TSTP Solution File: MGT023-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : MGT023-1 : TPTP v8.1.0. Released v2.4.0.
% 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 22:26:14 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   30 (  13 unt;  10 nHn;  30 RR)
%            Number of literals    :   72 (   0 equ;  31 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ environment(u)
    | ~ in_environment(u,v)
    | equal(v,critical_point(u))
    | greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v))
    | subpopulations(first_movers,efficient_producers,u,sk1(v,u)) ),
    file('MGT023-1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ environment(u)
    | ~ in_environment(u,v)
    | equal(v,critical_point(u))
    | greater(sk1(v,u),v)
    | greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
    file('MGT023-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ environment(u)
    | ~ in_environment(u,v)
    | ~ greater(growth_rate(efficient_producers,sk1(v,u)),growth_rate(first_movers,sk1(v,u)))
    | equal(v,critical_point(u))
    | greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
    file('MGT023-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ stable(u)
    | ~ environment(u)
    | in_environment(u,sk2(u)) ),
    file('MGT023-1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ stable(u)
    | ~ environment(u)
    | ~ greater(growth_rate(efficient_producers,sk2(u)),growth_rate(first_movers,sk2(u))) ),
    file('MGT023-1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ stable(u)
    | ~ environment(u)
    | ~ greater(v,sk2(u))
    | ~ subpopulations(first_movers,efficient_producers,u,v)
    | greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) ),
    file('MGT023-1.p',unknown),
    [] ).

cnf(7,axiom,
    environment(sk3),
    file('MGT023-1.p',unknown),
    [] ).

cnf(8,axiom,
    stable(sk3),
    file('MGT023-1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ in_environment(sk3,critical_point(sk3)),
    file('MGT023-1.p',unknown),
    [] ).

cnf(11,plain,
    ( ~ environment(sk3)
    | ~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
    inference(res,[status(thm),theory(equality)],[8,5]),
    [iquote('0:Res:8.0,5.1')] ).

cnf(12,plain,
    ( ~ environment(sk3)
    | in_environment(sk3,sk2(sk3)) ),
    inference(res,[status(thm),theory(equality)],[8,4]),
    [iquote('0:Res:8.0,4.1')] ).

cnf(19,plain,
    in_environment(sk3,sk2(sk3)),
    inference(mrr,[status(thm)],[12,7]),
    [iquote('0:MRR:12.0,7.0')] ).

cnf(20,plain,
    ~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))),
    inference(mrr,[status(thm)],[11,7]),
    [iquote('0:MRR:11.0,7.0')] ).

cnf(24,plain,
    ( ~ environment(sk3)
    | equal(sk2(sk3),critical_point(sk3))
    | greater(sk1(sk2(sk3),sk3),sk2(sk3))
    | greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
    inference(res,[status(thm),theory(equality)],[19,2]),
    [iquote('0:Res:19.0,2.1')] ).

cnf(26,plain,
    ( equal(sk2(sk3),critical_point(sk3))
    | greater(sk1(sk2(sk3),sk3),sk2(sk3))
    | greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
    inference(ssi,[status(thm)],[24,8,7]),
    [iquote('0:SSi:24.0,8.0,7.0')] ).

cnf(27,plain,
    ( equal(sk2(sk3),critical_point(sk3))
    | greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
    inference(mrr,[status(thm)],[26,20]),
    [iquote('0:MRR:26.2,20.0')] ).

cnf(30,plain,
    equal(sk2(sk3),critical_point(sk3)),
    inference(spt,[spt(split,[position(s1)])],[27]),
    [iquote('1:Spt:27.0')] ).

cnf(31,plain,
    in_environment(sk3,critical_point(sk3)),
    inference(rew,[status(thm),theory(equality)],[30,19]),
    [iquote('1:Rew:30.0,19.0')] ).

cnf(36,plain,
    $false,
    inference(mrr,[status(thm)],[31,9]),
    [iquote('1:MRR:31.0,9.0')] ).

cnf(38,plain,
    ~ equal(sk2(sk3),critical_point(sk3)),
    inference(spt,[spt(split,[position(sa)])],[36,30]),
    [iquote('1:Spt:36.0,27.0,30.0')] ).

cnf(39,plain,
    greater(sk1(sk2(sk3),sk3),sk2(sk3)),
    inference(spt,[spt(split,[position(s2)])],[27]),
    [iquote('1:Spt:36.0,27.1')] ).

cnf(43,plain,
    ( ~ environment(sk3)
    | equal(sk2(sk3),critical_point(sk3))
    | greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
    | subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
    inference(res,[status(thm),theory(equality)],[19,1]),
    [iquote('0:Res:19.0,1.1')] ).

cnf(45,plain,
    ( equal(sk2(sk3),critical_point(sk3))
    | greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
    | subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
    inference(ssi,[status(thm)],[43,8,7]),
    [iquote('0:SSi:43.0,8.0,7.0')] ).

cnf(46,plain,
    subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)),
    inference(mrr,[status(thm)],[45,38,20]),
    [iquote('1:MRR:45.0,45.1,38.0,20.0')] ).

cnf(49,plain,
    ( ~ stable(sk3)
    | ~ environment(sk3)
    | ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
    | greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
    inference(res,[status(thm),theory(equality)],[46,6]),
    [iquote('1:Res:46.0,6.3')] ).

cnf(50,plain,
    ( ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
    | greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
    inference(ssi,[status(thm)],[49,8,7]),
    [iquote('1:SSi:49.1,49.0,8.0,7.0,8.0,7.0')] ).

cnf(51,plain,
    greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))),
    inference(mrr,[status(thm)],[50,39]),
    [iquote('1:MRR:50.0,39.0')] ).

cnf(59,plain,
    ( ~ environment(sk3)
    | ~ in_environment(sk3,sk2(sk3))
    | equal(sk2(sk3),critical_point(sk3))
    | greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
    inference(res,[status(thm),theory(equality)],[51,3]),
    [iquote('1:Res:51.0,3.2')] ).

cnf(60,plain,
    ( ~ in_environment(sk3,sk2(sk3))
    | equal(sk2(sk3),critical_point(sk3))
    | greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
    inference(ssi,[status(thm)],[59,8,7]),
    [iquote('1:SSi:59.0,8.0,7.0')] ).

cnf(61,plain,
    $false,
    inference(mrr,[status(thm)],[60,19,38,20]),
    [iquote('1:MRR:60.0,60.1,60.2,19.0,38.0,20.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : MGT023-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  9 10:28:21 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 31 clauses, backtracked 7 clauses, performed 1 splits and kept 40 clauses.
% 0.19/0.42  SPASS allocated 75665 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 4, length 30 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : d1_17 d1_18 d1_19 l12_20 l12_21 l12_22 prove_l5_23 prove_l5_24 prove_l5_25
% 0.19/0.42  
%------------------------------------------------------------------------------