%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 0.22s 0.51s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 10 unt; 3 nHn; 25 RR)
% Number of literals : 60 ( 0 equ; 38 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
environment(skc3),
file('MGT021+1.p',unknown),
[] ).
cnf(2,axiom,
subpopulations(first_movers,efficient_producers,skc3,skc2),
file('MGT021+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ decreases(u)
| ~ increases(u) ),
file('MGT021+1.p',unknown),
[] ).
cnf(4,axiom,
decreases(difference(disbanding_rate(first_movers,skc2),disbanding_rate(efficient_producers,skc2))),
file('MGT021+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ environment(u)
| ~ subpopulations(first_movers,efficient_producers,u,v)
| in_environment(u,v) ),
file('MGT021+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(u)
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(number_of_organizations(u,v),zero) ),
file('MGT021+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| ~ greater(number_of_organizations(u,v),zero)
| constant(resources(u,v))
| greater(equilibrium(u),v) ),
file('MGT021+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(u)
| ~ decreases(resources(u,v))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| increases(difference(disbanding_rate(first_movers,v),disbanding_rate(efficient_producers,v))) ),
file('MGT021+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| ~ greater(equilibrium(u),v)
| ~ greater(number_of_organizations(u,v),zero)
| decreases(resources(u,v)) ),
file('MGT021+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ environment(u)
| ~ constant(resources(u,v))
| ~ decreases(difference(disbanding_rate(first_movers,v),disbanding_rate(efficient_producers,v)))
| ~ subpopulations(first_movers,efficient_producers,u,v) ),
file('MGT021+1.p',unknown),
[] ).
cnf(13,plain,
( ~ in_environment(skc3,u)
| ~ greater(equilibrium(skc3),u)
| ~ greater(number_of_organizations(skc3,u),zero)
| decreases(resources(skc3,u)) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(15,plain,
( ~ in_environment(skc3,u)
| ~ greater(number_of_organizations(skc3,u),zero)
| constant(resources(skc3,u))
| greater(equilibrium(skc3),u) ),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.0')] ).
cnf(18,plain,
( ~ environment(skc3)
| ~ decreases(difference(disbanding_rate(first_movers,skc2),disbanding_rate(efficient_producers,skc2)))
| ~ constant(resources(skc3,skc2)) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.2')] ).
cnf(19,plain,
( ~ environment(skc3)
| ~ decreases(resources(skc3,skc2))
| increases(difference(disbanding_rate(first_movers,skc2),disbanding_rate(efficient_producers,skc2))) ),
inference(res,[status(thm),theory(equality)],[2,9]),
[iquote('0:Res:2.0,9.1')] ).
cnf(20,plain,
( ~ environment(skc3)
| greater(number_of_organizations(skc3,skc2),zero) ),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.1')] ).
cnf(21,plain,
( ~ environment(skc3)
| in_environment(skc3,skc2) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.0,6.1')] ).
cnf(22,plain,
~ increases(difference(disbanding_rate(first_movers,skc2),disbanding_rate(efficient_producers,skc2))),
inference(res,[status(thm),theory(equality)],[4,3]),
[iquote('0:Res:4.0,3.1')] ).
cnf(24,plain,
in_environment(skc3,skc2),
inference(mrr,[status(thm)],[21,1]),
[iquote('0:MRR:21.0,1.0')] ).
cnf(25,plain,
greater(number_of_organizations(skc3,skc2),zero),
inference(mrr,[status(thm)],[20,1]),
[iquote('0:MRR:20.0,1.0')] ).
cnf(26,plain,
~ decreases(resources(skc3,skc2)),
inference(mrr,[status(thm)],[19,1,22]),
[iquote('0:MRR:19.0,19.2,1.0,22.0')] ).
cnf(27,plain,
~ constant(resources(skc3,skc2)),
inference(mrr,[status(thm)],[18,1,4]),
[iquote('0:MRR:18.0,18.1,1.0,4.0')] ).
cnf(31,plain,
( ~ in_environment(skc3,skc2)
| constant(resources(skc3,skc2))
| greater(equilibrium(skc3),skc2) ),
inference(res,[status(thm),theory(equality)],[25,15]),
[iquote('0:Res:25.0,15.1')] ).
cnf(35,plain,
greater(equilibrium(skc3),skc2),
inference(mrr,[status(thm)],[31,24,27]),
[iquote('0:MRR:31.0,31.1,24.0,27.0')] ).
cnf(47,plain,
( ~ in_environment(skc3,skc2)
| ~ greater(equilibrium(skc3),skc2)
| decreases(resources(skc3,skc2)) ),
inference(res,[status(thm),theory(equality)],[25,13]),
[iquote('0:Res:25.0,13.2')] ).
cnf(51,plain,
$false,
inference(mrr,[status(thm)],[47,24,35,26]),
[iquote('0:MRR:47.0,47.1,47.2,24.0,35.0,26.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 12:02:37 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.22/0.51
% 0.22/0.51 SPASS V 3.9
% 0.22/0.51 SPASS beiseite: Proof found.
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.51 SPASS derived 31 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.22/0.51 SPASS allocated 97657 KBytes.
% 0.22/0.51 SPASS spent 0:00:00.15 on the problem.
% 0.22/0.51 0:00:00.06 for the input.
% 0.22/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.22/0.51 0:00:00.00 for inferences.
% 0.22/0.51 0:00:00.00 for the backtracking.
% 0.22/0.51 0:00:00.00 for the reduction.
% 0.22/0.51
% 0.22/0.51
% 0.22/0.51 Here is a proof with depth 2, length 25 :
% 0.22/0.51 % SZS output start Refutation
% See solution above
% 0.22/0.51 Formulae used in the proof : prove_l3 mp_increase_not_decrease mp_time_point_in_environment mp_environment_not_empty a3 l4
% 0.22/0.51
%------------------------------------------------------------------------------