%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 01:25:23 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 24
% Syntax : Number of formulae : 139 ( 19 unt; 0 def)
% Number of atoms : 474 ( 128 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 550 ( 215 ~; 335 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( in_environment(A,sk1(B,A))
| cardinality_at_time(efficient_producers,B) != zero
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( greater(zero,growth_rate(efficient_producers,sk1(B,A)))
| cardinality_at_time(efficient_producers,B) != zero
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( number_of_organizations(A,B) = zero
| ~ greater(appear(an_organisation,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( subpopulation(sk2(B,A),A,B)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( greater(cardinality_at_time(sk2(B,A),B),zero)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( ~ greater(zero,growth_rate(sk2(B,A),B))
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( cardinality_at_time(C,B) = zero
| ~ subpopulation(C,A,B)
| number_of_organizations(A,B) != zero
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( ~ greater(zero,growth_rate(A,B))
| cardinality_at_time(A,B) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| cardinality_at_time(efficient_producers,B) = zero
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( ~ decreases(A)
| ~ constant(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( greater(appear(an_organisation,A),B)
| greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
! [A,B] :
( decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [A,B] :
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [A,B] :
( greater(number_of_organizations(A,B),zero)
| ~ greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
! [A,B] :
( ~ decreases(number_of_organizations(A,B))
| ~ decreases(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [A,B] :
( constant(number_of_organizations(A,B))
| ~ constant(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
! [A,B,C] :
( B = first_movers
| B = efficient_producers
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
in_environment(sk3,sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,plain,
! [X0,X1] :
( in_environment(X0,sk1(X1,X0))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0,X1] :
( greater(zero,growth_rate(efficient_producers,sk1(X1,X0)))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( number_of_organizations(X0,X1) = zero
| ~ greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( subpopulation(sk2(X1,X0),X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f34,plain,
! [X0,X1] :
( greater(cardinality_at_time(sk2(X1,X0),X1),zero)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f35,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(sk2(X1,X0),X1))
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [B,C] :
( cardinality_at_time(C,B) = zero
| ! [A] :
( ~ subpopulation(C,A,B)
| number_of_organizations(A,B) != zero
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f37,plain,
! [X0,X1,X2] :
( cardinality_at_time(X2,X1) = zero
| ~ subpopulation(X2,X0,X1)
| number_of_organizations(X0,X1) != zero
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(X0,X1))
| cardinality_at_time(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f41,plain,
! [B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| cardinality_at_time(efficient_producers,B) = zero
| ! [A] :
( ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f42,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
! [X0,X1] :
( greater(appear(an_organisation,X0),X1)
| greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
! [X0,X1] :
( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
! [B,D] :
( ~ greater(zero,growth_rate(D,B))
| ! [C] :
( ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ! [A] :
( ~ in_environment(A,B)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X3,X1))
| ~ greater(resilience(X3),resilience(X2))
| greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f53,plain,
! [B] :
( B = first_movers
| B = efficient_producers
| ! [C] :
( ~ greater(cardinality_at_time(B,C),zero)
| ! [A] :
( ~ subpopulation(B,A,C)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f54,plain,
! [X0,X1,X2] :
( X1 = first_movers
| X1 = efficient_producers
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
environment(sk3),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f56,plain,
in_environment(sk3,sk4),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f57,plain,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f58,plain,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f59,plain,
( greater(cardinality_at_time(efficient_producers,sk4),zero)
| cardinality_at_time(efficient_producers,sk4) = zero
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f42,f56]) ).
fof(f60,plain,
( greater(cardinality_at_time(efficient_producers,sk4),zero)
| cardinality_at_time(efficient_producers,sk4) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f55]) ).
fof(f62,plain,
cardinality_at_time(efficient_producers,sk4) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f60,f58]) ).
fof(f70,plain,
! [X0] :
( in_environment(X0,sk1(sk4,X0))
| ~ greater_or_equal(sk4,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f29,f62]) ).
fof(f76,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,sk1(sk4,X0)))
| ~ greater_or_equal(sk4,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f31,f62]) ).
fof(f83,plain,
( in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f70,f57]) ).
fof(f84,plain,
in_environment(sk3,sk1(sk4,sk3)),
inference(forward_subsumption_resolution,[status(thm)],[f83,f55]) ).
fof(f87,plain,
( greater(cardinality_at_time(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f84,f34]) ).
fof(f88,plain,
( subpopulation(sk2(sk1(sk4,sk3),sk3),sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f84,f33]) ).
fof(f91,plain,
( greater(cardinality_at_time(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f55]) ).
fof(f92,plain,
( subpopulation(sk2(sk1(sk4,sk3),sk3),sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f55]) ).
fof(f95,plain,
( subpopulation(efficient_producers,sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f39,f84]) ).
fof(f97,plain,
subpopulation(efficient_producers,sk3,sk1(sk4,sk3)),
inference(forward_subsumption_resolution,[status(thm)],[f95,f55]) ).
fof(f102,plain,
( greater(appear(an_organisation,sk3),sk1(sk4,sk3))
| greater_or_equal(sk1(sk4,sk3),appear(an_organisation,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f44,f84]) ).
fof(f104,plain,
( greater(appear(an_organisation,sk3),sk1(sk4,sk3))
| greater_or_equal(sk1(sk4,sk3),appear(an_organisation,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f55]) ).
fof(f106,plain,
( greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f76,f57]) ).
fof(f107,plain,
greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3))),
inference(forward_subsumption_resolution,[status(thm)],[f106,f55]) ).
fof(f110,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f51,f52]) ).
fof(f111,plain,
! [X0] :
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| ~ subpopulation(sk2(sk1(sk4,sk3),sk3),X0,sk1(sk4,sk3))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f54,f91]) ).
fof(f114,plain,
! [X0] :
( greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| ~ in_environment(X0,sk1(sk4,sk3))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f110,f107]) ).
fof(f127,plain,
( greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f114,f84]) ).
fof(f128,plain,
greater(zero,growth_rate(first_movers,sk1(sk4,sk3))),
inference(forward_subsumption_resolution,[status(thm)],[f127,f55]) ).
fof(f130,plain,
( greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero)
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[f104,f47]) ).
fof(f131,plain,
( greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero)
| ~ in_environment(sk3,sk1(sk4,sk3))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f130,f55]) ).
fof(f136,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f111,f92]) ).
fof(f137,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| ~ environment(sk3) ),
inference(duplicate_literals_removal,[status(thm)],[f136]) ).
fof(f138,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f55]) ).
fof(f141,plain,
( greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero)
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f84]) ).
fof(f142,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[f141,f46]) ).
fof(f143,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| ~ greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[f141,f45]) ).
fof(f144,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f55]) ).
fof(f145,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| ~ greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f55]) ).
fof(f147,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f84]) ).
fof(f148,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[f147,f32]) ).
fof(f149,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ in_environment(sk3,sk1(sk4,sk3))
| constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f55]) ).
fof(f150,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| ~ greater(equilibrium(sk3),sk1(sk4,sk3))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f84]) ).
fof(f155,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f84]) ).
fof(f156,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[f155,f49]) ).
fof(f158,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f55]) ).
fof(f159,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f84]) ).
fof(f160,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[f159,f43]) ).
fof(f161,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[f160,f138]) ).
fof(f167,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f161,f150]) ).
fof(f171,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f167,f32]) ).
fof(f172,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(duplicate_literals_removal,[status(thm)],[f171]) ).
fof(f173,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f55]) ).
fof(f180,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f84]) ).
fof(f182,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f180,f48]) ).
fof(f184,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f55]) ).
fof(f186,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f84]) ).
fof(f187,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f186,f138]) ).
fof(f188,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(duplicate_literals_removal,[status(thm)],[f187]) ).
fof(f191,plain,
( sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(paramodulation,[status(thm)],[f188,f35]) ).
fof(f193,plain,
( sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f55]) ).
fof(f195,plain,
( sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f84]) ).
fof(f196,plain,
( sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[f195,f128]) ).
fof(f197,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater(equilibrium(sk3),sk1(sk4,sk3))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f196,f160]) ).
fof(f198,plain,
( greater(equilibrium(sk3),sk1(sk4,sk3))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(duplicate_literals_removal,[status(thm)],[f197]) ).
fof(f199,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f198,f150]) ).
fof(f200,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f199,f32]) ).
fof(f201,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(duplicate_literals_removal,[status(thm)],[f200]) ).
fof(f202,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f55]) ).
fof(f203,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f84]) ).
fof(f205,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f203,f48]) ).
fof(f207,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f55]) ).
fof(f208,plain,
( sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(backward_subsumption_resolution,[status(thm)],[f196,f209]) ).
fof(f209,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f84]) ).
fof(f214,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(paramodulation,[status(thm)],[f208,f35]) ).
fof(f215,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f55]) ).
fof(f217,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f84]) ).
fof(f218,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[f217,f107]) ).
fof(f219,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f160,f218]) ).
fof(f220,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| greater(appear(an_organisation,sk3),sk1(sk4,sk3))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f219,f150]) ).
fof(f221,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f220,f32]) ).
fof(f222,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(duplicate_literals_removal,[status(thm)],[f221]) ).
fof(f223,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| decreases(resources(sk3,sk1(sk4,sk3)))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f55]) ).
fof(f224,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f84]) ).
fof(f225,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[f224,f48]) ).
fof(f226,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f55]) ).
fof(f227,plain,
number_of_organizations(sk3,sk1(sk4,sk3)) = zero,
inference(backward_subsumption_resolution,[status(thm)],[f218,f228]) ).
fof(f228,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f84]) ).
fof(f238,plain,
! [X0] :
( cardinality_at_time(X0,sk1(sk4,sk3)) = zero
| ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f227,f37]) ).
fof(f243,plain,
! [X0] :
( cardinality_at_time(X0,sk1(sk4,sk3)) = zero
| ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f55]) ).
fof(f248,plain,
! [X0] :
( cardinality_at_time(X0,sk1(sk4,sk3)) = zero
| ~ subpopulation(X0,sk3,sk1(sk4,sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f84]) ).
fof(f249,plain,
cardinality_at_time(efficient_producers,sk1(sk4,sk3)) = zero,
inference(resolution,[status(thm)],[f248,f97]) ).
fof(f257,plain,
~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3))),
inference(resolution,[status(thm)],[f249,f40]) ).
fof(f264,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f257,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 01:25:47 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.050626 seconds
% 0.11/0.42 % CPU time: 0.164039 seconds
% 0.11/0.42 % Total memory used: 71.906 MB
% 0.11/0.42 % Net memory used: 71.690 MB
%------------------------------------------------------------------------------