
[] ).
cnf(2,axiom,
subpopulations(first_movers,efficient_producers,skc3,skc2),
file('MGT036+3.p',unknown),
[] ).
cnf(3,axiom,
greater(zero,growth_rate(efficient_producers,skc2)),
file('MGT036+3.p',unknown),
[] ).
cnf(4,axiom,
greater_or_equal(growth_rate(first_movers,skc2),zero),
file('MGT036+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ environment(u)
| ~ outcompetes(first_movers,efficient_producers,v)
| ~ subpopulations(first_movers,efficient_producers,u,v) ),
file('MGT036+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ environment(u)
| ~ subpopulations(v,w,u,x)
| subpopulations(w,v,u,x) ),
file('MGT036+3.p',unknown),
[] ).
cnf(9,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(11,plain,
( ~ environment(skc3)
| ~ outcompetes(first_movers,efficient_producers,skc2) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.0,5.1')] ).
cnf(12,plain,
~ outcompetes(first_movers,efficient_producers,skc2),
inference(mrr,[status(thm)],[11,1]),
[iquote('0:MRR:11.0,1.0')] ).
cnf(16,plain,
( ~ environment(skc3)
| subpopulations(efficient_producers,first_movers,skc3,skc2) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.0,6.1')] ).
cnf(17,plain,
subpopulations(efficient_producers,first_movers,skc3,skc2),
inference(ssi,[status(thm)],[16,1]),
[iquote('0:SSi:16.0,1.0')] ).
cnf(25,plain,
( ~ environment(u)
| ~ greater_or_equal(growth_rate(v,skc2),zero)
| ~ subpopulations(efficient_producers,v,u,skc2)
| outcompetes(v,efficient_producers,skc2) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.1')] ).
cnf(27,plain,
( ~ environment(u)
| ~ subpopulations(efficient_producers,first_movers,u,skc2)
| outcompetes(first_movers,efficient_producers,skc2) ),
inference(res,[status(thm),theory(equality)],[4,25]),
[iquote('0:Res:4.0,25.1')] ).
cnf(29,plain,
( ~ environment(u)
| ~ subpopulations(efficient_producers,first_movers,u,skc2) ),
inference(mrr,[status(thm)],[27,12]),
[iquote('0:MRR:27.2,12.0')] ).
cnf(30,plain,
~ environment(skc3),
inference(res,[status(thm),theory(equality)],[17,29]),
[iquote('0:Res:17.0,29.1')] ).
cnf(31,plain,
$false,
inference(ssi,[status(thm)],[30,1]),
[iquote('0:SSi:30.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n011.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 12:42:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.23/0.52
% 0.23/0.52 SPASS V 3.9
% 0.23/0.52 SPASS beiseite: Proof found.
% 0.23/0.52 % SZS status Theorem
% 0.23/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.52 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.23/0.52 SPASS allocated 97653 KBytes.
% 0.23/0.52 SPASS spent 0:00:00.14 on the problem.
% 0.23/0.52 0:00:00.06 for the input.
% 0.23/0.52 0:00:00.04 for the FLOTTER CNF translation.
% 0.23/0.52 0:00:00.00 for inferences.
% 0.23/0.52 0:00:00.00 for the backtracking.
% 0.23/0.52 0:00:00.00 for the reduction.
% 0.23/0.52
% 0.23/0.52
% 0.23/0.52 Here is a proof with depth 3, length 16 :
% 0.23/0.52 % SZS output start Refutation
% See solution above
% 0.23/0.52 Formulae used in the proof : a13_star prove_t5_star mp_symmetry_of_subpopulations d2
% 0.23/0.52
%------------------------------------------------------------------------------