%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT025+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 : 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 01:25:18 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 8
% Syntax : Number of formulae : 130 ( 14 unt; 1 def)
% Number of atoms : 452 ( 46 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 514 ( 192 ~; 242 |; 67 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 117 ( 113 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,X,T] :
( ( ( greater(cardinality_at_time(X,T),zero)
=> ( X = first_movers
| X = efficient_producers ) )
& subpopulation(X,E,T)
& environment(E) )
=> number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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(f3,axiom,
! [A,B,C] :
( ( constant(A)
& A = sum(B,C) )
=> ( ( increases(C)
& decreases(B) )
| ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,E,T] :
( ( greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T)
& in_environment(E,T)
& environment(E) )
=> ( ( decreases(cardinality_at_time(X,T))
=> greater(zero,growth_rate(X,T)) )
& ( increases(cardinality_at_time(X,T))
=> greater(growth_rate(X,T),zero) )
& ( constant(cardinality_at_time(X,T))
=> growth_rate(X,T) = zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [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 ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [E,X,T] :
( number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,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)],[f1]) ).
fof(f11,plain,
! [E,T] :
( number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T))
| ! [X] :
( ( X != first_movers
& X != efficient_producers
& greater(cardinality_at_time(X,T),zero) )
| ~ subpopulation(X,E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f14,plain,
! [X0,X1,X2] :
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| X1 != first_movers
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,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)],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [A,B,C] :
( ( increases(C)
& decreases(B) )
| ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) )
| ~ constant(A)
| A != sum(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f19,definition,
! [B,C] :
( sP0_prd(C,B)
<=> ( ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f20,plain,
! [A,B,C] :
( ( increases(C)
& decreases(B) )
| sP0_prd(C,B)
| ~ constant(A)
| A != sum(B,C) ),
inference(formula_renaming,[status(thm)],[f18,f19]) ).
fof(f21,plain,
! [B,C] :
( ( increases(C)
& decreases(B) )
| sP0_prd(C,B)
| ! [A] :
( ~ constant(A)
| A != sum(B,C) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( decreases(X1)
| sP0_prd(X2,X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( increases(X2)
| sP0_prd(X2,X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,plain,
! [X,E,T] :
( ( ( greater(zero,growth_rate(X,T))
| ~ decreases(cardinality_at_time(X,T)) )
& ( greater(growth_rate(X,T),zero)
| ~ increases(cardinality_at_time(X,T)) )
& ( growth_rate(X,T) = zero
| ~ constant(cardinality_at_time(X,T)) ) )
| ~ greater(cardinality_at_time(X,T),zero)
| ~ subpopulation(X,E,T)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X,T] :
( ( ( greater(zero,growth_rate(X,T))
| ~ decreases(cardinality_at_time(X,T)) )
& ( greater(growth_rate(X,T),zero)
| ~ increases(cardinality_at_time(X,T)) )
& ( growth_rate(X,T) = zero
| ~ constant(cardinality_at_time(X,T)) ) )
| ~ greater(cardinality_at_time(X,T),zero)
| ! [E] :
( ~ subpopulation(X,E,T)
| ~ in_environment(E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( growth_rate(X2,X1) = zero
| ~ constant(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( greater(growth_rate(X2,X1),zero)
| ~ increases(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2] :
( greater(zero,growth_rate(X2,X1))
| ~ decreases(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero) )
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero) )
| ! [E] :
( ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( greater(cardinality_at_time(first_movers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f34,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f38,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)],[f9]) ).
fof(f39,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] :
( constant(number_of_organizations(E,T))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,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 )
& constant(number_of_organizations(sK1_skl,sK0_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)],[f39]) ).
fof(f41,plain,
environment(sK1_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
constant(number_of_organizations(sK1_skl,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
( growth_rate(efficient_producers,sK0_skl) != zero
| growth_rate(first_movers,sK0_skl) != zero ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK0_skl))
| ~ greater(growth_rate(first_movers,sK0_skl),zero) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f46,plain,
( ~ greater(zero,growth_rate(first_movers,sK0_skl))
| ~ greater(growth_rate(efficient_producers,sK0_skl),zero) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f47,plain,
! [B,C] :
( ( ( ( ~ decreases(C)
| ~ increases(B) )
& ( ~ constant(C)
| ~ constant(B) ) )
| sP0_prd(C,B) )
& ( ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) )
| ~ sP0_prd(C,B) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
( ! [B,C] :
( ( ( ~ decreases(C)
| ~ increases(B) )
& ( ~ constant(C)
| ~ constant(B) ) )
| sP0_prd(C,B) )
& ! [B,C] :
( ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) )
| ~ sP0_prd(C,B) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( increases(X1)
| constant(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( decreases(X0)
| constant(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( increases(X1)
| constant(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( decreases(X0)
| constant(X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f56,plain,
! [X0,X1] :
( number_of_organizations(X0,X1) = sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1))
| ~ subpopulation(first_movers,X0,X1)
| ~ environment(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f14]) ).
fof(f57,plain,
! [X0,X1] :
( decreases(X0)
| sP0_prd(X1,X0)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f22]) ).
fof(f58,plain,
! [X0,X1] :
( increases(X1)
| sP0_prd(X1,X0)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f23]) ).
fof(f59,plain,
( in_environment(sK1_skl,sK0_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f34,f42]) ).
fof(f60,plain,
in_environment(sK1_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f59,f41]) ).
fof(f61,plain,
( greater(cardinality_at_time(first_movers,sK0_skl),zero)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f31,f42]) ).
fof(f62,plain,
greater(cardinality_at_time(first_movers,sK0_skl),zero),
inference(forward_subsumption_resolution,[status(thm)],[f61,f41]) ).
fof(f63,plain,
( subpopulation(first_movers,sK1_skl,sK0_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f16,f60]) ).
fof(f64,plain,
subpopulation(first_movers,sK1_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f63,f41]) ).
fof(f67,plain,
( number_of_organizations(sK1_skl,sK0_skl) = sum(cardinality_at_time(first_movers,sK0_skl),cardinality_at_time(efficient_producers,sK0_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f64,f56]) ).
fof(f69,plain,
number_of_organizations(sK1_skl,sK0_skl) = sum(cardinality_at_time(first_movers,sK0_skl),cardinality_at_time(efficient_producers,sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f67,f41]) ).
fof(f75,plain,
! [X0] :
( greater(growth_rate(first_movers,sK0_skl),zero)
| ~ increases(cardinality_at_time(first_movers,sK0_skl))
| ~ subpopulation(first_movers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f62,f27]) ).
fof(f76,plain,
! [X0] :
( growth_rate(first_movers,sK0_skl) = zero
| ~ constant(cardinality_at_time(first_movers,sK0_skl))
| ~ subpopulation(first_movers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f62,f26]) ).
fof(f77,plain,
! [X0] :
( greater(growth_rate(first_movers,sK0_skl),zero)
| ~ increases(cardinality_at_time(first_movers,sK0_skl))
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f16]) ).
fof(f78,plain,
! [X0] :
( growth_rate(first_movers,sK0_skl) = zero
| ~ constant(cardinality_at_time(first_movers,sK0_skl))
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f16]) ).
fof(f79,plain,
( greater(cardinality_at_time(efficient_producers,sK0_skl),zero)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f80,plain,
greater(cardinality_at_time(efficient_producers,sK0_skl),zero),
inference(forward_subsumption_resolution,[status(thm)],[f79,f41]) ).
fof(f81,plain,
! [X0] :
( greater(growth_rate(efficient_producers,sK0_skl),zero)
| ~ increases(cardinality_at_time(efficient_producers,sK0_skl))
| ~ subpopulation(efficient_producers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f80,f27]) ).
fof(f82,plain,
! [X0] :
( growth_rate(efficient_producers,sK0_skl) = zero
| ~ constant(cardinality_at_time(efficient_producers,sK0_skl))
| ~ subpopulation(efficient_producers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f80,f26]) ).
fof(f83,plain,
! [X0] :
( greater(growth_rate(efficient_producers,sK0_skl),zero)
| ~ increases(cardinality_at_time(efficient_producers,sK0_skl))
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f17]) ).
fof(f84,plain,
! [X0] :
( growth_rate(efficient_producers,sK0_skl) = zero
| ~ constant(cardinality_at_time(efficient_producers,sK0_skl))
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f17]) ).
fof(f85,plain,
( greater(growth_rate(first_movers,sK0_skl),zero)
| ~ increases(cardinality_at_time(first_movers,sK0_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f77,f60]) ).
fof(f86,plain,
( greater(growth_rate(first_movers,sK0_skl),zero)
| ~ increases(cardinality_at_time(first_movers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f41]) ).
fof(f88,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| ~ decreases(cardinality_at_time(efficient_producers,sK0_skl))
| ~ subpopulation(efficient_producers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f28,f80]) ).
fof(f89,plain,
! [X0] :
( greater(zero,growth_rate(first_movers,sK0_skl))
| ~ decreases(cardinality_at_time(first_movers,sK0_skl))
| ~ subpopulation(first_movers,X0,sK0_skl)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f28,f62]) ).
fof(f90,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| ~ decreases(cardinality_at_time(efficient_producers,sK0_skl))
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f17]) ).
fof(f91,plain,
! [X0] :
( greater(zero,growth_rate(first_movers,sK0_skl))
| ~ decreases(cardinality_at_time(first_movers,sK0_skl))
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f16]) ).
fof(f95,plain,
( greater(growth_rate(efficient_producers,sK0_skl),zero)
| ~ increases(cardinality_at_time(efficient_producers,sK0_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f83,f60]) ).
fof(f96,plain,
( greater(growth_rate(efficient_producers,sK0_skl),zero)
| ~ increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f41]) ).
fof(f101,plain,
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| ~ decreases(cardinality_at_time(efficient_producers,sK0_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f90,f60]) ).
fof(f102,plain,
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| ~ decreases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f41]) ).
fof(f103,plain,
( greater(zero,growth_rate(first_movers,sK0_skl))
| ~ decreases(cardinality_at_time(first_movers,sK0_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f91,f60]) ).
fof(f104,plain,
( greater(zero,growth_rate(first_movers,sK0_skl))
| ~ decreases(cardinality_at_time(first_movers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f41]) ).
fof(f105,plain,
( increases(cardinality_at_time(efficient_producers,sK0_skl))
| sP0_prd(cardinality_at_time(efficient_producers,sK0_skl),cardinality_at_time(first_movers,sK0_skl))
| ~ constant(number_of_organizations(sK1_skl,sK0_skl)) ),
inference(paramodulation,[status(thm)],[f69,f58]) ).
fof(f106,plain,
( decreases(cardinality_at_time(first_movers,sK0_skl))
| sP0_prd(cardinality_at_time(efficient_producers,sK0_skl),cardinality_at_time(first_movers,sK0_skl))
| ~ constant(number_of_organizations(sK1_skl,sK0_skl)) ),
inference(paramodulation,[status(thm)],[f69,f57]) ).
fof(f107,plain,
( increases(cardinality_at_time(efficient_producers,sK0_skl))
| sP0_prd(cardinality_at_time(efficient_producers,sK0_skl),cardinality_at_time(first_movers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f43]) ).
fof(f108,plain,
( decreases(cardinality_at_time(first_movers,sK0_skl))
| sP0_prd(cardinality_at_time(efficient_producers,sK0_skl),cardinality_at_time(first_movers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f43]) ).
fof(f109,plain,
( decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f107,f52]) ).
fof(f110,plain,
( increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f107,f51]) ).
fof(f111,plain,
( decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f107,f50]) ).
fof(f112,plain,
( increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f107,f49]) ).
fof(f113,plain,
( decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl))
| decreases(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f108,f52]) ).
fof(f114,plain,
( increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl))
| decreases(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f108,f51]) ).
fof(f115,plain,
( decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl))
| decreases(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f108,f50]) ).
fof(f116,plain,
( increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl))
| decreases(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f108,f49]) ).
fof(f117,plain,
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f109,f102]) ).
fof(f119,plain,
( greater(growth_rate(first_movers,sK0_skl),zero)
| constant(cardinality_at_time(efficient_producers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f110,f86]) ).
fof(f120,plain,
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f111,f102]) ).
fof(f122,plain,
( greater(growth_rate(first_movers,sK0_skl),zero)
| constant(cardinality_at_time(first_movers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f112,f86]) ).
fof(f123,plain,
( greater(zero,growth_rate(first_movers,sK0_skl))
| decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f113,f104]) ).
fof(f125,plain,
( greater(zero,growth_rate(first_movers,sK0_skl))
| increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f114,f104]) ).
fof(f127,plain,
( greater(zero,growth_rate(first_movers,sK0_skl))
| decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f115,f104]) ).
fof(f129,plain,
( greater(zero,growth_rate(first_movers,sK0_skl))
| increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f116,f104]) ).
fof(f131,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f119,f45]) ).
fof(f132,plain,
( constant(cardinality_at_time(efficient_producers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f117]) ).
fof(f141,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f122,f45]) ).
fof(f142,plain,
( constant(cardinality_at_time(first_movers,sK0_skl))
| increases(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f120]) ).
fof(f143,plain,
( greater(growth_rate(efficient_producers,sK0_skl),zero)
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f132,f96]) ).
fof(f145,plain,
( greater(growth_rate(efficient_producers,sK0_skl),zero)
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f142,f96]) ).
fof(f146,plain,
( ~ greater(zero,growth_rate(first_movers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f143,f46]) ).
fof(f156,plain,
( ~ greater(zero,growth_rate(first_movers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f145,f46]) ).
fof(f160,plain,
( increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f125,f146]) ).
fof(f161,plain,
( decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f146]) ).
fof(f164,plain,
( greater(growth_rate(first_movers,sK0_skl),zero)
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f160,f86]) ).
fof(f169,plain,
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f161,f102]) ).
fof(f171,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK0_skl))
| constant(cardinality_at_time(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f164,f45]) ).
fof(f172,plain,
( increases(cardinality_at_time(first_movers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f129,f156]) ).
fof(f173,plain,
( decreases(cardinality_at_time(efficient_producers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f127,f156]) ).
fof(f174,plain,
( greater(growth_rate(first_movers,sK0_skl),zero)
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f172,f86]) ).
fof(f177,plain,
( greater(zero,growth_rate(efficient_producers,sK0_skl))
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f173,f102]) ).
fof(f192,plain,
! [X0] :
( growth_rate(efficient_producers,sK0_skl) = zero
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f84,f193]) ).
fof(f193,plain,
constant(cardinality_at_time(efficient_producers,sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f171,f169]) ).
fof(f196,plain,
( growth_rate(efficient_producers,sK0_skl) = zero
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f192,f60]) ).
fof(f197,plain,
growth_rate(efficient_producers,sK0_skl) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f196,f41]) ).
fof(f199,plain,
( greater(zero,zero)
| constant(cardinality_at_time(first_movers,sK0_skl)) ),
inference(backward_demodulation,[status(thm)],[f197,f177]) ).
fof(f204,plain,
( ~ greater(zero,zero)
| ~ greater(growth_rate(first_movers,sK0_skl),zero) ),
inference(backward_demodulation,[status(thm)],[f197,f45]) ).
fof(f205,plain,
( zero != zero
| growth_rate(first_movers,sK0_skl) != zero ),
inference(backward_demodulation,[status(thm)],[f197,f44]) ).
fof(f206,plain,
growth_rate(first_movers,sK0_skl) != zero,
inference(trivial_equality_resolution,[status(thm)],[f205]) ).
fof(f207,plain,
! [X0] :
( ~ constant(cardinality_at_time(first_movers,sK0_skl))
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f78,f206]) ).
fof(f210,plain,
( constant(cardinality_at_time(first_movers,sK0_skl))
| ~ greater(zero,zero) ),
inference(resolution,[status(thm)],[f204,f174]) ).
fof(f229,plain,
! [X0] :
( ~ in_environment(X0,sK0_skl)
| ~ environment(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f207,f230]) ).
fof(f230,plain,
constant(cardinality_at_time(first_movers,sK0_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f210,f199]) ).
fof(f234,plain,
~ environment(sK1_skl),
inference(resolution,[status(thm)],[f229,f60]) ).
fof(f235,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f234,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT025+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 01:24:16 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.055178 seconds
% 0.12/0.41 % CPU time: 0.162284 seconds
% 0.12/0.41 % Total memory used: 82.008 MB
% 0.12/0.41 % Net memory used: 81.666 MB
%------------------------------------------------------------------------------