%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 144 ( 17 unt; 0 def)
% Number of atoms : 470 ( 47 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 553 ( 227 ~; 326 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 154 ( 154 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C))
| B != first_movers
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( decreases(B)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( increases(C)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( increases(C)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( decreases(B)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B,C] :
( increases(C)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] :
( decreases(B)
| decreases(C)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( increases(C)
| decreases(C)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C] :
( growth_rate(C,B) = zero
| ~ constant(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( greater(growth_rate(C,B),zero)
| ~ increases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( greater(zero,growth_rate(C,B))
| ~ decreases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B] :
( greater(cardinality_at_time(first_movers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [A,C] :
( number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C))
| ! [B] :
( B != first_movers
| ~ subpopulation(B,A,C)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f32,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)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
! [B] :
( decreases(B)
| increases(B)
| constant(B)
| ! [A] :
( ~ constant(A)
| ! [C] : A != sum(B,C) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f36,plain,
! [X0,X1,X2] :
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [C] :
( increases(C)
| ! [B] :
( increases(B)
| constant(B)
| ! [A] :
( ~ constant(A)
| A != sum(B,C) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f38,plain,
! [X0,X1,X2] :
( increases(X2)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,plain,
! [C] :
( increases(C)
| decreases(C)
| ! [B] :
( constant(B)
| ! [A] :
( ~ constant(A)
| A != sum(B,C) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0,X1,X2] :
( increases(X2)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [B] :
( decreases(B)
| increases(B)
| ! [C] :
( constant(C)
| ! [A] :
( ~ constant(A)
| A != sum(B,C) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f44,plain,
! [X0,X1,X2] :
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [C] :
( increases(C)
| ! [B] :
( increases(B)
| constant(C)
| ! [A] :
( ~ constant(A)
| A != sum(B,C) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f46,plain,
! [X0,X1,X2] :
( increases(X2)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [B] :
( decreases(B)
| ! [C] :
( decreases(C)
| constant(C)
| ! [A] :
( ~ constant(A)
| A != sum(B,C) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f48,plain,
! [X0,X1,X2] :
( decreases(X1)
| decreases(X2)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [C] :
( increases(C)
| decreases(C)
| constant(C)
| ! [A] :
( ~ constant(A)
| ! [B] : A != sum(B,C) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f50,plain,
! [X0,X1,X2] :
( increases(X2)
| decreases(X2)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [B,C] :
( growth_rate(C,B) = zero
| ~ constant(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ! [A] :
( ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f52,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)],[f51]) ).
fof(f53,plain,
! [B,C] :
( greater(growth_rate(C,B),zero)
| ~ increases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ! [A] :
( ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f54,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)],[f53]) ).
fof(f55,plain,
! [B,C] :
( greater(zero,growth_rate(C,B))
| ~ decreases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ! [A] :
( ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f56,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)],[f55]) ).
fof(f57,plain,
! [B] :
( greater(cardinality_at_time(first_movers,B),zero)
| ! [A] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f58,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)],[f57]) ).
fof(f59,plain,
! [B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ! [A] :
( ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f60,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)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f64,plain,
environment(sk1),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f65,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f66,plain,
constant(number_of_organizations(sk1,sk2)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f67,plain,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f68,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f69,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f71,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)],[f32]) ).
fof(f72,plain,
! [X0,X1] :
( decreases(X0)
| increases(X0)
| constant(X0)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f36]) ).
fof(f73,plain,
! [X0,X1] :
( increases(X1)
| increases(X0)
| constant(X0)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f38]) ).
fof(f75,plain,
! [X0,X1] :
( increases(X1)
| decreases(X1)
| constant(X0)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f42]) ).
fof(f76,plain,
! [X0,X1] :
( decreases(X0)
| increases(X0)
| constant(X1)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f44]) ).
fof(f77,plain,
! [X0,X1] :
( increases(X1)
| increases(X0)
| constant(X1)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f78,plain,
! [X0,X1] :
( decreases(X0)
| decreases(X1)
| constant(X1)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f79,plain,
! [X0,X1] :
( increases(X1)
| decreases(X1)
| constant(X1)
| ~ constant(sum(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f80,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f61,f65]) ).
fof(f81,plain,
in_environment(sk1,sk2),
inference(forward_subsumption_resolution,[status(thm)],[f80,f64]) ).
fof(f82,plain,
( greater(cardinality_at_time(first_movers,sk2),zero)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f58,f65]) ).
fof(f83,plain,
greater(cardinality_at_time(first_movers,sk2),zero),
inference(forward_subsumption_resolution,[status(thm)],[f82,f64]) ).
fof(f84,plain,
( subpopulation(first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f33,f81]) ).
fof(f85,plain,
subpopulation(first_movers,sk1,sk2),
inference(forward_subsumption_resolution,[status(thm)],[f84,f64]) ).
fof(f86,plain,
( number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f85,f71]) ).
fof(f88,plain,
number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)),
inference(forward_subsumption_resolution,[status(thm)],[f86,f64]) ).
fof(f95,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f60,f65]) ).
fof(f96,plain,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(forward_subsumption_resolution,[status(thm)],[f95,f64]) ).
fof(f97,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(paramodulation,[status(thm)],[f88,f76]) ).
fof(f98,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(paramodulation,[status(thm)],[f88,f75]) ).
fof(f100,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(paramodulation,[status(thm)],[f88,f73]) ).
fof(f101,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(paramodulation,[status(thm)],[f88,f72]) ).
fof(f102,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f66]) ).
fof(f103,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f66]) ).
fof(f105,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f66]) ).
fof(f106,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f101,f66]) ).
fof(f107,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(paramodulation,[status(thm)],[f88,f77]) ).
fof(f108,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f66]) ).
fof(f109,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(paramodulation,[status(thm)],[f88,f78]) ).
fof(f110,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f66]) ).
fof(f111,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(paramodulation,[status(thm)],[f88,f79]) ).
fof(f112,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f66]) ).
fof(f113,plain,
! [X0] :
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f52,f96]) ).
fof(f114,plain,
! [X0] :
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ subpopulation(first_movers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f52,f83]) ).
fof(f115,plain,
! [X0] :
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f34]) ).
fof(f116,plain,
! [X0] :
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f33]) ).
fof(f117,plain,
! [X0] :
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f54,f96]) ).
fof(f118,plain,
! [X0] :
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ subpopulation(first_movers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f54,f83]) ).
fof(f119,plain,
! [X0] :
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f34]) ).
fof(f120,plain,
! [X0] :
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f33]) ).
fof(f121,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f56,f96]) ).
fof(f122,plain,
! [X0] :
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ subpopulation(first_movers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f56,f83]) ).
fof(f123,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f121,f34]) ).
fof(f124,plain,
! [X0] :
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f33]) ).
fof(f127,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f119,f81]) ).
fof(f128,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f64]) ).
fof(f129,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f120,f81]) ).
fof(f130,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f64]) ).
fof(f131,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f123,f81]) ).
fof(f132,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f64]) ).
fof(f133,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f124,f81]) ).
fof(f134,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f64]) ).
fof(f135,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f134,f102]) ).
fof(f136,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f103,f132]) ).
fof(f138,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f105,f128]) ).
fof(f139,plain,
( greater(zero,growth_rate(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f106,f134]) ).
fof(f140,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f108,f128]) ).
fof(f141,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f110,f132]) ).
fof(f142,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f112,f132]) ).
fof(f143,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f138,f69]) ).
fof(f144,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f140,f69]) ).
fof(f145,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f135]) ).
fof(f146,plain,
( greater(growth_rate(first_movers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f145,f130]) ).
fof(f147,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f139]) ).
fof(f148,plain,
( greater(growth_rate(first_movers,sk2),zero)
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f147,f130]) ).
fof(f149,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f146,f68]) ).
fof(f151,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f142,f149]) ).
fof(f152,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f141,f149]) ).
fof(f155,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f151,f128]) ).
fof(f156,plain,
( greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f152,f134]) ).
fof(f157,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[f155,f69]) ).
fof(f158,plain,
! [X0] :
( growth_rate(efficient_producers,sk2) = zero
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f159]) ).
fof(f159,plain,
constant(cardinality_at_time(efficient_producers,sk2)),
inference(forward_subsumption_resolution,[status(thm)],[f157,f156]) ).
fof(f160,plain,
( growth_rate(efficient_producers,sk2) = zero
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[f158,f81]) ).
fof(f161,plain,
growth_rate(efficient_producers,sk2) = zero,
inference(forward_subsumption_resolution,[status(thm)],[f160,f64]) ).
fof(f164,plain,
( greater(zero,zero)
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(backward_demodulation,[status(thm)],[f161,f136]) ).
fof(f166,plain,
( greater(zero,zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(backward_demodulation,[status(thm)],[f161,f128]) ).
fof(f168,plain,
( ~ greater(zero,zero)
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(backward_demodulation,[status(thm)],[f161,f68]) ).
fof(f169,plain,
( zero != zero
| growth_rate(first_movers,sk2) != zero ),
inference(backward_demodulation,[status(thm)],[f161,f67]) ).
fof(f170,plain,
growth_rate(first_movers,sk2) != zero,
inference(trivial_equality_resolution,[status(thm)],[f169]) ).
fof(f171,plain,
! [X0] :
( ~ constant(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f116,f170]) ).
fof(f172,plain,
( constant(cardinality_at_time(first_movers,sk2))
| ~ greater(zero,zero) ),
inference(resolution,[status(thm)],[f168,f148]) ).
fof(f176,plain,
( greater(zero,zero)
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f166]) ).
fof(f178,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f171,f179]) ).
fof(f179,plain,
constant(cardinality_at_time(first_movers,sk2)),
inference(forward_subsumption_resolution,[status(thm)],[f172,f176]) ).
fof(f180,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[f178,f81]) ).
fof(f181,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f180,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 01:26:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.044699 seconds
% 0.13/0.41 % CPU time: 0.137479 seconds
% 0.13/0.41 % Total memory used: 58.779 MB
% 0.13/0.41 % Net memory used: 58.590 MB
%------------------------------------------------------------------------------