%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:02:33 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 36
% Syntax : Number of formulae : 164 ( 23 unt; 13 def)
% Number of atoms : 494 ( 37 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 539 ( 209 ~; 317 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 14 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| X1 != efficient_producers
| number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_28) ).
fof(f3,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| efficient_producers != X1
| number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
inference(reorient_equations,[],[f2]) ).
fof(f6,axiom,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_30) ).
fof(f7,axiom,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_31) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X1)
| increases(X1)
| decreases(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_32) ).
fof(f9,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X1)
| increases(X1)
| increases(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_33) ).
fof(f11,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X1)
| increases(X1)
| increases(X2) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X1)
| decreases(X2)
| decreases(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_34) ).
fof(f13,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X1)
| decreases(X2)
| decreases(X1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X1)
| decreases(X2)
| increases(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_35) ).
fof(f15,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X1)
| decreases(X2)
| increases(X2) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X2)
| increases(X1)
| decreases(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_36) ).
fof(f17,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X2)
| increases(X1)
| increases(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_37) ).
fof(f19,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X2)
| increases(X1)
| increases(X2) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X2)
| decreases(X2)
| decreases(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_38) ).
fof(f21,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X2)
| decreases(X2)
| decreases(X1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X2,X0,X1] :
( X0 != sum(X1,X2)
| ~ constant(X0)
| constant(X2)
| decreases(X2)
| increases(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_39) ).
fof(f23,plain,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| ~ constant(X0)
| constant(X2)
| decreases(X2)
| increases(X2) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ subpopulation(X2,X0,X1)
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ constant(cardinality_at_time(X2,X1))
| growth_rate(X2,X1) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_40) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X2,X1),zero)
| ~ in_environment(X0,X1)
| ~ subpopulation(X2,X0,X1)
| ~ environment(X0)
| ~ constant(cardinality_at_time(X2,X1))
| zero = growth_rate(X2,X1) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X2,X1),zero)
| ~ in_environment(X0,X1)
| ~ subpopulation(X2,X0,X1)
| ~ environment(X0)
| ~ increases(cardinality_at_time(X2,X1))
| greater(growth_rate(X2,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_41) ).
fof(f27,axiom,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X2,X1),zero)
| ~ in_environment(X0,X1)
| ~ subpopulation(X2,X0,X1)
| ~ environment(X0)
| ~ decreases(cardinality_at_time(X2,X1))
| greater(zero,growth_rate(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_42) ).
fof(f28,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(first_movers,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_43) ).
fof(f29,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_44) ).
fof(f30,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_45) ).
fof(f33,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_47) ).
fof(f34,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_48) ).
fof(f35,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_49) ).
fof(f36,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_50) ).
fof(f37,plain,
( zero != growth_rate(first_movers,sk2)
| zero != growth_rate(efficient_producers,sk2) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_51) ).
fof(f39,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_52) ).
fof(f40,plain,
! [X2,X0] :
( ~ subpopulation(efficient_producers,X0,X2)
| ~ environment(X0)
| number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
inference(equality_resolution,[],[f3]) ).
fof(f42,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(equality_resolution,[],[f9]) ).
fof(f43,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X1)
| increases(X2) ),
inference(equality_resolution,[],[f11]) ).
fof(f44,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| decreases(X2)
| decreases(X1) ),
inference(equality_resolution,[],[f13]) ).
fof(f45,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| decreases(X2)
| increases(X2) ),
inference(equality_resolution,[],[f15]) ).
fof(f46,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(equality_resolution,[],[f17]) ).
fof(f47,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| increases(X1)
| increases(X2) ),
inference(equality_resolution,[],[f19]) ).
fof(f48,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| decreases(X2)
| decreases(X1) ),
inference(equality_resolution,[],[f21]) ).
fof(f49,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| decreases(X2)
| increases(X2) ),
inference(equality_resolution,[],[f23]) ).
fof(f51,definition,
( spl0_1
<=> greater(zero,growth_rate(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f53,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl0_2
<=> greater(growth_rate(efficient_producers,sk2),zero) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f58,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f39,f55,f51]) ).
fof(f60,definition,
( spl0_3
<=> greater(zero,growth_rate(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f64,definition,
( spl0_4
<=> greater(growth_rate(first_movers,sk2),zero) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f66,plain,
( ~ greater(growth_rate(first_movers,sk2),zero)
| spl0_4 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f38,f64,f60]) ).
fof(f69,definition,
( spl0_5
<=> zero = growth_rate(efficient_producers,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f73,definition,
( spl0_6
<=> zero = growth_rate(first_movers,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f76,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f37,f73,f69]) ).
fof(f77,plain,
( ~ environment(sk1)
| in_environment(sk1,sk2) ),
inference(resolution,[],[f30,f34]) ).
fof(f78,plain,
in_environment(sk1,sk2),
inference(forward_subsumption_resolution,[],[f77,f33]) ).
fof(f79,plain,
( ~ environment(sk1)
| greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[],[f28,f34]) ).
fof(f80,plain,
greater(cardinality_at_time(first_movers,sk2),zero),
inference(forward_subsumption_resolution,[],[f79,f33]) ).
fof(f81,plain,
( ~ environment(sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolution,[],[f29,f34]) ).
fof(f82,plain,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(forward_subsumption_resolution,[],[f81,f33]) ).
fof(f85,plain,
! [X0,X1] :
( ~ environment(X0)
| number_of_organizations(X0,X1) = sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(resolution,[],[f40,f7]) ).
fof(f86,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| number_of_organizations(X0,X1) = sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1))
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f85]) ).
fof(f87,plain,
( number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
| ~ environment(sk1) ),
inference(resolution,[],[f86,f78]) ).
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,[],[f87,f33]) ).
fof(f91,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(superposition,[],[f42,f88]) ).
fof(f92,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(superposition,[],[f43,f88]) ).
fof(f93,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(superposition,[],[f44,f88]) ).
fof(f94,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(superposition,[],[f45,f88]) ).
fof(f95,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(superposition,[],[f46,f88]) ).
fof(f96,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(superposition,[],[f47,f88]) ).
fof(f97,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(superposition,[],[f48,f88]) ).
fof(f98,plain,
( ~ constant(number_of_organizations(sk1,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(superposition,[],[f49,f88]) ).
fof(f99,plain,
( constant(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[],[f98,f35]) ).
fof(f100,plain,
( constant(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[],[f97,f35]) ).
fof(f101,plain,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[],[f96,f35]) ).
fof(f102,plain,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[],[f95,f35]) ).
fof(f103,plain,
( constant(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[],[f94,f35]) ).
fof(f104,plain,
( constant(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[],[f93,f35]) ).
fof(f105,plain,
( constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[],[f92,f35]) ).
fof(f106,plain,
( constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[],[f91,f35]) ).
fof(f108,definition,
( spl0_7
<=> increases(cardinality_at_time(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f110,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f112,definition,
( spl0_8
<=> decreases(cardinality_at_time(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f116,definition,
( spl0_9
<=> constant(cardinality_at_time(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f119,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f99,f116,f112,f108]) ).
fof(f121,definition,
( spl0_10
<=> decreases(cardinality_at_time(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f123,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_10
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f100,f116,f112,f121]) ).
fof(f126,definition,
( spl0_11
<=> increases(cardinality_at_time(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f129,plain,
( spl0_7
| spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f101,f116,f126,f108]) ).
fof(f130,plain,
( spl0_10
| spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f102,f116,f126,f121]) ).
fof(f132,definition,
( spl0_12
<=> constant(cardinality_at_time(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f135,plain,
( spl0_7
| spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f103,f132,f112,f108]) ).
fof(f136,plain,
( spl0_10
| spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f104,f132,f112,f121]) ).
fof(f137,plain,
( spl0_7
| spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f105,f132,f126,f108]) ).
fof(f138,plain,
( spl0_10
| spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f106,f132,f126,f121]) ).
fof(f143,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ constant(cardinality_at_time(first_movers,sk2))
| zero = growth_rate(first_movers,sk2) ),
inference(resolution,[],[f25,f80]) ).
fof(f144,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| zero = growth_rate(efficient_producers,sk2) ),
inference(resolution,[],[f25,f82]) ).
fof(f145,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| zero = growth_rate(efficient_producers,sk2) ),
inference(forward_subsumption_resolution,[],[f144,f7]) ).
fof(f148,definition,
( spl0_13
<=> ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f149,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f150,plain,
( spl0_5
| ~ spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f145,f148,f116,f69]) ).
fof(f153,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ increases(cardinality_at_time(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero) ),
inference(resolution,[],[f26,f80]) ).
fof(f154,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(resolution,[],[f26,f82]) ).
fof(f155,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sk2),zero) )
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f154,f110]) ).
fof(f156,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ increases(cardinality_at_time(first_movers,sk2)) )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f153,f66]) ).
fof(f157,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sk2),zero) )
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f155,f7]) ).
fof(f158,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ increases(cardinality_at_time(first_movers,sk2)) )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f156,f6]) ).
fof(f159,plain,
( spl0_2
| spl0_13
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f157,f108,f148,f55]) ).
fof(f160,plain,
( ~ spl0_11
| spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f158,f64,f148,f126]) ).
fof(f161,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ constant(cardinality_at_time(first_movers,sk2))
| zero = growth_rate(first_movers,sk2) ),
inference(forward_subsumption_resolution,[],[f143,f6]) ).
fof(f162,plain,
( spl0_6
| ~ spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f161,f148,f132,f73]) ).
fof(f165,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ decreases(cardinality_at_time(first_movers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolution,[],[f27,f80]) ).
fof(f166,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolution,[],[f27,f82]) ).
fof(f167,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[],[f166,f7]) ).
fof(f168,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,sk2)) )
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f165,f123]) ).
fof(f169,plain,
( spl0_3
| ~ spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f167,f148,f112,f60]) ).
fof(f170,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0) )
| spl0_1
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f168,f53]) ).
fof(f171,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| spl0_1
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f170,f6]) ).
fof(f172,plain,
( spl0_13
| spl0_1
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f171,f121,f51,f148]) ).
fof(f173,plain,
( ~ environment(sk1)
| ~ spl0_13 ),
inference(resolution,[],[f149,f78]) ).
fof(f174,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f173,f33]) ).
fof(f175,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f174]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f76]) ).
cnf(s4,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s5,plain,
( spl0_8
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f124]) ).
cnf(s6,plain,
( spl0_7
| spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f129]) ).
cnf(s7,plain,
( spl0_9
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f130]) ).
cnf(s8,plain,
( spl0_7
| spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s9,plain,
( spl0_8
| spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_7
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s11,plain,
( spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s12,plain,
( spl0_5
| ~ spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f150]) ).
cnf(s14,plain,
( spl0_2
| ~ spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f159]) ).
cnf(s15,plain,
( spl0_4
| ~ spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f160]) ).
cnf(s16,plain,
( spl0_6
| ~ spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f162]) ).
cnf(s17,plain,
( spl0_3
| ~ spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s18,plain,
( spl0_1
| ~ spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f172]) ).
cnf(s19,plain,
~ spl0_13,
inference(sat_conversion,[],[f175]) ).
cnf(s20,plain,
( spl0_1
| ~ spl0_10 ),
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
( spl0_3
| ~ spl0_8 ),
inference(rat,[],[s17,s19]) ).
cnf(s22,plain,
( spl0_6
| ~ spl0_12 ),
inference(rat,[],[s16,s19]) ).
cnf(s23,plain,
( spl0_4
| ~ spl0_11 ),
inference(rat,[],[s15,s19]) ).
cnf(s24,plain,
( spl0_2
| ~ spl0_7 ),
inference(rat,[],[s14,s19]) ).
cnf(s26,plain,
( spl0_5
| ~ spl0_9 ),
inference(rat,[],[s12,s19]) ).
cnf(s27,plain,
( spl0_8
| spl0_10 ),
inference(rat,[],[s3,s26,s22,s5,s9]) ).
cnf(s28,plain,
( spl0_11
| spl0_7 ),
inference(rat,[],[s3,s26,s22,s6,s10]) ).
cnf(s29,plain,
( spl0_11
| spl0_10 ),
inference(rat,[],[s3,s26,s22,s7,s11]) ).
cnf(s30,plain,
spl0_10,
inference(rat,[],[s29,s23,s2,s21,s27]) ).
cnf(s31,plain,
spl0_1,
inference(rat,[],[s20,s30]) ).
cnf(s32,plain,
~ spl0_2,
inference(rat,[],[s1,s31]) ).
cnf(s33,plain,
~ spl0_7,
inference(rat,[],[s24,s32]) ).
cnf(s34,plain,
spl0_11,
inference(rat,[],[s28,s33]) ).
cnf(s35,plain,
spl0_4,
inference(rat,[],[s23,s34]) ).
cnf(s36,plain,
~ spl0_3,
inference(rat,[],[s2,s35]) ).
cnf(s37,plain,
~ spl0_8,
inference(rat,[],[s21,s36]) ).
cnf(s38,plain,
spl0_12,
inference(rat,[],[s8,s33,s37]) ).
cnf(s39,plain,
spl0_9,
inference(rat,[],[s4,s33,s37]) ).
cnf(s40,plain,
spl0_6,
inference(rat,[],[s22,s38]) ).
cnf(s41,plain,
spl0_5,
inference(rat,[],[s26,s39]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s3,s40,s41]) ).
fof(f176,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 17:20:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.46 % (2637738)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2637743)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=234851522_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % TRYING [3]
% 0.15/0.46 % (2637744)% WARNING: option uhcvi not known.
% 0.15/0.46 % TRYING [4]
% 0.15/0.46 % (2637747)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2605894356:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (2637744)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3607896807:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (2637745)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1962617479:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (2637746)dis+10_1_sil=32000:sp=arity:random_seed=1934063088:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (2637748)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1402415443:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (2637749)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3983299221:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % TRYING [5]
% 0.15/0.46 % (2637746) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2637738-2637746"...
% 0.15/0.46 % (2637748) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2637738-2637748"...
% 0.15/0.46 % (2637749) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2637738-2637749"...
% 0.15/0.46 % (2637744) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2637738-2637744"...
% 0.15/0.46 % (2637747) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2637738-2637747"...
% 0.15/0.46 % (2637746)...printing done.
% 0.15/0.46 % (2637746)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (2637746)------------------------------
% 0.15/0.46 % (2637746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (2637746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (2637746)CaDiCaL version: 2.1.3
% 0.15/0.46 % (2637746)Termination reason: Refutation
% 0.15/0.46 % (2637746)Time elapsed: 0.006 s
% 0.15/0.46 % (2637746)Peak memory usage: 12 MB
% 0.15/0.46 % (2637746)Instructions burned: 7 (million)
% 0.15/0.46 % (2637738)Success in time 0.042 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------