%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 : Unsatisfiable 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 137 ( 30 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 153 ( 61 ~; 92 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,hypothesis,
! [A,B] :
( B = critical_point(A)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [A,B] :
( B = critical_point(A)
| greater(sk1(B,A),B)
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,hypothesis,
! [A,B] :
( B = critical_point(A)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,hypothesis,
! [A] :
( in_environment(A,sk2(A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,hypothesis,
! [A] :
( ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A)))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [A,B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| greater(sk1(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)],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0] :
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [B] :
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ! [A] :
( ~ greater(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
environment(sk3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
stable(sk3),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
~ in_environment(sk3,critical_point(sk3)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
( in_environment(sk3,sk2(sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f13,f18]) ).
fof(f21,plain,
in_environment(sk3,sk2(sk3)),
inference(forward_subsumption_resolution,[status(thm)],[f20,f17]) ).
fof(f22,plain,
( 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)))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f11,f21]) ).
fof(f23,plain,
( 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(forward_subsumption_resolution,[status(thm)],[f22,f17]) ).
fof(f24,plain,
( ~ stable(sk3)
| ~ environment(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolution,[status(thm)],[f23,f14]) ).
fof(f25,plain,
( ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f17]) ).
fof(f26,plain,
( sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f18]) ).
fof(f27,plain,
( sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f10,f21]) ).
fof(f28,plain,
( sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f17]) ).
fof(f29,plain,
( ~ stable(sk3)
| ~ environment(sk3)
| sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolution,[status(thm)],[f28,f14]) ).
fof(f30,plain,
( ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f17]) ).
fof(f31,plain,
( sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f18]) ).
fof(f32,plain,
( greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| ~ environment(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(resolution,[status(thm)],[f31,f16]) ).
fof(f33,plain,
( greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f17]) ).
fof(f34,plain,
( greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| sk2(sk3) = critical_point(sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f18]) ).
fof(f35,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(resolution,[status(thm)],[f34,f26]) ).
fof(f36,plain,
( greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(duplicate_literals_removal,[status(thm)],[f35]) ).
fof(f37,plain,
( sk2(sk3) = critical_point(sk3)
| ~ in_environment(sk3,sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ~ environment(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(resolution,[status(thm)],[f36,f12]) ).
fof(f38,plain,
( ~ in_environment(sk3,sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ~ environment(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(duplicate_literals_removal,[status(thm)],[f37]) ).
fof(f39,plain,
( ~ in_environment(sk3,sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f17]) ).
fof(f40,plain,
( greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| sk2(sk3) = critical_point(sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f39,f21]) ).
fof(f41,plain,
( ~ stable(sk3)
| ~ environment(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(resolution,[status(thm)],[f40,f14]) ).
fof(f42,plain,
( ~ stable(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f17]) ).
fof(f47,plain,
in_environment(sk3,critical_point(sk3)),
inference(backward_demodulation,[status(thm)],[f48,f21]) ).
fof(f48,plain,
sk2(sk3) = critical_point(sk3),
inference(forward_subsumption_resolution,[status(thm)],[f42,f18]) ).
fof(f51,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f47,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n019.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 21 01:21:49 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.34 % Drodi V4.1.1
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.055830 seconds
% 0.11/0.40 % CPU time: 0.152216 seconds
% 0.11/0.40 % Total memory used: 80.185 MB
% 0.11/0.40 % Net memory used: 79.715 MB
%------------------------------------------------------------------------------