%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 : Tue Sep 29 12:02:09 PM UTC 2026
% Result : Unsatisfiable 2.32s 1.07s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 30
% Syntax : Number of formulae : 138 ( 18 unt; 6 def)
% Number of atoms : 472 ( 85 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 606 ( 272 ~; 328 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| in_environment(X0,sk1(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_previous_negative_growth_29) ).
fof(f4,axiom,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sk1(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_previous_negative_growth_31) ).
fof(f5,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(appear(an_organisation,X0),X1)
| number_of_organizations(X0,X1) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_start_of_organizations_32) ).
fof(f6,plain,
! [X0,X1] :
( ~ greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( subpopulation(sk2(X1,X0),X0,X1)
| ~ in_environment(X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_decreasing_33) ).
fof(f8,axiom,
! [X0,X1] :
( greater(cardinality_at_time(sk2(X1,X0),X1),zero)
| ~ in_environment(X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_decreasing_34) ).
fof(f9,axiom,
! [X0,X1] :
( ~ greater(zero,growth_rate(sk2(X1,X0),X1))
| ~ in_environment(X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_decreasing_35) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| number_of_organizations(X0,X1) != zero
| ~ subpopulation(X2,X0,X1)
| cardinality_at_time(X2,X1) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_no_members_36) ).
fof(f11,plain,
! [X2,X0,X1] :
( zero != number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulation(X2,X0,X1)
| zero = cardinality_at_time(X2,X1) ),
inference(reorient_equations,[],[f10]) ).
fof(f13,axiom,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_38) ).
fof(f14,axiom,
! [X0,X1] :
( cardinality_at_time(X0,X1) != zero
| ~ greater(zero,growth_rate(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_empty_not_decreasing_39) ).
fof(f15,plain,
! [X0,X1] :
( zero != cardinality_at_time(X0,X1)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| cardinality_at_time(efficient_producers,X1) = zero
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_efficient_producers_exist_40) ).
fof(f17,axiom,
! [X0] :
( ~ constant(X0)
| ~ decreases(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease_41) ).
fof(f18,axiom,
! [X0,X1] :
( greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| greater_or_equal(X1,appear(an_organisation,X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_inequality_42) ).
fof(f19,axiom,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_43) ).
fof(f20,axiom,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_44) ).
fof(f21,axiom,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_45) ).
fof(f22,axiom,
! [X0,X1] :
( ~ decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ decreases(number_of_organizations(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_46) ).
fof(f23,axiom,
! [X0,X1] :
( ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| constant(number_of_organizations(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_47) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( ~ greater(resilience(X3),resilience(X2))
| ~ in_environment(X0,X1)
| greater(zero,growth_rate(X2,X1))
| ~ environment(X0)
| ~ greater(zero,growth_rate(X3,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12_48) ).
fof(f25,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_49) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| X1 = efficient_producers
| X1 = first_movers ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a9_50) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0)
| efficient_producers = X1
| first_movers = X1 ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t6_51) ).
fof(f29,negated_conjecture,
in_environment(sk3,sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t6_52) ).
fof(f30,negated_conjecture,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t6_53) ).
fof(f31,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t6_54) ).
fof(f32,plain,
( ~ environment(sk3)
| zero = cardinality_at_time(efficient_producers,sk4)
| greater(cardinality_at_time(efficient_producers,sk4),zero) ),
inference(resolution,[],[f16,f29]) ).
fof(f33,plain,
( zero = cardinality_at_time(efficient_producers,sk4)
| greater(cardinality_at_time(efficient_producers,sk4),zero) ),
inference(forward_subsumption_resolution,[],[f32,f28]) ).
fof(f34,plain,
zero = cardinality_at_time(efficient_producers,sk4),
inference(forward_subsumption_resolution,[],[f33,f31]) ).
fof(f35,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| greater_or_equal(X1,appear(an_organisation,X0))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1) ),
inference(resolution,[],[f18,f6]) ).
fof(f36,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1) ),
inference(duplicate_literal_removal,[],[f35]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ subpopulation(sk2(X0,X1),X2,X0)
| ~ environment(X2)
| efficient_producers = sk2(X0,X1)
| first_movers = sk2(X0,X1)
| ~ in_environment(X1,X0)
| decreases(number_of_organizations(X1,X0))
| ~ environment(X1) ),
inference(resolution,[],[f27,f8]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(resolution,[],[f36,f21]) ).
fof(f42,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1) ),
inference(duplicate_literal_removal,[],[f41]) ).
fof(f43,plain,
! [X0] :
( zero != zero
| ~ greater_or_equal(sk4,appear(efficient_producers,X0))
| ~ environment(X0)
| in_environment(X0,sk1(sk4,X0)) ),
inference(superposition,[],[f2,f34]) ).
fof(f44,plain,
! [X0] :
( ~ greater_or_equal(sk4,appear(efficient_producers,X0))
| ~ environment(X0)
| in_environment(X0,sk1(sk4,X0)) ),
inference(trivial_inequality_removal,[],[f43]) ).
fof(f45,plain,
( ~ environment(sk3)
| in_environment(sk3,sk1(sk4,sk3)) ),
inference(resolution,[],[f44,f30]) ).
fof(f46,plain,
in_environment(sk3,sk1(sk4,sk3)),
inference(forward_subsumption_resolution,[],[f45,f28]) ).
fof(f56,definition,
( spl0_2
<=> zero = cardinality_at_time(efficient_producers,sk1(sk4,sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f57,plain,
( zero != cardinality_at_time(efficient_producers,sk1(sk4,sk3))
| spl0_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( zero = cardinality_at_time(efficient_producers,sk1(sk4,sk3))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f62,plain,
( zero != zero
| ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| ~ spl0_2 ),
inference(superposition,[],[f15,f58]) ).
fof(f63,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f62]) ).
fof(f72,plain,
! [X0] :
( zero != zero
| ~ greater_or_equal(sk4,appear(efficient_producers,X0))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sk1(sk4,X0))) ),
inference(superposition,[],[f4,f34]) ).
fof(f75,plain,
! [X0] :
( greater(zero,growth_rate(efficient_producers,sk1(sk4,X0)))
| ~ environment(X0)
| ~ greater_or_equal(sk4,appear(efficient_producers,X0)) ),
inference(trivial_inequality_removal,[],[f72]) ).
fof(f76,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(resolution,[],[f24,f25]) ).
fof(f77,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| ~ spl0_2 ),
inference(resolution,[],[f75,f63]) ).
fof(f78,plain,
( ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f77,f28]) ).
fof(f79,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f78,f30]) ).
fof(f80,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ in_environment(X1,sk1(sk4,X0))
| ~ environment(X1)
| greater(zero,growth_rate(first_movers,sk1(sk4,X0)))
| ~ environment(X0)
| ~ greater_or_equal(sk4,appear(efficient_producers,X0)) ),
inference(resolution,[],[f76,f75]) ).
fof(f83,plain,
! [X0,X1] :
( ~ environment(X0)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| ~ in_environment(X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ environment(X0) ),
inference(resolution,[],[f40,f7]) ).
fof(f84,plain,
! [X0,X1] :
( decreases(number_of_organizations(X0,X1))
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(resolution,[],[f42,f20]) ).
fof(f86,plain,
! [X0,X1] :
( ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ),
inference(resolution,[],[f42,f19]) ).
fof(f87,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| decreases(resources(X0,X1)) ),
inference(duplicate_literal_removal,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| greater(equilibrium(X0),X1)
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f85]) ).
fof(f89,plain,
( ~ environment(sk3)
| greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| ~ environment(sk3)
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3)) ),
inference(resolution,[],[f81,f46]) ).
fof(f90,plain,
( ~ environment(sk3)
| greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3)) ),
inference(duplicate_literal_removal,[],[f89]) ).
fof(f91,plain,
( greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3)) ),
inference(forward_subsumption_resolution,[],[f90,f28]) ).
fof(f92,plain,
greater(zero,growth_rate(first_movers,sk1(sk4,sk3))),
inference(forward_subsumption_resolution,[],[f91,f30]) ).
fof(f93,plain,
! [X0,X1] :
( zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| constant(number_of_organizations(X0,X1)) ),
inference(resolution,[],[f88,f23]) ).
fof(f95,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1) ),
inference(duplicate_literal_removal,[],[f93]) ).
fof(f96,plain,
! [X0,X1] :
( ~ decreases(number_of_organizations(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1) ),
inference(resolution,[],[f95,f17]) ).
fof(f97,plain,
! [X0,X1] :
( greater(equilibrium(X0),X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(resolution,[],[f96,f84]) ).
fof(f98,plain,
! [X0,X1] :
( greater(equilibrium(X0),X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers ),
inference(duplicate_literal_removal,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ environment(X0)
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| decreases(resources(X0,X1)) ),
inference(resolution,[],[f98,f87]) ).
fof(f100,plain,
! [X0,X1] :
( decreases(resources(X0,X1))
| zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f99]) ).
fof(f102,plain,
! [X0,X1] :
( zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ decreases(number_of_organizations(X0,X1)) ),
inference(resolution,[],[f100,f22]) ).
fof(f103,plain,
! [X0,X1] :
( zero = number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| ~ environment(X0)
| ~ decreases(number_of_organizations(X0,X1)) ),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| zero = number_of_organizations(X0,X1)
| efficient_producers = sk2(X1,X0)
| sk2(X1,X0) = first_movers
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f103,f84]) ).
fof(f107,plain,
( zero = number_of_organizations(sk3,sk1(sk4,sk3))
| efficient_producers = sk2(sk1(sk4,sk3),sk3)
| first_movers = sk2(sk1(sk4,sk3),sk3)
| ~ environment(sk3) ),
inference(resolution,[],[f105,f46]) ).
fof(f108,plain,
( zero = number_of_organizations(sk3,sk1(sk4,sk3))
| efficient_producers = sk2(sk1(sk4,sk3),sk3)
| first_movers = sk2(sk1(sk4,sk3),sk3) ),
inference(forward_subsumption_resolution,[],[f107,f28]) ).
fof(f111,definition,
( spl0_3
<=> first_movers = sk2(sk1(sk4,sk3),sk3) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f113,plain,
( first_movers = sk2(sk1(sk4,sk3),sk3)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f115,definition,
( spl0_4
<=> efficient_producers = sk2(sk1(sk4,sk3),sk3) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f117,plain,
( efficient_producers = sk2(sk1(sk4,sk3),sk3)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f119,definition,
( spl0_5
<=> zero = number_of_organizations(sk3,sk1(sk4,sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f120,plain,
( zero != number_of_organizations(sk3,sk1(sk4,sk3))
| spl0_5 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f121,plain,
( zero = number_of_organizations(sk3,sk1(sk4,sk3))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f108,f119,f115,f111]) ).
fof(f176,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ environment(sk3)
| ~ spl0_4 ),
inference(superposition,[],[f9,f117]) ).
fof(f179,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ environment(sk3)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f176,f46]) ).
fof(f180,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f179,f28]) ).
fof(f182,definition,
( spl0_12
<=> decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f183,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| spl0_12 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f184,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f186,definition,
( spl0_13
<=> greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f188,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| spl0_13 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f189,plain,
( spl0_12
| ~ spl0_13
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f180,f115,f186,f182]) ).
fof(f190,plain,
( ~ environment(sk3)
| ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| spl0_13 ),
inference(resolution,[],[f188,f75]) ).
fof(f191,plain,
( ~ greater_or_equal(sk4,appear(efficient_producers,sk3))
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f190,f28]) ).
fof(f192,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f191,f30]) ).
fof(f193,plain,
spl0_13,
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f194,plain,
( ! [X0] :
( zero != zero
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| zero = cardinality_at_time(X0,sk1(sk4,sk3)) )
| ~ spl0_5 ),
inference(superposition,[],[f11,f121]) ).
fof(f198,plain,
( ! [X0] :
( ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| zero = cardinality_at_time(X0,sk1(sk4,sk3)) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f194]) ).
fof(f199,plain,
( ! [X0] :
( ~ environment(sk3)
| ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| zero = cardinality_at_time(X0,sk1(sk4,sk3)) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f198,f46]) ).
fof(f200,plain,
( ! [X0] :
( ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| zero = cardinality_at_time(X0,sk1(sk4,sk3)) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f199,f28]) ).
fof(f211,plain,
( zero = cardinality_at_time(efficient_producers,sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| ~ spl0_5 ),
inference(resolution,[],[f200,f13]) ).
fof(f214,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f211,f57]) ).
fof(f217,plain,
( ~ environment(sk3)
| spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f214,f46]) ).
fof(f220,plain,
( $false
| spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f217,f28]) ).
fof(f221,plain,
( spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f220]) ).
fof(f228,plain,
( greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ environment(sk3)
| zero = number_of_organizations(sk3,sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ spl0_12 ),
inference(resolution,[],[f184,f96]) ).
fof(f229,plain,
( greater(equilibrium(sk3),sk1(sk4,sk3))
| zero = number_of_organizations(sk3,sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f228,f28]) ).
fof(f230,plain,
( greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f229,f120]) ).
fof(f231,plain,
( greater(equilibrium(sk3),sk1(sk4,sk3))
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f230,f46]) ).
fof(f232,plain,
( zero = number_of_organizations(sk3,sk1(sk4,sk3))
| ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| spl0_5
| ~ spl0_12 ),
inference(resolution,[],[f231,f87]) ).
fof(f233,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f232,f120]) ).
fof(f234,plain,
( ~ environment(sk3)
| decreases(resources(sk3,sk1(sk4,sk3)))
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f233,f46]) ).
fof(f235,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f234,f28]) ).
fof(f237,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| ~ environment(sk3)
| ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| spl0_5
| ~ spl0_12 ),
inference(resolution,[],[f235,f22]) ).
fof(f238,plain,
( ~ environment(sk3)
| ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f237,f46]) ).
fof(f239,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f238,f28]) ).
fof(f240,plain,
( $false
| spl0_5
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f239,f184]) ).
fof(f241,plain,
( spl0_5
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f244,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| ~ in_environment(sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ environment(sk3)
| ~ spl0_3 ),
inference(superposition,[],[f9,f113]) ).
fof(f248,plain,
( ~ in_environment(sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ environment(sk3)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f244,f92]) ).
fof(f250,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ environment(sk3)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f248,f46]) ).
fof(f252,plain,
( ~ environment(sk3)
| ~ spl0_3
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f250,f183]) ).
fof(f253,plain,
( $false
| ~ spl0_3
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f252,f28]) ).
fof(f254,plain,
( ~ spl0_3
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f253]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f80]) ).
cnf(s3,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f122]) ).
cnf(s8,plain,
( ~ spl0_4
| spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f189]) ).
cnf(s9,plain,
spl0_13,
inference(sat_conversion,[],[f193]) ).
cnf(s10,plain,
( spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f221]) ).
cnf(s12,plain,
( spl0_5
| ~ spl0_12 ),
inference(sat_conversion,[],[f241]) ).
cnf(s13,plain,
( ~ spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f254]) ).
cnf(s14,plain,
( ~ spl0_4
| spl0_12 ),
inference(rat,[],[s8,s9]) ).
cnf(s15,plain,
~ spl0_5,
inference(rat,[],[s10,s2]) ).
cnf(s16,plain,
~ spl0_12,
inference(rat,[],[s12,s15]) ).
cnf(s17,plain,
~ spl0_3,
inference(rat,[],[s13,s16]) ).
cnf(s18,plain,
~ spl0_4,
inference(rat,[],[s14,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s3,s15,s18,s17]) ).
fof(f255,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 17:23:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.32/1.07 % (3289967)Input is clausal, will run a generic CNF schedule.
% 2.32/1.07 % (3290013)dis-21_1_sil=8000:lcm=predicate:random_seed=836262197:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.32/1.07 % (3290013)Instruction limit reached!
% 2.32/1.07 % (3290013)------------------------------
% 2.32/1.07 % (3290013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.07 % (3290013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.07 % (3290013)CaDiCaL version: 2.1.3
% 2.32/1.07 % (3290013)Termination reason: Instruction limit
% 2.32/1.07 % (3290013)Termination phase: Saturation
% 2.32/1.07 % (3290013)Time elapsed: 0.024 s
% 2.32/1.07 % (3290013)Peak memory usage: 88 MB
% 2.32/1.07 % (3290013)Instructions burned: 118 (million)
% 2.32/1.07 % (3290012)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3456459491:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.32/1.07 % (3290009)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1307520084:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.32/1.07 % (3290008)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3615073440:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.32/1.07 % (3290010)lrs+10_1_sil=8000:sp=occurrence:random_seed=4106664600:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.32/1.07 % (3290011)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=75143351:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.32/1.07 % (3290007)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3618357453:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.32/1.07 % (3290010)First to succeed.
% 2.32/1.07 % (3290010)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3289967"
% 2.32/1.07 % (3290012)Also succeeded, but the first one will report.
% 2.32/1.07 % (3290011)Also succeeded, but the first one will report.
% 2.32/1.07 % (3290015)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1226117083:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.32/1.07 % (3290015)Refutation not found, incomplete strategy
% 2.32/1.07 % (3290015)------------------------------
% 2.32/1.07 % (3290015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/1.07 % (3290015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/1.07 % (3290015)CaDiCaL version: 2.1.3
% 2.32/1.07 % (3290015)Termination reason: Refutation not found, incomplete strategy
% 2.32/1.07 % (3290015)Time elapsed: 0.012 s
% 2.32/1.07 % (3290015)Peak memory usage: 88 MB
% 2.32/1.07 % (3290015)Instructions burned: 4 (million)
% 2.32/1.07 % (3290010)Refutation found. Thanks to Tanya!
% 2.32/1.07 % SZS status Unsatisfiable for theBenchmark
% 2.32/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.31 % (3290010)------------------------------
% 3.53/1.31 % (3290010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.31 % (3290010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.31 % (3290010)CaDiCaL version: 2.1.3
% 3.53/1.31 % (3290010)Termination reason: Refutation
% 3.53/1.31 % (3290010)Time elapsed: 0.010 s
% 3.53/1.31 % (3290010)Peak memory usage: 89 MB
% 3.53/1.31 % (3290010)Instructions burned: 12 (million)
% 3.53/1.31 % (3290010)------------------------------
% 3.53/1.31 % (3290010)------------------------------
% 3.53/1.31 % (3289967)Success in time 0.437 s
% 3.53/1.31 % Vampire exiting
%------------------------------------------------------------------------------