%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT027+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 : n008.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 01:25:19 PM UTC 2026
% Result : Theorem 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 128 ( 5 unt; 18 def)
% Number of atoms : 429 ( 9 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 539 ( 238 ~; 234 |; 37 &)
% ( 19 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 19 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 104 ( 97 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,To] :
( ( ! [T] :
( ( greater_or_equal(T,To)
& greater(cardinality_at_time(first_movers,T),zero) )
=> greater(zero,growth_rate(first_movers,T)) )
& in_environment(E,To)
& stable(E)
& environment(E) )
=> contracts_from(To,first_movers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero)
& in_environment(E,T)
& environment(E) )
=> subpopulations(first_movers,efficient_producers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [E,T1,T2] :
( ( greater(T2,T1)
& in_environment(E,T1)
& stable(E)
& environment(E) )
=> in_environment(E,T2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [E] :
( ( stable(E)
& environment(E) )
=> in_environment(E,appear(efficient_producers,E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
<=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(zero,growth_rate(first_movers,T)) )
& greater(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( contracts_from(To,first_movers)
& greater(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( contracts_from(To,first_movers)
& greater(To,appear(efficient_producers,E)) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [E,To] :
( contracts_from(To,first_movers)
| ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,To)
& greater(cardinality_at_time(first_movers,T),zero) )
| ~ in_environment(E,To)
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [To] :
( contracts_from(To,first_movers)
| ? [T] :
( ~ greater(zero,growth_rate(first_movers,T))
& greater_or_equal(T,To)
& greater(cardinality_at_time(first_movers,T),zero) )
| ! [E] :
( ~ in_environment(E,To)
| ~ stable(E)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
! [To] :
( contracts_from(To,first_movers)
| ( ~ greater(zero,growth_rate(first_movers,sK0_skl(To)))
& greater_or_equal(sK0_skl(To),To)
& greater(cardinality_at_time(first_movers,sK0_skl(To)),zero) )
| ! [E] :
( ~ in_environment(E,To)
| ~ stable(E)
| ~ environment(E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(T,sK0_skl(To))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sK0_skl(X1)),zero)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| greater_or_equal(sK0_skl(X1),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ~ greater(zero,growth_rate(first_movers,sK0_skl(X1)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [E,T] :
( subpopulations(first_movers,efficient_producers,E,T)
| ~ greater(cardinality_at_time(efficient_producers,T),zero)
| ~ greater(cardinality_at_time(first_movers,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [E,T1,T2] :
( in_environment(E,T2)
| ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [E,T2] :
( in_environment(E,T2)
| ! [T1] :
( ~ greater(T2,T1)
| ~ in_environment(E,T1)
| ~ stable(E)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [E] :
( in_environment(E,appear(efficient_producers,E))
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X,Y,Z] :
( greater(X,Z)
| ~ greater(Y,Z)
| ~ greater(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X,Z] :
( greater(X,Z)
| ! [Y] :
( ~ greater(Y,Z)
| ~ greater(X,Y) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X,Y] :
( ( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
( ! [X,Y] :
( ( X != Y
& ~ greater(X,Y) )
| greater_or_equal(X,Y) )
& ! [X,Y] :
( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,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)],[f7]) ).
fof(f33,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)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(To,appear(efficient_producers,E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
! [E] :
( ( ! [T] :
( greater(zero,growth_rate(first_movers,T))
| ~ greater_or_equal(T,sK1_skl(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& greater(sK1_skl(E),appear(efficient_producers,E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(To,sK1_skl(E))],[f35]) ).
fof(f37,plain,
! [X0] :
( greater(sK1_skl(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK1_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
? [E] :
( ! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,E)) )
& stable(E)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( ! [To] :
( ~ contracts_from(To,first_movers)
| ~ greater(To,appear(efficient_producers,sK2_skl)) )
& stable(sK2_skl)
& environment(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(E,sK2_skl)],[f39]) ).
fof(f41,plain,
environment(sK2_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
stable(sK2_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0] :
( ~ contracts_from(X0,first_movers)
| ~ greater(X0,appear(efficient_producers,sK2_skl)) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f50,plain,
( greater(sK1_skl(sK2_skl),appear(efficient_producers,sK2_skl))
| ~ stable(sK2_skl) ),
inference(resolution,[status(thm)],[f37,f41]) ).
fof(f51,definition,
( sQ0_spl
<=> stable(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ0_spl
| ~ stable(sK2_skl) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> greater(sK1_skl(sK2_skl),appear(efficient_producers,sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ1_spl
| greater(sK1_skl(sK2_skl),appear(efficient_producers,sK2_skl)) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f51,f54]) ).
fof(f58,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f42]) ).
fof(f59,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f60,plain,
( ~ sQ1_spl
| ~ contracts_from(sK1_skl(sK2_skl),first_movers) ),
inference(resolution,[status(thm)],[f55,f43]) ).
fof(f61,plain,
( ~ sQ1_spl
| greater_or_equal(sK1_skl(sK2_skl),appear(efficient_producers,sK2_skl)) ),
inference(resolution,[status(thm)],[f55,f30]) ).
fof(f62,plain,
! [X0] :
( ~ sQ1_spl
| greater(X0,appear(efficient_producers,sK2_skl))
| ~ greater(X0,sK1_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f55,f26]) ).
fof(f63,plain,
! [X0] :
( ~ sQ1_spl
| greater_or_equal(sK0_skl(sK1_skl(sK2_skl)),sK1_skl(sK2_skl))
| ~ in_environment(X0,sK1_skl(sK2_skl))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f60,f15]) ).
fof(f64,plain,
! [X0] :
( ~ sQ1_spl
| greater(cardinality_at_time(first_movers,sK0_skl(sK1_skl(sK2_skl))),zero)
| ~ in_environment(X0,sK1_skl(sK2_skl))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f60,f14]) ).
fof(f65,definition,
! [X0] :
( sQ2_spl
<=> ( ~ in_environment(X0,sK1_skl(sK2_skl))
| ~ stable(X0)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f66,plain,
! [X0] :
( ~ sQ2_spl
| ~ in_environment(X0,sK1_skl(sK2_skl))
| ~ stable(X0)
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,definition,
( sQ3_spl
<=> greater_or_equal(sK0_skl(sK1_skl(sK2_skl)),sK1_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( ~ sQ3_spl
| greater_or_equal(sK0_skl(sK1_skl(sK2_skl)),sK1_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f68]) ).
fof(f71,plain,
( ~ sQ1_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f63,f65,f68,f54]) ).
fof(f72,definition,
( sQ4_spl
<=> greater(cardinality_at_time(first_movers,sK0_skl(sK1_skl(sK2_skl))),zero) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f73,plain,
( ~ sQ4_spl
| greater(cardinality_at_time(first_movers,sK0_skl(sK1_skl(sK2_skl))),zero) ),
inference(component_clause,[status(thm)],[f72]) ).
fof(f75,plain,
( ~ sQ1_spl
| sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f64,f65,f72,f54]) ).
fof(f76,plain,
( ~ sQ1_spl
| greater(cardinality_at_time(efficient_producers,sK1_skl(sK2_skl)),zero)
| ~ in_environment(sK2_skl,sK1_skl(sK2_skl))
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f61,f34]) ).
fof(f78,definition,
( sQ5_spl
<=> environment(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( sQ5_spl
| ~ environment(sK2_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,definition,
( sQ6_spl
<=> in_environment(sK2_skl,sK1_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ6_spl
| in_environment(sK2_skl,sK1_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f83,plain,
( sQ6_spl
| ~ in_environment(sK2_skl,sK1_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ7_spl
<=> greater(cardinality_at_time(efficient_producers,sK1_skl(sK2_skl)),zero) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ7_spl
| greater(cardinality_at_time(efficient_producers,sK1_skl(sK2_skl)),zero) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f76,f78,f81,f84,f54]) ).
fof(f99,plain,
( ~ sQ2_spl
| ~ in_environment(sK2_skl,sK1_skl(sK2_skl))
| ~ stable(sK2_skl) ),
inference(resolution,[status(thm)],[f66,f41]) ).
fof(f100,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f99,f51,f81,f65]) ).
fof(f101,plain,
! [X0] :
( sQ6_spl
| ~ greater(sK1_skl(sK2_skl),X0)
| ~ in_environment(sK2_skl,X0)
| ~ stable(sK2_skl)
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f83,f21]) ).
fof(f102,definition,
! [X0] :
( sQ10_spl
<=> ( ~ greater(sK1_skl(sK2_skl),X0)
| ~ in_environment(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f103,plain,
! [X0] :
( ~ sQ10_spl
| ~ greater(sK1_skl(sK2_skl),X0)
| ~ in_environment(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( sQ6_spl
| sQ10_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f101,f78,f51,f102,f81]) ).
fof(f106,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f41]) ).
fof(f107,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ in_environment(sK2_skl,appear(efficient_producers,sK2_skl)) ),
inference(resolution,[status(thm)],[f103,f55]) ).
fof(f109,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ stable(sK2_skl)
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f108,f23]) ).
fof(f111,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f109,f78,f51,f102,f54]) ).
fof(f120,plain,
( ~ sQ3_spl
| sK0_skl(sK1_skl(sK2_skl)) = sK1_skl(sK2_skl)
| greater(sK0_skl(sK1_skl(sK2_skl)),sK1_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f69,f29]) ).
fof(f121,definition,
( sQ12_spl
<=> greater(sK0_skl(sK1_skl(sK2_skl)),sK1_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ12_spl
| greater(sK0_skl(sK1_skl(sK2_skl)),sK1_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
( sQ13_spl
<=> sK0_skl(sK1_skl(sK2_skl)) = sK1_skl(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ13_spl
| sK0_skl(sK1_skl(sK2_skl)) = sK1_skl(sK2_skl) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ3_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f120,f121,f124,f68]) ).
fof(f130,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| greater(sK0_skl(sK1_skl(sK2_skl)),appear(efficient_producers,sK2_skl)) ),
inference(resolution,[status(thm)],[f62,f122]) ).
fof(f131,plain,
! [X0] :
( ~ sQ4_spl
| subpopulations(first_movers,efficient_producers,X0,sK0_skl(sK1_skl(sK2_skl)))
| ~ greater(cardinality_at_time(efficient_producers,sK0_skl(sK1_skl(sK2_skl))),zero)
| ~ in_environment(X0,sK0_skl(sK1_skl(sK2_skl)))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f73,f18]) ).
fof(f134,definition,
! [X0] :
( sQ14_spl
<=> ( subpopulations(first_movers,efficient_producers,X0,sK0_skl(sK1_skl(sK2_skl)))
| ~ in_environment(X0,sK0_skl(sK1_skl(sK2_skl)))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f135,plain,
! [X0] :
( ~ sQ14_spl
| subpopulations(first_movers,efficient_producers,X0,sK0_skl(sK1_skl(sK2_skl)))
| ~ in_environment(X0,sK0_skl(sK1_skl(sK2_skl)))
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,definition,
( sQ15_spl
<=> greater(cardinality_at_time(efficient_producers,sK0_skl(sK1_skl(sK2_skl))),zero) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ15_spl
| ~ greater(cardinality_at_time(efficient_producers,sK0_skl(sK1_skl(sK2_skl))),zero) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f131,f134,f137,f72]) ).
fof(f142,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| greater_or_equal(sK0_skl(sK1_skl(sK2_skl)),appear(efficient_producers,sK2_skl)) ),
inference(resolution,[status(thm)],[f130,f30]) ).
fof(f162,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| greater(cardinality_at_time(efficient_producers,sK0_skl(sK1_skl(sK2_skl))),zero)
| ~ in_environment(sK2_skl,sK0_skl(sK1_skl(sK2_skl)))
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f142,f34]) ).
fof(f164,definition,
( sQ20_spl
<=> in_environment(sK2_skl,sK0_skl(sK1_skl(sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( sQ20_spl
| ~ in_environment(sK2_skl,sK0_skl(sK1_skl(sK2_skl))) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| sQ15_spl
| ~ sQ20_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f162,f78,f164,f137,f54,f121]) ).
fof(f175,plain,
! [X0] :
( sQ20_spl
| ~ greater(sK0_skl(sK1_skl(sK2_skl)),X0)
| ~ in_environment(sK2_skl,X0)
| ~ stable(sK2_skl)
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f166,f21]) ).
fof(f176,definition,
! [X0] :
( sQ23_spl
<=> ( ~ greater(sK0_skl(sK1_skl(sK2_skl)),X0)
| ~ in_environment(sK2_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f177,plain,
! [X0] :
( ~ sQ23_spl
| ~ greater(sK0_skl(sK1_skl(sK2_skl)),X0)
| ~ in_environment(sK2_skl,X0) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( sQ20_spl
| sQ23_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f175,f78,f51,f176,f164]) ).
fof(f181,plain,
( ~ sQ12_spl
| ~ sQ23_spl
| ~ in_environment(sK2_skl,sK1_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f177,f122]) ).
fof(f182,plain,
( ~ sQ12_spl
| ~ sQ23_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f181,f81,f176,f121]) ).
fof(f237,definition,
( sQ33_spl
<=> greater(zero,growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ33_spl
| greater(zero,growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl)))) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f241,plain,
( ~ sQ14_spl
| subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl)))
| ~ in_environment(sK2_skl,sK0_skl(sK1_skl(sK2_skl))) ),
inference(resolution,[status(thm)],[f135,f41]) ).
fof(f242,definition,
( sQ34_spl
<=> subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ34_spl
| subpopulations(first_movers,efficient_producers,sK2_skl,sK0_skl(sK1_skl(sK2_skl))) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,plain,
( ~ sQ14_spl
| sQ34_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f241,f164,f242,f134]) ).
fof(f255,definition,
( sQ35_spl
<=> contracts_from(sK1_skl(sK2_skl),first_movers) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( ~ sQ35_spl
| contracts_from(sK1_skl(sK2_skl),first_movers) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f259,plain,
( ~ sQ35_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f60]) ).
fof(f260,plain,
( ~ sQ35_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f265,plain,
( sQ20_spl
| ~ sQ13_spl
| ~ in_environment(sK2_skl,sK1_skl(sK2_skl)) ),
inference(forward_demodulation,[status(thm)],[f125,f166]) ).
fof(f266,plain,
( sQ20_spl
| ~ sQ13_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f82]) ).
fof(f267,plain,
( sQ20_spl
| ~ sQ13_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f384,plain,
( ~ sQ34_spl
| greater(zero,growth_rate(first_movers,sK0_skl(sK1_skl(sK2_skl))))
| ~ greater_or_equal(sK0_skl(sK1_skl(sK2_skl)),sK1_skl(sK2_skl))
| ~ stable(sK2_skl)
| ~ environment(sK2_skl) ),
inference(resolution,[status(thm)],[f243,f38]) ).
fof(f385,plain,
( ~ sQ34_spl
| sQ33_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f384,f78,f51,f68,f237,f242]) ).
fof(f386,plain,
! [X0] :
( ~ sQ33_spl
| contracts_from(sK1_skl(sK2_skl),first_movers)
| ~ in_environment(X0,sK1_skl(sK2_skl))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f238,f16]) ).
fof(f389,plain,
( ~ sQ33_spl
| sQ35_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f386,f65,f255,f237]) ).
fof(f416,plain,
( sQ15_spl
| ~ sQ13_spl
| ~ greater(cardinality_at_time(efficient_producers,sK1_skl(sK2_skl)),zero) ),
inference(forward_demodulation,[status(thm)],[f125,f139]) ).
fof(f417,plain,
( sQ15_spl
| ~ sQ13_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f85]) ).
fof(f418,plain,
( sQ15_spl
| ~ sQ13_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f417]) ).
fof(f419,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f59,f71,f75,f87,f100,f105,f107,f111,f127,f140,f167,f179,f182,f245,f260,f267,f385,f389,f418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT027+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n008.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 01:23:16 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.059827 seconds
% 0.13/5.42 % CPU time: 0.182605 seconds
% 0.13/5.42 % Total memory used: 81.735 MB
% 0.13/5.42 % Net memory used: 81.279 MB
%------------------------------------------------------------------------------