%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT037+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 : n007.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 : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 180 ( 10 unt; 23 def)
% Number of atoms : 744 ( 91 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 982 ( 418 ~; 465 |; 56 &)
% ( 23 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 24 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 202 ( 194 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,T] :
( ( cardinality_at_time(efficient_producers,T) = zero
& greater_or_equal(T,appear(efficient_producers,E))
& environment(E) )
=> ? [To] :
( greater(zero,growth_rate(efficient_producers,To))
& greater(T,To)
& in_environment(E,To)
& greater(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,T] :
( ( greater(appear(an_organisation,E),T)
& in_environment(E,T)
& environment(E) )
=> number_of_organizations(E,T) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [E,T] :
( ( ~ decreases(number_of_organizations(E,T))
& in_environment(E,T)
& environment(E) )
=> ? [X] :
( ~ greater(zero,growth_rate(X,T))
& greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [E,T,X] :
( ( subpopulation(X,E,T)
& number_of_organizations(E,T) = zero
& in_environment(E,T)
& environment(E) )
=> cardinality_at_time(X,T) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [S,T] :
( cardinality_at_time(S,T) = zero
=> ~ greater(zero,growth_rate(S,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( greater(cardinality_at_time(efficient_producers,T),zero)
| cardinality_at_time(efficient_producers,T) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( greater(appear(an_organisation,E),T)
| greater_or_equal(T,appear(an_organisation,E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
! [E,T] :
( ( greater(number_of_organizations(E,T),zero)
& in_environment(E,T)
& environment(E) )
=> ( ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) )
& ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
! [E,T] :
( ( greater_or_equal(T,appear(an_organisation,E))
& in_environment(E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> constant(number_of_organizations(E,T)) )
& ( decreases(resources(E,T))
=> ~ decreases(number_of_organizations(E,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& ~ greater(zero,growth_rate(S1,T))
& in_environment(E,T)
& environment(E) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [E,X,T] :
( ( greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T)
& environment(E) )
=> ( X = first_movers
| X = efficient_producers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [E,T] :
( ( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [E,T] :
( ( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
! [E,T] :
( ? [To] :
( greater(zero,growth_rate(efficient_producers,To))
& greater(T,To)
& in_environment(E,To)
& greater(To,appear(efficient_producers,E)) )
| cardinality_at_time(efficient_producers,T) != zero
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [E,T] :
( ( greater(zero,growth_rate(efficient_producers,sK0_skl(T,E)))
& greater(T,sK0_skl(T,E))
& in_environment(E,sK0_skl(T,E))
& greater(sK0_skl(T,E),appear(efficient_producers,E)) )
| cardinality_at_time(efficient_producers,T) != zero
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(To,sK0_skl(T,E))],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( in_environment(X0,sK0_skl(X1,X0))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( greater(zero,growth_rate(efficient_producers,sK0_skl(X1,X0)))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f24,plain,
! [E,T] :
( number_of_organizations(E,T) = zero
| ~ greater(appear(an_organisation,E),T)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
! [E,T] :
( ? [X] :
( ~ greater(zero,growth_rate(X,T))
& greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T) )
| decreases(number_of_organizations(E,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [E,T] :
( ( ~ greater(zero,growth_rate(sK1_skl(T,E),T))
& greater(cardinality_at_time(sK1_skl(T,E),T),zero)
& subpopulation(sK1_skl(T,E),E,T) )
| decreases(number_of_organizations(E,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl(T,E))],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( subpopulation(sK1_skl(X1,X0),X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( greater(cardinality_at_time(sK1_skl(X1,X0),X1),zero)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(sK1_skl(X1,X0),X1))
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [E,T,X] :
( cardinality_at_time(X,T) = zero
| ~ subpopulation(X,E,T)
| number_of_organizations(E,T) != zero
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [T,X] :
( cardinality_at_time(X,T) = zero
| ! [E] :
( ~ subpopulation(X,E,T)
| number_of_organizations(E,T) != zero
| ~ in_environment(E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,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)],[f32]) ).
fof(f34,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [S,T] :
( ~ greater(zero,growth_rate(S,T))
| cardinality_at_time(S,T) != zero ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f38,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(X0,X1))
| cardinality_at_time(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| cardinality_at_time(efficient_producers,T) = zero
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f40,plain,
! [T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| cardinality_at_time(efficient_producers,T) = zero
| ! [E] :
( ~ in_environment(E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,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)],[f40]) ).
fof(f42,plain,
! [X] :
( ~ decreases(X)
| ~ constant(X) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [E,T] :
( greater(appear(an_organisation,E),T)
| greater_or_equal(T,appear(an_organisation,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f45,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)],[f44]) ).
fof(f46,plain,
! [E,T] :
( ( ( constant(resources(E,T))
| greater(equilibrium(E),T) )
& ( decreases(resources(E,T))
| ~ greater(equilibrium(E),T) ) )
| ~ greater(number_of_organizations(E,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f47,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)],[f46]) ).
fof(f48,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)],[f46]) ).
fof(f49,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ greater_or_equal(T,appear(an_organisation,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f50,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)],[f49]) ).
fof(f51,plain,
! [E,T] :
( ( ( constant(number_of_organizations(E,T))
| ~ constant(resources(E,T)) )
& ( ~ decreases(number_of_organizations(E,T))
| ~ decreases(resources(E,T)) ) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
! [X0,X1] :
( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
! [E,S1,S2,T] :
( ~ greater(zero,growth_rate(S2,T))
| ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f55,plain,
! [S2,T] :
( ~ greater(zero,growth_rate(S2,T))
| ! [S1] :
( ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ! [E] :
( ~ in_environment(E,T)
| ~ environment(E) ) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,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)],[f55]) ).
fof(f57,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f58,plain,
! [E,X,T] :
( X = first_movers
| X = efficient_producers
| ~ greater(cardinality_at_time(X,T),zero)
| ~ subpopulation(X,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f59,plain,
! [X] :
( X = first_movers
| X = efficient_producers
| ! [T] :
( ~ greater(cardinality_at_time(X,T),zero)
| ! [E] :
( ~ subpopulation(X,E,T)
| ~ environment(E) ) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,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)],[f59]) ).
fof(f61,plain,
? [E,T] :
( ~ greater(cardinality_at_time(efficient_producers,T),zero)
& greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f62,plain,
? [T] :
( ~ greater(cardinality_at_time(efficient_producers,T),zero)
& ? [E] :
( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) ) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f63,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK2_skl),zero)
& greater_or_equal(sK2_skl,appear(efficient_producers,sK3_skl))
& in_environment(sK3_skl,sK2_skl)
& environment(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(T,sK2_skl),skolemize(E,sK3_skl)],[f62]) ).
fof(f64,plain,
environment(sK3_skl),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
in_environment(sK3_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f66,plain,
greater_or_equal(sK2_skl,appear(efficient_producers,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f67,plain,
~ greater(cardinality_at_time(efficient_producers,sK2_skl),zero),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f68,plain,
! [X0] :
( cardinality_at_time(efficient_producers,sK2_skl) = zero
| ~ in_environment(X0,sK2_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f41,f67]) ).
fof(f69,definition,
! [X0] :
( sQ0_spl
<=> ( ~ in_environment(X0,sK2_skl)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f70,plain,
! [X0] :
( ~ sQ0_spl
| ~ in_environment(X0,sK2_skl)
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,definition,
( sQ1_spl
<=> cardinality_at_time(efficient_producers,sK2_skl) = zero ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f69,f72]) ).
fof(f76,plain,
( ~ sQ0_spl
| ~ environment(sK3_skl) ),
inference(resolution,[status(thm)],[f70,f65]) ).
fof(f77,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f64]) ).
fof(f78,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = first_movers
| X0 = efficient_producers
| ~ greater(cardinality_at_time(X0,X1),zero)
| ~ subpopulation(X0,sK3_skl,X1) ),
inference(resolution,[status(thm)],[f60,f64]) ).
fof(f103,plain,
! [X0,X1] :
( cardinality_at_time(efficient_producers,sK0_skl(X1,X0)) != zero
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f23,f38]) ).
fof(f114,definition,
( sQ8_spl
<=> environment(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( sQ8_spl
| ~ environment(sK3_skl) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f134,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f64]) ).
fof(f135,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f144,plain,
! [X0,X1] :
( cardinality_at_time(X1,X0) = zero
| ~ subpopulation(X1,sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) != zero
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f33,f64]) ).
fof(f166,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f48,f50]) ).
fof(f167,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(an_organisation,X0))
| constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f166]) ).
fof(f168,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)],[f56,f57]) ).
fof(f170,plain,
! [X0] :
( cardinality_at_time(efficient_producers,sK0_skl(X0,sK3_skl)) != zero
| cardinality_at_time(efficient_producers,X0) != zero
| ~ greater_or_equal(X0,appear(efficient_producers,sK3_skl)) ),
inference(resolution,[status(thm)],[f103,f64]) ).
fof(f171,plain,
! [X0] :
( ~ greater_or_equal(X0,appear(an_organisation,sK3_skl))
| constant(resources(sK3_skl,X0))
| greater(equilibrium(sK3_skl),X0)
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f167,f64]) ).
fof(f172,plain,
( cardinality_at_time(efficient_producers,sK0_skl(sK2_skl,sK3_skl)) != zero
| cardinality_at_time(efficient_producers,sK2_skl) != zero ),
inference(resolution,[status(thm)],[f170,f66]) ).
fof(f173,definition,
( sQ17_spl
<=> cardinality_at_time(efficient_producers,sK0_skl(sK2_skl,sK3_skl)) = zero ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ17_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f172,f72,f173]) ).
fof(f177,plain,
! [X0] :
( greater(appear(an_organisation,sK3_skl),X0)
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| constant(resources(sK3_skl,X0))
| greater(equilibrium(sK3_skl),X0)
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f171,f45]) ).
fof(f178,definition,
! [X0] :
( sQ18_spl
<=> ( greater(appear(an_organisation,sK3_skl),X0)
| ~ in_environment(sK3_skl,X0)
| constant(resources(sK3_skl,X0))
| greater(equilibrium(sK3_skl),X0)
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0] :
( ~ sQ18_spl
| greater(appear(an_organisation,sK3_skl),X0)
| ~ in_environment(sK3_skl,X0)
| constant(resources(sK3_skl,X0))
| greater(equilibrium(sK3_skl),X0)
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ8_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f177,f178,f114]) ).
fof(f182,plain,
! [X0] :
( ~ sQ18_spl
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| greater(equilibrium(sK3_skl),X0)
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f179]) ).
fof(f184,definition,
( sQ19_spl
<=> number_of_organizations(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) = zero ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f187,definition,
! [X0] :
( sQ20_spl
<=> ( cardinality_at_time(X0,sK0_skl(sK2_skl,sK3_skl)) = zero
| ~ subpopulation(X0,sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0] :
( ~ sQ20_spl
| cardinality_at_time(X0,sK0_skl(sK2_skl,sK3_skl)) = zero
| ~ subpopulation(X0,sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f192,plain,
( ~ sQ20_spl
| ~ in_environment(sK3_skl,sK0_skl(sK2_skl,sK3_skl))
| ~ environment(sK3_skl)
| cardinality_at_time(efficient_producers,sK0_skl(sK2_skl,sK3_skl)) = zero ),
inference(resolution,[status(thm)],[f188,f36]) ).
fof(f196,definition,
( sQ22_spl
<=> in_environment(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ22_spl
| in_environment(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f198,plain,
( sQ22_spl
| ~ in_environment(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f200,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| ~ sQ8_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f192,f173,f114,f196,f187]) ).
fof(f201,plain,
( sQ22_spl
| cardinality_at_time(efficient_producers,sK2_skl) != zero
| ~ greater_or_equal(sK2_skl,appear(efficient_producers,sK3_skl))
| ~ environment(sK3_skl) ),
inference(resolution,[status(thm)],[f198,f21]) ).
fof(f202,definition,
( sQ23_spl
<=> greater_or_equal(sK2_skl,appear(efficient_producers,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ23_spl
| ~ greater_or_equal(sK2_skl,appear(efficient_producers,sK3_skl)) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( sQ22_spl
| ~ sQ1_spl
| ~ sQ23_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f201,f114,f202,f72,f196]) ).
fof(f206,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f66]) ).
fof(f207,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f208,plain,
! [X0] :
( ~ sQ22_spl
| cardinality_at_time(X0,sK0_skl(sK2_skl,sK3_skl)) = zero
| ~ subpopulation(X0,sK3_skl,sK0_skl(sK2_skl,sK3_skl))
| number_of_organizations(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) != zero ),
inference(resolution,[status(thm)],[f197,f144]) ).
fof(f209,plain,
( ~ sQ22_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f208,f184,f187,f196]) ).
fof(f210,plain,
! [X0] :
( ~ sQ18_spl
| decreases(resources(sK3_skl,X0))
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f182,f47]) ).
fof(f211,definition,
! [X0] :
( sQ24_spl
<=> ( decreases(resources(sK3_skl,X0))
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| ~ in_environment(sK3_skl,X0)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0] :
( ~ sQ24_spl
| decreases(resources(sK3_skl,X0))
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| ~ in_environment(sK3_skl,X0)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ18_spl
| ~ sQ8_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f210,f211,f114,f178]) ).
fof(f215,plain,
! [X0] :
( ~ sQ24_spl
| decreases(resources(sK3_skl,X0))
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f212]) ).
fof(f216,plain,
! [X0] :
( ~ sQ24_spl
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f215,f52]) ).
fof(f217,definition,
! [X0] :
( sQ25_spl
<=> ( ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0)
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ25_spl
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0)
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( ~ sQ24_spl
| ~ sQ8_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f216,f217,f114,f211]) ).
fof(f221,plain,
! [X0] :
( ~ sQ25_spl
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ greater(number_of_organizations(sK3_skl,X0),zero)
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f218]) ).
fof(f222,plain,
! [X0] :
( ~ sQ25_spl
| ~ greater_or_equal(X0,appear(an_organisation,sK3_skl))
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f221,f50]) ).
fof(f223,definition,
! [X0] :
( sQ26_spl
<=> ( ~ greater_or_equal(X0,appear(an_organisation,sK3_skl))
| ~ in_environment(sK3_skl,X0)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0] :
( ~ sQ26_spl
| ~ greater_or_equal(X0,appear(an_organisation,sK3_skl))
| ~ in_environment(sK3_skl,X0)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f222,f223,f114,f217]) ).
fof(f227,plain,
! [X0] :
( ~ sQ26_spl
| ~ greater_or_equal(X0,appear(an_organisation,sK3_skl))
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f224]) ).
fof(f228,plain,
! [X0,X1,X2] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| ~ environment(X2)
| greater(zero,growth_rate(first_movers,sK0_skl(X1,X2)))
| ~ in_environment(X0,sK0_skl(X1,X2))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f168,f23]) ).
fof(f229,plain,
! [X0] :
( ~ sQ26_spl
| greater(appear(an_organisation,sK3_skl),X0)
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f227,f45]) ).
fof(f230,definition,
! [X0] :
( sQ27_spl
<=> ( greater(appear(an_organisation,sK3_skl),X0)
| ~ in_environment(sK3_skl,X0)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f231,plain,
! [X0] :
( ~ sQ27_spl
| greater(appear(an_organisation,sK3_skl),X0)
| ~ in_environment(sK3_skl,X0)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ26_spl
| ~ sQ8_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f229,f230,f114,f223]) ).
fof(f234,plain,
! [X0] :
( ~ sQ27_spl
| ~ decreases(number_of_organizations(sK3_skl,X0))
| greater(appear(an_organisation,sK3_skl),X0)
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f231]) ).
fof(f235,plain,
! [X0] :
( ~ sQ27_spl
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f234,f25]) ).
fof(f236,definition,
! [X0] :
( sQ28_spl
<=> ( number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f237,plain,
! [X0] :
( ~ sQ28_spl
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0)
| ~ decreases(number_of_organizations(sK3_skl,X0))
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,plain,
( ~ sQ27_spl
| ~ sQ8_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f235,f236,f114,f230]) ).
fof(f240,plain,
! [X0] :
( ~ sQ28_spl
| number_of_organizations(sK3_skl,X0) = zero
| ~ decreases(number_of_organizations(sK3_skl,X0))
| constant(resources(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f237]) ).
fof(f241,plain,
! [X0] :
( ~ sQ28_spl
| constant(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| number_of_organizations(sK3_skl,X0) = zero
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f240,f53]) ).
fof(f243,definition,
! [X0] :
( sQ29_spl
<=> ( constant(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f244,plain,
! [X0] :
( ~ sQ29_spl
| constant(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( ~ sQ28_spl
| ~ sQ8_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f241,f243,f114,f236]) ).
fof(f247,plain,
! [X0] :
( ~ sQ29_spl
| constant(number_of_organizations(sK3_skl,X0))
| number_of_organizations(sK3_skl,X0) = zero
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f244]) ).
fof(f248,plain,
! [X0] :
( ~ sQ29_spl
| number_of_organizations(sK3_skl,X0) = zero
| ~ decreases(number_of_organizations(sK3_skl,X0))
| ~ in_environment(sK3_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f247,f43]) ).
fof(f249,plain,
! [X0] :
( ~ sQ29_spl
| ~ greater(zero,growth_rate(sK1_skl(X0,sK3_skl),X0))
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f248,f30]) ).
fof(f250,plain,
! [X0] :
( ~ sQ29_spl
| greater(cardinality_at_time(sK1_skl(X0,sK3_skl),X0),zero)
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f248,f29]) ).
fof(f251,plain,
! [X0] :
( ~ sQ29_spl
| subpopulation(sK1_skl(X0,sK3_skl),sK3_skl,X0)
| ~ in_environment(sK3_skl,X0)
| ~ environment(sK3_skl)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f248,f28]) ).
fof(f252,definition,
! [X0] :
( sQ30_spl
<=> ( ~ greater(zero,growth_rate(sK1_skl(X0,sK3_skl),X0))
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f253,plain,
! [X0] :
( ~ sQ30_spl
| ~ greater(zero,growth_rate(sK1_skl(X0,sK3_skl),X0))
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,plain,
( ~ sQ29_spl
| ~ sQ8_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f249,f252,f114,f243]) ).
fof(f256,definition,
! [X0] :
( sQ31_spl
<=> ( greater(cardinality_at_time(sK1_skl(X0,sK3_skl),X0),zero)
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f257,plain,
! [X0] :
( ~ sQ31_spl
| greater(cardinality_at_time(sK1_skl(X0,sK3_skl),X0),zero)
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( ~ sQ29_spl
| ~ sQ8_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f250,f256,f114,f243]) ).
fof(f260,definition,
! [X0] :
( sQ32_spl
<=> ( subpopulation(sK1_skl(X0,sK3_skl),sK3_skl,X0)
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f261,plain,
! [X0] :
( ~ sQ32_spl
| subpopulation(sK1_skl(X0,sK3_skl),sK3_skl,X0)
| ~ in_environment(sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( ~ sQ29_spl
| ~ sQ8_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f251,f260,f114,f243]) ).
fof(f264,plain,
! [X0] :
( ~ sQ30_spl
| ~ greater(zero,growth_rate(sK1_skl(X0,sK3_skl),X0))
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f253]) ).
fof(f265,plain,
! [X0] :
( ~ sQ31_spl
| greater(cardinality_at_time(sK1_skl(X0,sK3_skl),X0),zero)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f257]) ).
fof(f266,plain,
! [X0] :
( ~ sQ32_spl
| subpopulation(sK1_skl(X0,sK3_skl),sK3_skl,X0)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f261]) ).
fof(f267,plain,
! [X0] :
( ~ sQ32_spl
| sK1_skl(X0,sK3_skl) = first_movers
| sK1_skl(X0,sK3_skl) = efficient_producers
| ~ greater(cardinality_at_time(sK1_skl(X0,sK3_skl),X0),zero)
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f266,f85]) ).
fof(f269,plain,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,sK3_skl))
| greater(zero,growth_rate(first_movers,sK0_skl(X1,sK3_skl)))
| ~ in_environment(X0,sK0_skl(X1,sK3_skl))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f228,f64]) ).
fof(f270,plain,
! [X0] :
( ~ sQ32_spl
| ~ sQ31_spl
| sK1_skl(X0,sK3_skl) = first_movers
| sK1_skl(X0,sK3_skl) = efficient_producers
| number_of_organizations(sK3_skl,X0) = zero
| ~ in_environment(sK3_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f265]) ).
fof(f271,plain,
( ~ sQ22_spl
| ~ sQ32_spl
| ~ sQ31_spl
| sK1_skl(sK0_skl(sK2_skl,sK3_skl),sK3_skl) = first_movers
| sK1_skl(sK0_skl(sK2_skl,sK3_skl),sK3_skl) = efficient_producers
| number_of_organizations(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) = zero ),
inference(resolution,[status(thm)],[f270,f197]) ).
fof(f274,definition,
( sQ33_spl
<=> sK1_skl(sK0_skl(sK2_skl,sK3_skl),sK3_skl) = efficient_producers ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ33_spl
| sK1_skl(sK0_skl(sK2_skl,sK3_skl),sK3_skl) = efficient_producers ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
( sQ34_spl
<=> sK1_skl(sK0_skl(sK2_skl,sK3_skl),sK3_skl) = first_movers ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ34_spl
| sK1_skl(sK0_skl(sK2_skl,sK3_skl),sK3_skl) = first_movers ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( ~ sQ22_spl
| ~ sQ32_spl
| ~ sQ31_spl
| sQ34_spl
| sQ33_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f271,f184,f274,f277,f256,f260,f196]) ).
fof(f337,plain,
! [X0] :
( cardinality_at_time(efficient_producers,sK2_skl) != zero
| greater(zero,growth_rate(first_movers,sK0_skl(sK2_skl,sK3_skl)))
| ~ in_environment(X0,sK0_skl(sK2_skl,sK3_skl))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f269,f66]) ).
fof(f338,definition,
! [X0] :
( sQ41_spl
<=> ( ~ in_environment(X0,sK0_skl(sK2_skl,sK3_skl))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f339,plain,
! [X0] :
( ~ sQ41_spl
| ~ in_environment(X0,sK0_skl(sK2_skl,sK3_skl))
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,definition,
( sQ42_spl
<=> greater(zero,growth_rate(first_movers,sK0_skl(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ1_spl
| sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f337,f338,f341,f72]) ).
fof(f414,plain,
( ~ sQ33_spl
| ~ sQ30_spl
| ~ greater(zero,growth_rate(efficient_producers,sK0_skl(sK2_skl,sK3_skl)))
| number_of_organizations(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) = zero
| ~ in_environment(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ),
inference(paramodulation,[status(thm)],[f275,f264]) ).
fof(f420,definition,
( sQ51_spl
<=> greater(zero,growth_rate(efficient_producers,sK0_skl(sK2_skl,sK3_skl))) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( sQ51_spl
| ~ greater(zero,growth_rate(efficient_producers,sK0_skl(sK2_skl,sK3_skl))) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( ~ sQ33_spl
| ~ sQ30_spl
| ~ sQ51_spl
| sQ19_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f414,f196,f184,f420,f252,f274]) ).
fof(f428,plain,
( ~ sQ41_spl
| ~ in_environment(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f339,f64]) ).
fof(f429,plain,
( ~ sQ41_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f428,f196,f338]) ).
fof(f434,plain,
( sQ51_spl
| cardinality_at_time(efficient_producers,sK2_skl) != zero
| ~ greater_or_equal(sK2_skl,appear(efficient_producers,sK3_skl))
| ~ environment(sK3_skl) ),
inference(resolution,[status(thm)],[f422,f23]) ).
fof(f435,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ23_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f434,f114,f202,f72,f420]) ).
fof(f437,plain,
( ~ sQ34_spl
| ~ sQ30_spl
| ~ greater(zero,growth_rate(first_movers,sK0_skl(sK2_skl,sK3_skl)))
| number_of_organizations(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) = zero
| ~ in_environment(sK3_skl,sK0_skl(sK2_skl,sK3_skl)) ),
inference(paramodulation,[status(thm)],[f278,f264]) ).
fof(f443,plain,
( ~ sQ34_spl
| ~ sQ30_spl
| ~ sQ42_spl
| sQ19_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f437,f196,f184,f341,f252,f277]) ).
fof(f448,plain,
$false,
inference(sat_refutation,[status(thm)],[f75,f78,f135,f176,f181,f200,f205,f207,f209,f214,f220,f226,f233,f239,f246,f255,f259,f263,f280,f344,f423,f429,f435,f443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 01:21:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.055283 seconds
% 0.14/0.41 % CPU time: 0.105136 seconds
% 0.14/0.41 % Total memory used: 19.122 MB
% 0.14/0.41 % Net memory used: 19.071 MB
%------------------------------------------------------------------------------