%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n012.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 12:02:04 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.81s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 36
% Syntax : Number of formulae : 174 ( 23 unt; 13 def)
% Number of atoms : 528 ( 39 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 587 ( 233 ~; 341 |; 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 : 122 ( 0 sgn 122 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| X1 != first_movers
| 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_29) ).
fof(f5,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulation(X1,X0,X2)
| first_movers != X1
| number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
inference(reorient_equations,[],[f4]) ).
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(first_movers,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,[],[f5]) ).
fof(f42,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| decreases(X2)
| increases(X2) ),
inference(equality_resolution,[],[f23]) ).
fof(f43,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| decreases(X2)
| decreases(X1) ),
inference(equality_resolution,[],[f21]) ).
fof(f44,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| increases(X1)
| decreases(X1) ),
inference(equality_resolution,[],[f17]) ).
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(X1)
| decreases(X2)
| decreases(X1) ),
inference(equality_resolution,[],[f13]) ).
fof(f47,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X1)
| decreases(X1) ),
inference(equality_resolution,[],[f9]) ).
fof(f48,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| increases(X1)
| increases(X2) ),
inference(equality_resolution,[],[f19]) ).
fof(f49,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X1)
| increases(X2) ),
inference(equality_resolution,[],[f11]) ).
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(f57,plain,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| spl0_2 ),
inference(avatar_component_clause,[],[f55]) ).
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(f62,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| spl0_3 ),
inference(avatar_component_clause,[],[f60]) ).
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(f75,plain,
( zero != growth_rate(first_movers,sk2)
| spl0_6 ),
inference(avatar_component_clause,[],[f73]) ).
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,f6]) ).
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(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(superposition,[],[f42,f88]) ).
fof(f92,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,[],[f43,f88]) ).
fof(f93,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,[],[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(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,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(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(superposition,[],[f47,f88]) ).
fof(f97,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,[],[f48,f88]) ).
fof(f98,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,[],[f49,f88]) ).
fof(f99,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,[],[f98,f35]) ).
fof(f100,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,[],[f97,f35]) ).
fof(f101,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,[],[f96,f35]) ).
fof(f102,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,[],[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(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(first_movers,sk2)) ),
inference(forward_subsumption_resolution,[],[f93,f35]) ).
fof(f105,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,[],[f92,f35]) ).
fof(f106,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,[],[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
<=> increases(cardinality_at_time(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f116,definition,
( spl0_9
<=> constant(cardinality_at_time(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f118,plain,
( constant(cardinality_at_time(first_movers,sk2))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f99,f116,f112,f108]) ).
fof(f121,definition,
( spl0_10
<=> constant(cardinality_at_time(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f123,plain,
( constant(cardinality_at_time(efficient_producers,sk2))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_7
| spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f100,f121,f112,f108]) ).
fof(f126,definition,
( spl0_11
<=> decreases(cardinality_at_time(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f128,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_11
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f101,f116,f112,f126]) ).
fof(f131,definition,
( spl0_12
<=> decreases(cardinality_at_time(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f133,plain,
( decreases(cardinality_at_time(efficient_producers,sk2))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_11
| spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f102,f116,f131,f126]) ).
fof(f135,plain,
( spl0_7
| spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f103,f116,f131,f108]) ).
fof(f136,plain,
( spl0_11
| spl0_8
| spl0_10 ),
inference(avatar_split_clause,[],[f104,f121,f112,f126]) ).
fof(f137,plain,
( spl0_11
| spl0_12
| spl0_10 ),
inference(avatar_split_clause,[],[f105,f121,f131,f126]) ).
fof(f138,plain,
( spl0_7
| spl0_12
| spl0_10 ),
inference(avatar_split_clause,[],[f106,f121,f131,f108]) ).
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)
| ~ subpopulation(efficient_producers,X0,sk2)
| ~ environment(X0)
| zero = growth_rate(efficient_producers,sk2) )
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f144,f123]) ).
fof(f146,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| zero = growth_rate(first_movers,sk2) )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f143,f118]) ).
fof(f147,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| zero = growth_rate(efficient_producers,sk2) )
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f145,f7]) ).
fof(f148,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0) )
| spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f146,f75]) ).
fof(f150,definition,
( spl0_13
<=> ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f151,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f152,plain,
( spl0_5
| spl0_13
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f147,f121,f150,f69]) ).
fof(f153,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f148,f6]) ).
fof(f154,plain,
( spl0_13
| spl0_6
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f153,f116,f73,f150]) ).
fof(f155,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(f156,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(f158,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,[],[f155,f66]) ).
fof(f160,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ increases(cardinality_at_time(first_movers,sk2)) )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f158,f6]) ).
fof(f162,plain,
( ~ spl0_8
| spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f160,f64,f150,f112]) ).
fof(f168,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(f169,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(f170,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,[],[f169,f7]) ).
fof(f171,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,sk2)) )
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f168,f128]) ).
fof(f173,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0) )
| spl0_1
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f171,f53]) ).
fof(f174,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| spl0_1
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f173,f6]) ).
fof(f175,plain,
( spl0_13
| spl0_1
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f174,f126,f51,f150]) ).
fof(f187,plain,
( ~ environment(sk1)
| ~ spl0_13 ),
inference(resolution,[],[f151,f78]) ).
fof(f188,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f187,f33]) ).
fof(f189,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f188]) ).
fof(f190,plain,
! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(forward_subsumption_resolution,[],[f156,f7]) ).
fof(f191,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sk2)) )
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f170,f133]) ).
fof(f192,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| spl0_3
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f191,f62]) ).
fof(f193,plain,
( spl0_13
| spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f192,f131,f60,f150]) ).
fof(f194,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sk2),zero) )
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f190,f110]) ).
fof(f195,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| spl0_2
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f194,f57]) ).
fof(f196,plain,
( spl0_13
| spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f195,f108,f55,f150]) ).
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_7
| spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f124]) ).
cnf(s6,plain,
( spl0_8
| spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f129]) ).
cnf(s7,plain,
( spl0_9
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s8,plain,
( spl0_7
| spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s9,plain,
( spl0_8
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s10,plain,
( spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s11,plain,
( spl0_7
| spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s12,plain,
( spl0_5
| ~ spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f152]) ).
cnf(s13,plain,
( spl0_6
| ~ spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f154]) ).
cnf(s14,plain,
( spl0_4
| ~ spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f162]) ).
cnf(s16,plain,
( spl0_1
| ~ spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f175]) ).
cnf(s22,plain,
~ spl0_13,
inference(sat_conversion,[],[f189]) ).
cnf(s23,plain,
( spl0_3
| ~ spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f193]) ).
cnf(s24,plain,
( spl0_2
| ~ spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f196]) ).
cnf(s26,plain,
( spl0_1
| ~ spl0_11 ),
inference(rat,[],[s16,s22]) ).
cnf(s28,plain,
( spl0_4
| ~ spl0_8 ),
inference(rat,[],[s14,s22]) ).
cnf(s29,plain,
( spl0_6
| ~ spl0_9 ),
inference(rat,[],[s13,s22]) ).
cnf(s30,plain,
( spl0_5
| ~ spl0_10 ),
inference(rat,[],[s12,s22]) ).
cnf(s31,plain,
( spl0_12
| spl0_7 ),
inference(rat,[],[s3,s29,s30,s8,s11]) ).
cnf(s32,plain,
( spl0_8
| spl0_11 ),
inference(rat,[],[s3,s29,s30,s6,s9]) ).
cnf(s33,plain,
( spl0_12
| spl0_11 ),
inference(rat,[],[s3,s29,s30,s7,s10]) ).
cnf(s34,plain,
spl0_11,
inference(rat,[],[s33,s23,s2,s28,s32,s22]) ).
cnf(s35,plain,
spl0_1,
inference(rat,[],[s26,s34]) ).
cnf(s36,plain,
~ spl0_2,
inference(rat,[],[s1,s35]) ).
cnf(s37,plain,
~ spl0_7,
inference(rat,[],[s24,s22,s36]) ).
cnf(s38,plain,
spl0_12,
inference(rat,[],[s31,s37]) ).
cnf(s39,plain,
spl0_3,
inference(rat,[],[s23,s22,s38]) ).
cnf(s40,plain,
~ spl0_4,
inference(rat,[],[s2,s39]) ).
cnf(s41,plain,
~ spl0_8,
inference(rat,[],[s28,s40]) ).
cnf(s42,plain,
spl0_10,
inference(rat,[],[s5,s37,s41]) ).
cnf(s43,plain,
spl0_9,
inference(rat,[],[s4,s37,s41]) ).
cnf(s44,plain,
spl0_5,
inference(rat,[],[s30,s42]) ).
cnf(s45,plain,
spl0_6,
inference(rat,[],[s29,s43]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s3,s45,s44]) ).
fof(f197,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 17:20:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.27/0.81 % (2607907)Input is clausal, will run a generic CNF schedule.
% 0.27/0.81 % (2607918)dis-21_1_sil=8000:lcm=predicate:random_seed=1097816358: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)
% 0.27/0.81 % (2607914)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1190778583:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.27/0.81 % (2607912)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=4170863336:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.27/0.81 % (2607917)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1062581732:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.27/0.81 % (2607916)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2200108372:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.27/0.81 % (2607915)lrs+10_1_sil=8000:sp=occurrence:random_seed=4154863737:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.27/0.81 % (2607913)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=45295057:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.27/0.81 % (2607916)Also succeeded, but the first one will report.
% 0.27/0.81 % (2607915)First to succeed.
% 0.27/0.81 % (2607918)Refutation not found, incomplete strategy
% 0.27/0.81 % (2607918)------------------------------
% 0.27/0.81 % (2607918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/0.81 % (2607918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.81 % (2607918)CaDiCaL version: 2.1.3
% 0.27/0.81 % (2607918)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.81 % (2607918)Time elapsed: 0.002 s
% 0.27/0.81 % (2607918)Peak memory usage: 88 MB
% 0.27/0.81 % (2607918)Instructions burned: 6 (million)
% 0.27/0.81 % (2607917)Also succeeded, but the first one will report.
% 0.27/0.81 % (2607915)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2607907"
% 0.27/0.81 % (2607918)------------------------------
% 0.27/0.81 % (2607918)------------------------------
% 0.27/0.81 % (2607915)Refutation found. Thanks to Tanya!
% 0.27/0.81 % SZS status Unsatisfiable for theBenchmark
% 0.27/0.81 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.90 % (2607915)------------------------------
% 0.07/0.90 % (2607915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.07/0.90 % (2607915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.90 % (2607915)CaDiCaL version: 2.1.3
% 0.07/0.90 % (2607915)Termination reason: Refutation
% 0.07/0.90 % (2607915)Time elapsed: 0.003 s
% 0.07/0.90 % (2607915)Peak memory usage: 89 MB
% 0.07/0.90 % (2607915)Instructions burned: 8 (million)
% 0.07/0.90 % (2607915)------------------------------
% 0.07/0.90 % (2607915)------------------------------
% 0.07/0.90 % (2607907)Success in time 0.279 s
% 0.07/0.90 % Vampire exiting
%------------------------------------------------------------------------------