%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:11:46 PM UTC 2026
% Result : Theorem 2.59s 0.78s
% Output : Proof 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 138 ( 17 unt; 0 def)
% Number of atoms : 457 ( 67 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 531 ( 212 ~; 243 |; 56 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 170 ( 0 sgn 97 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,hypothesis,
! [E,X,T] :
( ( greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T)
& environment(E) )
=> ( X = first_movers
| X = efficient_producers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a9) ).
fof(f14_nnf,plain,
! [E,X,T] :
( X = first_movers
| X = efficient_producers
| ~ greater(cardinality_at_time(X,T),zero)
| ~ subpopulation(X,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [E,X,T] :
( X = first_movers
| X = efficient_producers
| ~ greater(cardinality_at_time(X,T),zero)
| ~ subpopulation(X,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c22,plain,
( X1 = first_movers
| X1 = efficient_producers
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f15,conjecture,
! [E,T] :
( ( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t6) ).
fof(f15_neg,negated_conjecture,
~ ! [E,T] :
( ( greater_or_equal(T,appear(efficient_producers,E))
& in_environment(E,T)
& environment(E) )
=> greater(cardinality_at_time(efficient_producers,T),zero) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f15_nnf,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(nnf_transformation,[status(thm)],[f15_neg]) ).
fof(f15_sk,plain,
( ~ greater(cardinality_at_time(efficient_producers,sk3),zero)
& greater_or_equal(sk3,appear(efficient_producers,sk2))
& in_environment(sk2,sk3)
& environment(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f15_nnf]) ).
cnf(c23,plain,
environment(sk2),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p83,plain,
( X0 = first_movers
| X0 = efficient_producers
| ~ greater(cardinality_at_time(X0,X1),zero)
| ~ subpopulation(X0,sk2,X1) ),
inference(resolution,[status(thm)],[c22,c23]) ).
fof(f6,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( greater(cardinality_at_time(efficient_producers,T),zero)
| cardinality_at_time(efficient_producers,T) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_efficient_producers_exist) ).
fof(f6_nnf,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| cardinality_at_time(efficient_producers,T) = zero
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [E,T] :
( greater(cardinality_at_time(efficient_producers,T),zero)
| cardinality_at_time(efficient_producers,T) = zero
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c12,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p45,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| cardinality_at_time(efficient_producers,X0) = zero
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c12,c23]) ).
cnf(c24,plain,
in_environment(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p47,plain,
( greater(cardinality_at_time(efficient_producers,sk3),zero)
| cardinality_at_time(efficient_producers,sk3) = zero ),
inference(resolution,[status(thm)],[p45,c24]) ).
cnf(c26,plain,
~ greater(cardinality_at_time(efficient_producers,sk3),zero),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p48,plain,
cardinality_at_time(efficient_producers,sk3) = zero,
inference(resolution,[status(thm)],[p47,c26]) ).
fof(f0,axiom,
! [E,T] :
( ( cardinality_at_time(efficient_producers,T) = zero
& greater_or_equal(T,appear(efficient_producers,E))
& environment(E) )
=> ? [To] :
( greater(zero,growth_rate(efficient_producers,To))
& greater(T,To)
& in_environment(E,To)
& greater(To,appear(efficient_producers,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_previous_negative_growth) ).
fof(f0_nnf,plain,
! [E,T] :
( ? [To] :
( greater(zero,growth_rate(efficient_producers,To))
& greater(T,To)
& in_environment(E,To)
& greater(To,appear(efficient_producers,E)) )
| cardinality_at_time(efficient_producers,T) != zero
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,T] :
( ( greater(zero,growth_rate(efficient_producers,sk0(E,T)))
& greater(T,sk0(E,T))
& in_environment(E,sk0(E,T))
& greater(sk0(E,T),appear(efficient_producers,E)) )
| cardinality_at_time(efficient_producers,T) != zero
| ~ greater_or_equal(T,appear(efficient_producers,E))
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( in_environment(X0,sk0(X0,X1))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p30,plain,
( in_environment(sk2,sk0(sk2,X0))
| cardinality_at_time(efficient_producers,X0) != zero
| ~ greater_or_equal(X0,appear(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[c1,c23]) ).
cnf(c25,plain,
greater_or_equal(sk3,appear(efficient_producers,sk2)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p39,plain,
( in_environment(sk2,sk0(sk2,sk3))
| cardinality_at_time(efficient_producers,sk3) != zero ),
inference(resolution,[status(thm)],[p30,c25]) ).
cnf(p50,plain,
( in_environment(sk2,sk0(sk2,sk3))
| zero != zero ),
inference(demodulation,[status(thm)],[p48,p39]) ).
cnf(p54,plain,
in_environment(sk2,sk0(sk2,sk3)),
inference(equality_resolution,[status(thm)],[p50]) ).
fof(f2,axiom,
! [E,T] :
( ( ~ decreases(number_of_organizations(E,T))
& in_environment(E,T)
& environment(E) )
=> ? [X] :
( ~ greater(zero,growth_rate(X,T))
& greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_decreasing) ).
fof(f2_nnf,plain,
! [E,T] :
( ? [X] :
( ~ greater(zero,growth_rate(X,T))
& greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T) )
| decreases(number_of_organizations(E,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E,T] :
( ( ~ greater(zero,growth_rate(sk1(E,T),T))
& greater(cardinality_at_time(sk1(E,T),T),zero)
& subpopulation(sk1(E,T),E,T) )
| decreases(number_of_organizations(E,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c5,plain,
( subpopulation(sk1(X0,X1),X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p43,plain,
( subpopulation(sk1(sk2,X0),sk2,X0)
| decreases(number_of_organizations(sk2,X0))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c5,c23]) ).
cnf(p60,plain,
( subpopulation(sk1(sk2,sk0(sk2,sk3)),sk2,sk0(sk2,sk3))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p54,p43]) ).
cnf(p87,plain,
( decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| sk1(sk2,sk0(sk2,sk3)) = first_movers
| sk1(sk2,sk0(sk2,sk3)) = efficient_producers
| ~ greater(cardinality_at_time(sk1(sk2,sk0(sk2,sk3)),sk0(sk2,sk3)),zero) ),
inference(resolution,[status(thm)],[p83,p60]) ).
cnf(c6,plain,
( greater(cardinality_at_time(sk1(X0,X1),X1),zero)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p46,plain,
( greater(cardinality_at_time(sk1(sk2,X0),X0),zero)
| decreases(number_of_organizations(sk2,X0))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c6,c23]) ).
cnf(p72,plain,
( greater(cardinality_at_time(sk1(sk2,sk0(sk2,sk3)),sk0(sk2,sk3)),zero)
| decreases(number_of_organizations(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p46,p54]) ).
cnf(p119,plain,
( decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| sk1(sk2,sk0(sk2,sk3)) = first_movers
| sk1(sk2,sk0(sk2,sk3)) = efficient_producers ),
inference(resolution,[status(thm)],[p87,p72]) ).
cnf(p132,plain,
( decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| sk1(sk2,sk0(sk2,sk3)) = first_movers
| sk1(sk2,sk0(sk2,sk3)) = efficient_producers ),
inference(factoring,[status(thm)],[p119]) ).
cnf(c7,plain,
( ~ greater(zero,growth_rate(sk1(X0,X1),X1))
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p53,plain,
( ~ greater(zero,growth_rate(sk1(sk2,X0),X0))
| decreases(number_of_organizations(sk2,X0))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c7,c23]) ).
cnf(p74,plain,
( ~ greater(zero,growth_rate(sk1(sk2,sk0(sk2,sk3)),sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p53,p54]) ).
cnf(p136,plain,
( ~ greater(zero,growth_rate(first_movers,sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| sk1(sk2,sk0(sk2,sk3)) = efficient_producers ),
inference(superposition,[status(thm)],[p132,p74]) ).
cnf(p149,plain,
( ~ greater(zero,growth_rate(first_movers,sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| sk1(sk2,sk0(sk2,sk3)) = efficient_producers ),
inference(factoring,[status(thm)],[p136]) ).
fof(f12,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& ~ greater(zero,growth_rate(S1,T))
& in_environment(E,T)
& environment(E) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
fof(f12_nnf,plain,
! [E,S1,S2,T] :
( ~ greater(zero,growth_rate(S2,T))
| ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [E,T,S1,S2] :
( ~ greater(zero,growth_rate(S2,T))
| ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c20,plain,
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p80,plain,
( ~ greater(zero,growth_rate(X2,X0))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X0))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c20,c23]) ).
cnf(p108,plain,
( ~ greater(zero,growth_rate(X1,sk0(sk2,sk3)))
| ~ greater(resilience(X1),resilience(X0))
| greater(zero,growth_rate(X0,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p80,p54]) ).
fof(f13,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f13_nnf,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c21,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p117,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk0(sk2,sk3)))
| greater(zero,growth_rate(first_movers,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p108,c21]) ).
cnf(c3,plain,
( greater(zero,growth_rate(efficient_producers,sk0(X0,X1)))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p36,plain,
( greater(zero,growth_rate(efficient_producers,sk0(sk2,X0)))
| cardinality_at_time(efficient_producers,X0) != zero
| ~ greater_or_equal(X0,appear(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[c3,c23]) ).
cnf(p98,plain,
( greater(zero,growth_rate(efficient_producers,sk0(sk2,sk3)))
| zero != zero ),
inference(resolution,[status(thm)],[p36,c25]) ).
cnf(p99,plain,
greater(zero,growth_rate(efficient_producers,sk0(sk2,sk3))),
inference(equality_resolution,[status(thm)],[p98]) ).
cnf(p118,plain,
greater(zero,growth_rate(first_movers,sk0(sk2,sk3))),
inference(resolution,[status(thm)],[p117,p99]) ).
cnf(p151,plain,
( decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| sk1(sk2,sk0(sk2,sk3)) = efficient_producers ),
inference(resolution,[status(thm)],[p149,p118]) ).
cnf(p153,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3))) ),
inference(superposition,[status(thm)],[p151,p74]) ).
cnf(p156,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk0(sk2,sk3)))
| decreases(number_of_organizations(sk2,sk0(sk2,sk3))) ),
inference(factoring,[status(thm)],[p153]) ).
cnf(p157,plain,
decreases(number_of_organizations(sk2,sk0(sk2,sk3))),
inference(resolution,[status(thm)],[p156,p99]) ).
fof(f3,axiom,
! [E,T,X] :
( ( subpopulation(X,E,T)
& number_of_organizations(E,T) = zero
& in_environment(E,T)
& environment(E) )
=> cardinality_at_time(X,T) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_no_members) ).
fof(f3_nnf,plain,
! [E,T,X] :
( cardinality_at_time(X,T) = zero
| ~ subpopulation(X,E,T)
| number_of_organizations(E,T) != zero
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E,T,X] :
( cardinality_at_time(X,T) = zero
| ~ subpopulation(X,E,T)
| number_of_organizations(E,T) != zero
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( cardinality_at_time(X2,X1) = zero
| ~ subpopulation(X2,X0,X1)
| number_of_organizations(X0,X1) != zero
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p62,plain,
( cardinality_at_time(X1,X0) = zero
| ~ subpopulation(X1,sk2,X0)
| number_of_organizations(sk2,X0) != zero
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c8,c23]) ).
cnf(p103,plain,
( cardinality_at_time(X0,sk0(sk2,sk3)) = zero
| ~ subpopulation(X0,sk2,sk0(sk2,sk3))
| number_of_organizations(sk2,sk0(sk2,sk3)) != zero ),
inference(resolution,[status(thm)],[p62,p54]) ).
fof(f9,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',a3) ).
fof(f9_nnf,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(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,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(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c16,plain,
( 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(esa)],[f9_sk]) ).
cnf(p70,plain,
( constant(resources(sk2,X0))
| greater(equilibrium(sk2),X0)
| ~ greater(number_of_organizations(sk2,X0),zero)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c16,c23]) ).
cnf(p106,plain,
( constant(resources(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3))
| ~ greater(number_of_organizations(sk2,sk0(sk2,sk3)),zero) ),
inference(resolution,[status(thm)],[p70,p54]) ).
fof(f10,hypothesis,
! [E,T] :
( ( greater_or_equal(T,appear(an_organisation,E))
& in_environment(E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
fof(f10_nnf,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ greater_or_equal(T,appear(an_organisation,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ greater_or_equal(T,appear(an_organisation,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c17,plain,
( greater(number_of_organizations(X0,X1),zero)
| ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p75,plain,
( greater(number_of_organizations(sk2,X0),zero)
| ~ greater_or_equal(X0,appear(an_organisation,sk2))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c17,c23]) ).
cnf(p77,plain,
( greater(number_of_organizations(sk2,sk0(sk2,sk3)),zero)
| ~ greater_or_equal(sk0(sk2,sk3),appear(an_organisation,sk2)) ),
inference(resolution,[status(thm)],[p75,p54]) ).
fof(f8,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( greater(appear(an_organisation,E),T)
| greater_or_equal(T,appear(an_organisation,E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_inequality) ).
fof(f8_nnf,plain,
! [E,T] :
( greater(appear(an_organisation,E),T)
| greater_or_equal(T,appear(an_organisation,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [E,T] :
( greater(appear(an_organisation,E),T)
| greater_or_equal(T,appear(an_organisation,E))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c14,plain,
( greater(appear(an_organisation,X0),X1)
| greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p64,plain,
( greater(appear(an_organisation,sk2),X0)
| greater_or_equal(X0,appear(an_organisation,sk2))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c14,c23]) ).
cnf(p66,plain,
( greater(appear(an_organisation,sk2),sk0(sk2,sk3))
| greater_or_equal(sk0(sk2,sk3),appear(an_organisation,sk2)) ),
inference(resolution,[status(thm)],[p64,p54]) ).
fof(f1,axiom,
! [E,T] :
( ( greater(appear(an_organisation,E),T)
& in_environment(E,T)
& environment(E) )
=> number_of_organizations(E,T) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_start_of_organizations) ).
fof(f1_nnf,plain,
! [E,T] :
( number_of_organizations(E,T) = zero
| ~ greater(appear(an_organisation,E),T)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( number_of_organizations(E,T) = zero
| ~ greater(appear(an_organisation,E),T)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c4,plain,
( number_of_organizations(X0,X1) = zero
| ~ greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p40,plain,
( number_of_organizations(sk2,X0) = zero
| ~ greater(appear(an_organisation,sk2),X0)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c4,c23]) ).
cnf(p59,plain,
( number_of_organizations(sk2,sk0(sk2,sk3)) = zero
| ~ greater(appear(an_organisation,sk2),sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p54,p40]) ).
cnf(p69,plain,
( number_of_organizations(sk2,sk0(sk2,sk3)) = zero
| greater_or_equal(sk0(sk2,sk3),appear(an_organisation,sk2)) ),
inference(resolution,[status(thm)],[p66,p59]) ).
cnf(p79,plain,
( number_of_organizations(sk2,sk0(sk2,sk3)) = zero
| greater(number_of_organizations(sk2,sk0(sk2,sk3)),zero) ),
inference(resolution,[status(thm)],[p77,p69]) ).
cnf(p116,plain,
( number_of_organizations(sk2,sk0(sk2,sk3)) = zero
| constant(resources(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p106,p79]) ).
cnf(p130,plain,
( constant(resources(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3))
| cardinality_at_time(X0,sk0(sk2,sk3)) = zero
| ~ subpopulation(X0,sk2,sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p103,p116]) ).
fof(f4,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f4_nnf,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c9,plain,
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p28,plain,
( subpopulation(first_movers,sk2,X0)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c9,c23]) ).
cnf(p55,plain,
subpopulation(first_movers,sk2,sk0(sk2,sk3)),
inference(resolution,[status(thm)],[p54,p28]) ).
cnf(p138,plain,
( constant(resources(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3))
| cardinality_at_time(first_movers,sk0(sk2,sk3)) = zero ),
inference(resolution,[status(thm)],[p130,p55]) ).
fof(f5,axiom,
! [S,T] :
( cardinality_at_time(S,T) = zero
=> ~ greater(zero,growth_rate(S,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_empty_not_decreasing) ).
fof(f5_nnf,plain,
! [S,T] :
( ~ greater(zero,growth_rate(S,T))
| cardinality_at_time(S,T) != zero ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [S,T] :
( ~ greater(zero,growth_rate(S,T))
| cardinality_at_time(S,T) != zero ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c11,plain,
( ~ greater(zero,growth_rate(X0,X1))
| cardinality_at_time(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p143,plain,
( ~ greater(zero,growth_rate(first_movers,sk0(sk2,sk3)))
| constant(resources(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p138,c11]) ).
cnf(p146,plain,
( constant(resources(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p143,p118]) ).
fof(f11,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',a6) ).
fof(f11_nnf,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(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,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(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c19,plain,
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p37,plain,
( constant(number_of_organizations(sk2,X0))
| ~ constant(resources(sk2,X0))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c19,c23]) ).
cnf(p58,plain,
( constant(number_of_organizations(sk2,sk0(sk2,sk3)))
| ~ constant(resources(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p54,p37]) ).
cnf(p148,plain,
( constant(number_of_organizations(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p146,p58]) ).
fof(f7,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(f7_nnf,plain,
! [X] :
( ~ decreases(X)
| ~ constant(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] :
( ~ decreases(X)
| ~ constant(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c13,plain,
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p150,plain,
( ~ decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| greater(equilibrium(sk2),sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p148,c13]) ).
cnf(p158,plain,
greater(equilibrium(sk2),sk0(sk2,sk3)),
inference(resolution,[status(thm)],[p157,p150]) ).
cnf(c15,plain,
( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p67,plain,
( decreases(resources(sk2,X0))
| ~ greater(equilibrium(sk2),X0)
| ~ greater(number_of_organizations(sk2,X0),zero)
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c15,c23]) ).
cnf(p101,plain,
( decreases(resources(sk2,sk0(sk2,sk3)))
| ~ greater(equilibrium(sk2),sk0(sk2,sk3))
| ~ greater(number_of_organizations(sk2,sk0(sk2,sk3)),zero) ),
inference(resolution,[status(thm)],[p67,p54]) ).
cnf(p114,plain,
( number_of_organizations(sk2,sk0(sk2,sk3)) = zero
| decreases(resources(sk2,sk0(sk2,sk3)))
| ~ greater(equilibrium(sk2),sk0(sk2,sk3)) ),
inference(resolution,[status(thm)],[p101,p79]) ).
cnf(p159,plain,
( number_of_organizations(sk2,sk0(sk2,sk3)) = zero
| decreases(resources(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p158,p114]) ).
cnf(p160,plain,
( cardinality_at_time(X0,sk0(sk2,sk3)) = zero
| ~ subpopulation(X0,sk2,sk0(sk2,sk3))
| decreases(resources(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p159,p103]) ).
cnf(p163,plain,
( cardinality_at_time(first_movers,sk0(sk2,sk3)) = zero
| decreases(resources(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p160,p55]) ).
cnf(p166,plain,
( ~ greater(zero,growth_rate(first_movers,sk0(sk2,sk3)))
| decreases(resources(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p163,c11]) ).
cnf(p168,plain,
decreases(resources(sk2,sk0(sk2,sk3))),
inference(resolution,[status(thm)],[p166,p118]) ).
cnf(c18,plain,
( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p34,plain,
( ~ decreases(number_of_organizations(sk2,X0))
| ~ decreases(resources(sk2,X0))
| ~ in_environment(sk2,X0) ),
inference(resolution,[status(thm)],[c18,c23]) ).
cnf(p57,plain,
( ~ decreases(number_of_organizations(sk2,sk0(sk2,sk3)))
| ~ decreases(resources(sk2,sk0(sk2,sk3))) ),
inference(resolution,[status(thm)],[p54,p34]) ).
cnf(p169,plain,
~ decreases(number_of_organizations(sk2,sk0(sk2,sk3))),
inference(resolution,[status(thm)],[p168,p57]) ).
cnf(p170,plain,
$false,
inference(resolution,[status(thm)],[p169,p157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 01:09:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.59/0.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/0.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------