TSTP Solution File: MGT024+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:26:15 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of clauses : 51 ( 16 unt; 11 nHn; 51 RR)
% Number of literals : 120 ( 0 equ; 67 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
environment(skc3),
file('MGT024+1.p',unknown),
[] ).
cnf(2,axiom,
greater_or_equal(skc2,equilibrium(skc3)),
file('MGT024+1.p',unknown),
[] ).
cnf(3,axiom,
subpopulations(first_movers,efficient_producers,skc3,skc2),
file('MGT024+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ skP0(u)
| equal(growth_rate(first_movers,u),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ skP0(u)
| equal(growth_rate(efficient_producers,u),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ skP1(u)
| greater(growth_rate(first_movers,u),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ skP1(u)
| greater(zero,growth_rate(efficient_producers,u)) ),
file('MGT024+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ greater(zero,growth_rate(first_movers,skc2))
| ~ greater(growth_rate(efficient_producers,skc2),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ greater(zero,growth_rate(efficient_producers,skc2))
| ~ greater(growth_rate(first_movers,skc2),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(growth_rate(efficient_producers,skc2),zero)
| ~ equal(growth_rate(first_movers,skc2),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ environment(u)
| ~ subpopulations(first_movers,efficient_producers,u,v)
| in_environment(u,v) ),
file('MGT024+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ environment(u)
| ~ greater_or_equal(v,equilibrium(u))
| ~ greater(equilibrium(u),v) ),
file('MGT024+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ environment(u)
| ~ subpopulations(first_movers,efficient_producers,u,v)
| greater(number_of_organizations(u,v),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ environment(u)
| ~ constant(resources(u,v))
| ~ in_environment(u,v)
| constant(number_of_organizations(u,v)) ),
file('MGT024+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ environment(u)
| ~ in_environment(u,v)
| ~ greater(number_of_organizations(u,v),zero)
| constant(resources(u,v))
| greater(equilibrium(u),v) ),
file('MGT024+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ environment(u)
| ~ constant(number_of_organizations(u,v))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| skP0(v)
| skP1(v)
| greater(zero,growth_rate(first_movers,v)) ),
file('MGT024+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ environment(u)
| ~ constant(number_of_organizations(u,v))
| ~ subpopulations(first_movers,efficient_producers,u,v)
| skP0(v)
| skP1(v)
| greater(growth_rate(efficient_producers,v),zero) ),
file('MGT024+1.p',unknown),
[] ).
cnf(23,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)],[1,16]),
[iquote('0:Res:1.0,16.0')] ).
cnf(25,plain,
( ~ constant(resources(skc3,u))
| ~ in_environment(skc3,u)
| constant(number_of_organizations(skc3,u)) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.0,14.0')] ).
cnf(29,plain,
( ~ environment(skc3)
| ~ greater(equilibrium(skc3),skc2) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.2')] ).
cnf(30,plain,
( ~ environment(skc3)
| ~ constant(number_of_organizations(skc3,skc2))
| greater(growth_rate(efficient_producers,skc2),zero)
| skP1(skc2)
| skP0(skc2) ),
inference(res,[status(thm),theory(equality)],[3,19]),
[iquote('0:Res:3.0,19.1')] ).
cnf(31,plain,
( ~ environment(skc3)
| ~ constant(number_of_organizations(skc3,skc2))
| greater(zero,growth_rate(first_movers,skc2))
| skP1(skc2)
| skP0(skc2) ),
inference(res,[status(thm),theory(equality)],[3,18]),
[iquote('0:Res:3.0,18.1')] ).
cnf(32,plain,
( ~ environment(skc3)
| greater(number_of_organizations(skc3,skc2),zero) ),
inference(res,[status(thm),theory(equality)],[3,13]),
[iquote('0:Res:3.0,13.1')] ).
cnf(33,plain,
( ~ environment(skc3)
| in_environment(skc3,skc2) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.0,11.1')] ).
cnf(34,plain,
in_environment(skc3,skc2),
inference(mrr,[status(thm)],[33,1]),
[iquote('0:MRR:33.0,1.0')] ).
cnf(35,plain,
~ greater(equilibrium(skc3),skc2),
inference(mrr,[status(thm)],[29,1]),
[iquote('0:MRR:29.0,1.0')] ).
cnf(36,plain,
greater(number_of_organizations(skc3,skc2),zero),
inference(mrr,[status(thm)],[32,1]),
[iquote('0:MRR:32.0,1.0')] ).
cnf(37,plain,
( ~ constant(number_of_organizations(skc3,skc2))
| skP0(skc2)
| skP1(skc2)
| greater(growth_rate(efficient_producers,skc2),zero) ),
inference(mrr,[status(thm)],[30,1]),
[iquote('0:MRR:30.0,1.0')] ).
cnf(38,plain,
( ~ constant(number_of_organizations(skc3,skc2))
| skP0(skc2)
| skP1(skc2)
| greater(zero,growth_rate(first_movers,skc2)) ),
inference(mrr,[status(thm)],[31,1]),
[iquote('0:MRR:31.0,1.0')] ).
cnf(49,plain,
( ~ skP0(skc2)
| ~ equal(zero,zero)
| ~ equal(growth_rate(first_movers,skc2),zero) ),
inference(spl,[status(thm),theory(equality)],[5,10]),
[iquote('0:SpL:5.1,10.0')] ).
cnf(50,plain,
( ~ skP0(skc2)
| ~ equal(growth_rate(first_movers,skc2),zero) ),
inference(obv,[status(thm),theory(equality)],[49]),
[iquote('0:Obv:49.1')] ).
cnf(51,plain,
( ~ skP0(skc2)
| ~ equal(zero,zero) ),
inference(rew,[status(thm),theory(equality)],[4,50]),
[iquote('0:Rew:4.1,50.1')] ).
cnf(52,plain,
~ skP0(skc2),
inference(obv,[status(thm),theory(equality)],[51]),
[iquote('0:Obv:51.1')] ).
cnf(53,plain,
( ~ constant(number_of_organizations(skc3,skc2))
| skP1(skc2)
| greater(zero,growth_rate(first_movers,skc2)) ),
inference(mrr,[status(thm)],[38,52]),
[iquote('0:MRR:38.1,52.0')] ).
cnf(54,plain,
( ~ constant(number_of_organizations(skc3,skc2))
| skP1(skc2)
| greater(growth_rate(efficient_producers,skc2),zero) ),
inference(mrr,[status(thm)],[37,52]),
[iquote('0:MRR:37.1,52.0')] ).
cnf(56,plain,
( ~ skP1(skc2)
| ~ greater(zero,growth_rate(efficient_producers,skc2)) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.1,9.1')] ).
cnf(57,plain,
~ skP1(skc2),
inference(mrr,[status(thm)],[56,7]),
[iquote('0:MRR:56.1,7.1')] ).
cnf(58,plain,
( ~ constant(number_of_organizations(skc3,skc2))
| greater(zero,growth_rate(first_movers,skc2)) ),
inference(mrr,[status(thm)],[53,57]),
[iquote('0:MRR:53.1,57.0')] ).
cnf(59,plain,
( ~ constant(number_of_organizations(skc3,skc2))
| greater(growth_rate(efficient_producers,skc2),zero) ),
inference(mrr,[status(thm)],[54,57]),
[iquote('0:MRR:54.1,57.0')] ).
cnf(61,plain,
~ greater(zero,growth_rate(first_movers,skc2)),
inference(spt,[spt(split,[position(s1)])],[8]),
[iquote('1:Spt:8.0')] ).
cnf(62,plain,
~ constant(number_of_organizations(skc3,skc2)),
inference(mrr,[status(thm)],[58,61]),
[iquote('1:MRR:58.1,61.0')] ).
cnf(65,plain,
( ~ in_environment(skc3,skc2)
| constant(resources(skc3,skc2))
| greater(equilibrium(skc3),skc2) ),
inference(res,[status(thm),theory(equality)],[36,23]),
[iquote('0:Res:36.0,23.1')] ).
cnf(68,plain,
constant(resources(skc3,skc2)),
inference(mrr,[status(thm)],[65,34,35]),
[iquote('0:MRR:65.0,65.2,34.0,35.0')] ).
cnf(75,plain,
( ~ in_environment(skc3,skc2)
| constant(number_of_organizations(skc3,skc2)) ),
inference(res,[status(thm),theory(equality)],[68,25]),
[iquote('0:Res:68.0,25.0')] ).
cnf(76,plain,
( ~ environment(skc3)
| ~ in_environment(skc3,skc2)
| constant(number_of_organizations(skc3,skc2)) ),
inference(res,[status(thm),theory(equality)],[68,14]),
[iquote('0:Res:68.0,14.1')] ).
cnf(78,plain,
( ~ in_environment(skc3,skc2)
| constant(number_of_organizations(skc3,skc2)) ),
inference(ssi,[status(thm)],[76,1]),
[iquote('0:SSi:76.0,1.0')] ).
cnf(79,plain,
$false,
inference(mrr,[status(thm)],[78,34,62]),
[iquote('1:MRR:78.0,78.1,34.0,62.0')] ).
cnf(80,plain,
greater(zero,growth_rate(first_movers,skc2)),
inference(spt,[spt(split,[position(sa)])],[79,61]),
[iquote('1:Spt:79.0,8.0,61.0')] ).
cnf(81,plain,
~ greater(growth_rate(efficient_producers,skc2),zero),
inference(spt,[spt(split,[position(s2)])],[8]),
[iquote('1:Spt:79.0,8.1')] ).
cnf(82,plain,
constant(number_of_organizations(skc3,skc2)),
inference(mrr,[status(thm)],[75,34]),
[iquote('0:MRR:75.0,34.0')] ).
cnf(83,plain,
$false,
inference(mrr,[status(thm)],[59,82,81]),
[iquote('1:MRR:59.0,59.1,82.0,81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 07:49:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 44 clauses, backtracked 7 clauses, performed 1 splits and kept 51 clauses.
% 0.18/0.43 SPASS allocated 97676 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 3, length 51 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : prove_l6 l7 mp_time_point_occur mp_equilibrium mp_positive_number_of_organizations a6 a3
% 0.18/0.43
%------------------------------------------------------------------------------