%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Sep 24 01:25:18 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 157 ( 30 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 173 ( 61 ~; 84 |; 22 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,hypothesis,
! [E,To] :
( ( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To)
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& environment(E) )
=> To = critical_point(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,critical_point(E)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [E,To] :
( To = critical_point(E)
| ? [T] :
( ~ greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
& greater(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [E,To] :
( To = critical_point(E)
| ( ~ greater(growth_rate(efficient_producers,sK0_skl(To,E)),growth_rate(first_movers,sK0_skl(To,E)))
& greater(sK0_skl(To,E),To)
& subpopulations(first_movers,efficient_producers,E,sK0_skl(To,E)) )
| ~ in_environment(E,To)
| greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(T,sK0_skl(To,E))],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sK0_skl(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| greater(sK0_skl(X1,X0),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sK0_skl(X1,X0)),growth_rate(first_movers,sK0_skl(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To))
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [E] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater(T,sK1_skl(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ~ greater(growth_rate(efficient_producers,sK1_skl(E)),growth_rate(first_movers,sK1_skl(E)))
& in_environment(E,sK1_skl(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(To,sK1_skl(E))],[f10]) ).
fof(f12,plain,
! [X0] :
( in_environment(X0,sK1_skl(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK1_skl(X0)),growth_rate(first_movers,sK1_skl(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sK1_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
? [E] :
( ~ in_environment(E,critical_point(E))
& stable(E)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ~ in_environment(sK2_skl,critical_point(sK2_skl))
& stable(sK2_skl)
& environment(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(E,sK2_skl)],[f15]) ).
fof(f17,plain,
environment(sK2_skl),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
stable(sK2_skl),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
~ in_environment(sK2_skl,critical_point(sK2_skl)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
( in_environment(sK2_skl,sK1_skl(sK2_skl))
| ~ stable(sK2_skl) ),
inference(resolution,[status(thm)],[f12,f17]) ).
fof(f21,plain,
in_environment(sK2_skl,sK1_skl(sK2_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f20,f18]) ).
fof(f22,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl))
| greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl)))
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f8,f21]) ).
fof(f23,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl))
| greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f17]) ).
fof(f24,plain,
( ~ stable(sK2_skl)
| ~ environment(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl)
| greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f23,f13]) ).
fof(f25,plain,
( ~ stable(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl)
| greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f17]) ).
fof(f26,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f18]) ).
fof(f27,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl),sK2_skl))
| greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl)))
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f7,f21]) ).
fof(f28,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl),sK2_skl))
| greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f17]) ).
fof(f29,plain,
( ~ stable(sK2_skl)
| ~ environment(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl)
| subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl),sK2_skl)) ),
inference(resolution,[status(thm)],[f28,f13]) ).
fof(f30,plain,
( ~ stable(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl)
| subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl),sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f17]) ).
fof(f31,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl),sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f18]) ).
fof(f32,plain,
( greater(growth_rate(efficient_producers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)),growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)))
| ~ greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl))
| ~ stable(sK2_skl)
| ~ environment(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(resolution,[status(thm)],[f31,f14]) ).
fof(f33,plain,
( greater(growth_rate(efficient_producers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)),growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)))
| ~ greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl))
| ~ stable(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f17]) ).
fof(f34,plain,
( greater(growth_rate(efficient_producers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)),growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)))
| ~ greater(sK0_skl(sK1_skl(sK2_skl),sK2_skl),sK1_skl(sK2_skl))
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f18]) ).
fof(f35,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| greater(growth_rate(efficient_producers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)),growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)))
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(resolution,[status(thm)],[f34,f26]) ).
fof(f36,plain,
( greater(growth_rate(efficient_producers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)),growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl),sK2_skl)))
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f35]) ).
fof(f37,plain,
( sK1_skl(sK2_skl) = critical_point(sK2_skl)
| ~ in_environment(sK2_skl,sK1_skl(sK2_skl))
| greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl)))
| ~ environment(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(resolution,[status(thm)],[f36,f9]) ).
fof(f38,plain,
( ~ in_environment(sK2_skl,sK1_skl(sK2_skl))
| greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl)))
| ~ environment(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f37]) ).
fof(f39,plain,
( ~ in_environment(sK2_skl,sK1_skl(sK2_skl))
| greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl)))
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f17]) ).
fof(f40,plain,
( greater(growth_rate(efficient_producers,sK1_skl(sK2_skl)),growth_rate(first_movers,sK1_skl(sK2_skl)))
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f21]) ).
fof(f41,plain,
( ~ stable(sK2_skl)
| ~ environment(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(resolution,[status(thm)],[f40,f13]) ).
fof(f42,plain,
( ~ stable(sK2_skl)
| sK1_skl(sK2_skl) = critical_point(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f17]) ).
fof(f47,plain,
in_environment(sK2_skl,critical_point(sK2_skl)),
inference(backward_demodulation,[status(thm)],[f48,f21]) ).
fof(f48,plain,
sK1_skl(sK2_skl) = critical_point(sK2_skl),
inference(forward_subsumption_resolution,[status(thm)],[f42,f18]) ).
fof(f51,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f47,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 01:23:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.047741 seconds
% 0.13/0.42 % CPU time: 0.141528 seconds
% 0.13/0.42 % Total memory used: 80.260 MB
% 0.13/0.42 % Net memory used: 79.801 MB
%------------------------------------------------------------------------------