%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 104 ( 7 unt; 15 def)
% Number of atoms : 393 ( 37 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 476 ( 187 ~; 207 |; 55 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 15 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& environment(E) )
=> ~ greater(equilibrium(E),T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [E,T] :
( ( constant(number_of_organizations(E,T))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [E,T] :
( ~ greater(equilibrium(E),T)
| ~ greater_or_equal(T,equilibrium(E))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,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)],[f4]) ).
fof(f17,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)],[f15]) ).
fof(f18,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)],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [E,T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero )
| ~ constant(number_of_organizations(E,T))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f22,definition,
! [T] :
( sP0_prd(T)
<=> ( ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f23,plain,
! [E,T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| sP0_prd(T)
| ~ constant(number_of_organizations(E,T))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(formula_renaming,[status(thm)],[f21,f22]) ).
fof(f24,plain,
! [T] :
( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| sP0_prd(T)
| ! [E] :
( ~ constant(number_of_organizations(E,T))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| sP0_prd(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| sP0_prd(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
? [E,T] :
( ( ~ greater(zero,growth_rate(first_movers,T))
| ~ greater(growth_rate(efficient_producers,T),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,T))
| ~ greater(growth_rate(first_movers,T),zero) )
& ( growth_rate(efficient_producers,T) != zero
| growth_rate(first_movers,T) != zero )
& greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
? [T] :
( ( ~ greater(zero,growth_rate(first_movers,T))
| ~ greater(growth_rate(efficient_producers,T),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,T))
| ~ greater(growth_rate(first_movers,T),zero) )
& ( growth_rate(efficient_producers,T) != zero
| growth_rate(first_movers,T) != zero )
& ? [E] :
( greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
( ( ~ greater(zero,growth_rate(first_movers,sK0_skl))
| ~ greater(growth_rate(efficient_producers,sK0_skl),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK0_skl))
| ~ greater(growth_rate(first_movers,sK0_skl),zero) )
& ( growth_rate(efficient_producers,sK0_skl) != zero
| growth_rate(first_movers,sK0_skl) != zero )
& greater_or_equal(sK0_skl,equilibrium(sK1_skl))
& subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl)
& environment(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(T,sK0_skl),skolemize(E,sK1_skl)],[f28]) ).
fof(f30,plain,
environment(sK1_skl),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
greater_or_equal(sK0_skl,equilibrium(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
( growth_rate(efficient_producers,sK0_skl) != zero
| growth_rate(first_movers,sK0_skl) != zero ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f34,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK0_skl))
| ~ greater(growth_rate(first_movers,sK0_skl),zero) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f35,plain,
( ~ greater(zero,growth_rate(first_movers,sK0_skl))
| ~ greater(growth_rate(efficient_producers,sK0_skl),zero) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f36,plain,
! [T] :
( ( ( ( ~ greater(zero,growth_rate(efficient_producers,T))
| ~ greater(growth_rate(first_movers,T),zero) )
& ( growth_rate(efficient_producers,T) != zero
| growth_rate(first_movers,T) != zero ) )
| sP0_prd(T) )
& ( ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero )
| ~ sP0_prd(T) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f37,plain,
( ! [T] :
( ( ( ~ greater(zero,growth_rate(efficient_producers,T))
| ~ greater(growth_rate(first_movers,T),zero) )
& ( growth_rate(efficient_producers,T) != zero
| growth_rate(first_movers,T) != zero ) )
| sP0_prd(T) )
& ! [T] :
( ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero )
| ~ sP0_prd(T) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0] :
( greater(growth_rate(first_movers,X0),zero)
| growth_rate(first_movers,X0) = zero
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,X0))
| growth_rate(first_movers,X0) = zero
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [X0] :
( greater(growth_rate(first_movers,X0),zero)
| growth_rate(efficient_producers,X0) = zero
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,X0))
| growth_rate(efficient_producers,X0) = zero
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f44,definition,
( sQ0_spl
<=> growth_rate(first_movers,sK0_skl) = zero ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ0_spl
| growth_rate(first_movers,sK0_skl) = zero ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> growth_rate(efficient_producers,sK0_skl) = zero ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f44,f47]) ).
fof(f51,definition,
( sQ2_spl
<=> greater(growth_rate(first_movers,sK0_skl),zero) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ2_spl
| ~ greater(growth_rate(first_movers,sK0_skl),zero) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ3_spl
<=> greater(zero,growth_rate(efficient_producers,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ3_spl
| ~ greater(zero,growth_rate(efficient_producers,sK0_skl)) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f34,f51,f54]) ).
fof(f58,definition,
( sQ4_spl
<=> greater(growth_rate(efficient_producers,sK0_skl),zero) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f61,definition,
( sQ5_spl
<=> greater(zero,growth_rate(first_movers,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f63,plain,
( sQ5_spl
| ~ greater(zero,growth_rate(first_movers,sK0_skl)) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f35,f58,f61]) ).
fof(f65,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f17,f20]) ).
fof(f66,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f65]) ).
fof(f67,plain,
( sQ2_spl
| growth_rate(first_movers,sK0_skl) = zero
| ~ sP0_prd(sK0_skl) ),
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f68,definition,
( sQ6_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( sQ6_spl
| ~ sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( sQ2_spl
| sQ0_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f67,f68,f44,f51]) ).
fof(f74,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| sP0_prd(X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f66,f25]) ).
fof(f75,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| sP0_prd(X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| sP0_prd(X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f10]) ).
fof(f77,plain,
( sQ3_spl
| growth_rate(efficient_producers,sK0_skl) = zero
| ~ sP0_prd(sK0_skl) ),
inference(resolution,[status(thm)],[f56,f41]) ).
fof(f78,plain,
( sQ3_spl
| growth_rate(first_movers,sK0_skl) = zero
| ~ sP0_prd(sK0_skl) ),
inference(resolution,[status(thm)],[f56,f39]) ).
fof(f79,plain,
( sQ3_spl
| sQ1_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f77,f68,f47,f54]) ).
fof(f80,plain,
( sQ3_spl
| sQ0_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f78,f68,f44,f54]) ).
fof(f81,plain,
! [X0] :
( sQ6_spl
| greater(growth_rate(efficient_producers,sK0_skl),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f70,f76]) ).
fof(f83,definition,
! [X0] :
( sQ7_spl
<=> ( ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f84,plain,
! [X0] :
( ~ sQ7_spl
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ6_spl
| sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f81,f83,f58,f68]) ).
fof(f88,plain,
! [X0] :
( ~ sQ7_spl
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| greater(equilibrium(X0),sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f12]) ).
fof(f89,plain,
! [X0] :
( sQ5_spl
| sP0_prd(sK0_skl)
| ~ constant(number_of_organizations(X0,sK0_skl))
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f63,f26]) ).
fof(f90,definition,
! [X0] :
( sQ8_spl
<=> ( ~ constant(number_of_organizations(X0,sK0_skl))
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f91,plain,
! [X0] :
( ~ sQ8_spl
| ~ constant(number_of_organizations(X0,sK0_skl))
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( sQ5_spl
| sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f89,f90,f68,f61]) ).
fof(f94,plain,
! [X0] :
( ~ sQ8_spl
| greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f91,f66]) ).
fof(f95,plain,
! [X0] :
( ~ sQ8_spl
| greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ in_environment(X0,sK0_skl)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f94]) ).
fof(f96,plain,
( ~ sQ7_spl
| ~ subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl)
| greater(equilibrium(sK1_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f88,f30]) ).
fof(f97,definition,
( sQ9_spl
<=> greater(equilibrium(sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ9_spl
| greater(equilibrium(sK1_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
( sQ10_spl
<=> subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( sQ10_spl
| ~ subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f96,f97,f100,f83]) ).
fof(f104,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f31]) ).
fof(f105,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ2_spl
| ~ sQ0_spl
| ~ greater(zero,zero) ),
inference(forward_demodulation,[status(thm)],[f45,f53]) ).
fof(f107,plain,
( ~ sQ0_spl
| greater(zero,zero)
| growth_rate(efficient_producers,sK0_skl) = zero
| ~ sP0_prd(sK0_skl) ),
inference(paramodulation,[status(thm)],[f45,f40]) ).
fof(f110,definition,
( sQ11_spl
<=> greater(zero,zero) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ11_spl
| greater(zero,zero) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( ~ sQ0_spl
| sQ11_spl
| sQ1_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f107,f68,f47,f110,f44]) ).
fof(f116,plain,
( ~ sQ11_spl
| sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f106]) ).
fof(f117,plain,
( ~ sQ11_spl
| sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0] :
( ~ sQ8_spl
| greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f10]) ).
fof(f124,plain,
( ~ sQ9_spl
| ~ greater_or_equal(sK0_skl,equilibrium(sK1_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f98,f14]) ).
fof(f125,definition,
( sQ12_spl
<=> environment(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( sQ12_spl
| ~ environment(sK1_skl) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f138,definition,
( sQ16_spl
<=> greater_or_equal(sK0_skl,equilibrium(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ16_spl
| ~ greater_or_equal(sK0_skl,equilibrium(sK1_skl)) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f124,f125,f138,f97]) ).
fof(f142,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f30]) ).
fof(f143,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f144,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f32]) ).
fof(f145,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f146,plain,
( ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f118,f83,f90]) ).
fof(f147,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f57,f64,f71,f79,f80,f86,f93,f103,f105,f113,f117,f141,f143,f145,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:21:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.056458 seconds
% 0.12/0.43 % CPU time: 0.155646 seconds
% 0.12/0.43 % Total memory used: 80.840 MB
% 0.12/0.43 % Net memory used: 80.537 MB
%------------------------------------------------------------------------------