TSTP Solution File: MGT024+1 by SPASS---3.9

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%------------------------------------------------------------------------------
% 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  
%------------------------------------------------------------------------------