TSTP Solution File: MGT023+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 : 300s
% DateTime : Wed May 31 12:21:12 EDT 2023
% Result : Theorem 0.10s 0.33s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 7 unt; 0 def)
% Number of atoms : 195 ( 13 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 222 ( 87 ~; 98 |; 22 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 31 (; 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,hypothesis,
! [E,To] :
( ( environment(E)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) )
=> To = critical_point(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [E] :
( ( environment(E)
& stable(E) )
=> in_environment(E,critical_point(E)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [E,To] :
( ~ environment(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ in_environment(E,To)
| ? [T] :
( subpopulations(first_movers,efficient_producers,E,T)
& greater(T,To)
& ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
| To = critical_point(E) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f6,plain,
! [E,To] :
( ~ environment(E)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ in_environment(E,To)
| ( subpopulations(first_movers,efficient_producers,E,sk0_0(To,E))
& greater(sk0_0(To,E),To)
& ~ greater(growth_rate(efficient_producers,sk0_0(To,E)),growth_rate(first_movers,sk0_0(To,E))) )
| To = critical_point(E) ),
inference(skolemization,[status(esa)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk0_0(X1,X0))
| X1 = critical_point(X0) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| greater(sk0_0(X1,X0),X1)
| X1 = critical_point(X0) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk0_0(X1,X0)),growth_rate(first_movers,sk0_0(X1,X0)))
| X1 = critical_point(X0) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f10,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| ? [To] :
( in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& ! [T] :
( ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(T,To)
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f11,plain,
! [E] :
( ~ environment(E)
| ~ stable(E)
| ( in_environment(E,sk0_1(E))
& ~ greater(growth_rate(efficient_producers,sk0_1(E)),growth_rate(first_movers,sk0_1(E)))
& ! [T] :
( ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(T,sk0_1(E))
| greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ),
inference(skolemization,[status(esa)],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,sk0_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| ~ greater(growth_rate(efficient_producers,sk0_1(X0)),growth_rate(first_movers,sk0_1(X0))) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(X1,sk0_1(X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f15,plain,
? [E] :
( environment(E)
& stable(E)
& ~ in_environment(E,critical_point(E)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f16,plain,
( environment(sk0_2)
& stable(sk0_2)
& ~ in_environment(sk0_2,critical_point(sk0_2)) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f17,plain,
environment(sk0_2),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
stable(sk0_2),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f19,plain,
~ in_environment(sk0_2,critical_point(sk0_2)),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f20,plain,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk0_2,X0)
| greater(sk0_0(X0,sk0_2),X0)
| X0 = critical_point(sk0_2) ),
inference(resolution,[status(thm)],[f8,f17]) ).
fof(f23,plain,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk0_2,X0)
| subpopulations(first_movers,efficient_producers,sk0_2,sk0_0(X0,sk0_2))
| X0 = critical_point(sk0_2) ),
inference(resolution,[status(thm)],[f7,f17]) ).
fof(f24,plain,
( spl0_0
<=> greater(growth_rate(efficient_producers,sk0_1(sk0_2)),growth_rate(first_movers,sk0_1(sk0_2))) ),
introduced(split_symbol_definition) ).
fof(f25,plain,
( greater(growth_rate(efficient_producers,sk0_1(sk0_2)),growth_rate(first_movers,sk0_1(sk0_2)))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f26,plain,
( ~ greater(growth_rate(efficient_producers,sk0_1(sk0_2)),growth_rate(first_movers,sk0_1(sk0_2)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( spl0_1
<=> subpopulations(first_movers,efficient_producers,sk0_2,sk0_0(sk0_1(sk0_2),sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f28,plain,
( subpopulations(first_movers,efficient_producers,sk0_2,sk0_0(sk0_1(sk0_2),sk0_2))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( spl0_2
<=> sk0_1(sk0_2) = critical_point(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f31,plain,
( sk0_1(sk0_2) = critical_point(sk0_2)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( spl0_3
<=> environment(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f35,plain,
( ~ environment(sk0_2)
| spl0_3 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( spl0_4
<=> stable(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f38,plain,
( ~ stable(sk0_2)
| spl0_4 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( greater(growth_rate(efficient_producers,sk0_1(sk0_2)),growth_rate(first_movers,sk0_1(sk0_2)))
| subpopulations(first_movers,efficient_producers,sk0_2,sk0_0(sk0_1(sk0_2),sk0_2))
| sk0_1(sk0_2) = critical_point(sk0_2)
| ~ environment(sk0_2)
| ~ stable(sk0_2) ),
inference(resolution,[status(thm)],[f23,f12]) ).
fof(f40,plain,
( spl0_0
| spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f39,f24,f27,f30,f33,f36]) ).
fof(f41,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f18]) ).
fof(f42,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f43,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f17]) ).
fof(f44,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f45,plain,
( spl0_5
<=> in_environment(sk0_2,sk0_1(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f47,plain,
( ~ in_environment(sk0_2,sk0_1(sk0_2))
| spl0_5 ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f68,plain,
( spl0_10
<=> in_environment(sk0_2,critical_point(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f69,plain,
( in_environment(sk0_2,critical_point(sk0_2))
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( ~ environment(sk0_2)
| ~ stable(sk0_2)
| in_environment(sk0_2,critical_point(sk0_2))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f31,f12]) ).
fof(f72,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_10
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f71,f33,f36,f68,f30]) ).
fof(f73,plain,
( ~ environment(sk0_2)
| ~ stable(sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f25,f13]) ).
fof(f74,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f73,f33,f36,f24]) ).
fof(f75,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f19]) ).
fof(f76,plain,
~ spl0_10,
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( spl0_11
<=> greater(sk0_0(sk0_1(sk0_2),sk0_2),sk0_1(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f80,plain,
( ~ in_environment(sk0_2,sk0_1(sk0_2))
| greater(sk0_0(sk0_1(sk0_2),sk0_2),sk0_1(sk0_2))
| sk0_1(sk0_2) = critical_point(sk0_2)
| spl0_0 ),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f81,plain,
( ~ spl0_5
| spl0_11
| spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f80,f45,f77,f30,f24]) ).
fof(f82,plain,
( ~ environment(sk0_2)
| ~ stable(sk0_2)
| spl0_5 ),
inference(resolution,[status(thm)],[f47,f12]) ).
fof(f83,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5 ),
inference(split_clause,[status(thm)],[f82,f33,f36,f45]) ).
fof(f86,plain,
( spl0_12
<=> greater(growth_rate(efficient_producers,sk0_0(sk0_1(sk0_2),sk0_2)),growth_rate(first_movers,sk0_0(sk0_1(sk0_2),sk0_2))) ),
introduced(split_symbol_definition) ).
fof(f87,plain,
( greater(growth_rate(efficient_producers,sk0_0(sk0_1(sk0_2),sk0_2)),growth_rate(first_movers,sk0_0(sk0_1(sk0_2),sk0_2)))
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( ~ environment(sk0_2)
| ~ stable(sk0_2)
| ~ greater(sk0_0(sk0_1(sk0_2),sk0_2),sk0_1(sk0_2))
| greater(growth_rate(efficient_producers,sk0_0(sk0_1(sk0_2),sk0_2)),growth_rate(first_movers,sk0_0(sk0_1(sk0_2),sk0_2)))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f28,f14]) ).
fof(f90,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| spl0_12
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f89,f33,f36,f77,f86,f27]) ).
fof(f91,plain,
( ~ environment(sk0_2)
| greater(growth_rate(efficient_producers,sk0_1(sk0_2)),growth_rate(first_movers,sk0_1(sk0_2)))
| ~ in_environment(sk0_2,sk0_1(sk0_2))
| sk0_1(sk0_2) = critical_point(sk0_2)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f87,f9]) ).
fof(f92,plain,
( ~ spl0_3
| spl0_0
| ~ spl0_5
| spl0_2
| ~ spl0_12 ),
inference(split_clause,[status(thm)],[f91,f33,f24,f45,f30,f86]) ).
fof(f93,plain,
$false,
inference(sat_refutation,[status(thm)],[f40,f42,f44,f72,f74,f76,f81,f83,f90,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n001.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 11:39:15 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.5.1
% 0.10/0.33 % Refutation found
% 0.10/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.55 % Elapsed time: 0.012855 seconds
% 0.16/0.55 % CPU time: 0.012170 seconds
% 0.16/0.55 % Memory used: 2.899 MB
%------------------------------------------------------------------------------