%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT034-2 : 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 : n015.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 12:02:07 PM UTC 2026
% Result : Unsatisfiable 2.74s 1.32s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 41
% Syntax : Number of formulae : 165 ( 26 unt; 17 def)
% Number of atoms : 426 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 537 ( 276 ~; 244 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 18 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 89 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_33) ).
fof(f2,axiom,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_34) ).
fof(f3,axiom,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP_35) ).
fof(f4,axiom,
! [X0] :
( ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears_36) ).
fof(f5,axiom,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates_37) ).
fof(f6,axiom,
! [X2,X0,X1] :
( greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ greater(X1,X2)
| ~ decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function_38) ).
fof(f7,axiom,
! [X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference_39) ).
fof(f9,axiom,
! [X0] :
( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference_41) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| in_environment(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_durations_are_time_intervals_43) ).
fof(f14,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,critical_point(X0))
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points_46) ).
fof(f16,axiom,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_48) ).
fof(f17,axiom,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared_49) ).
fof(f18,axiom,
! [X0,X1] :
( greater(X0,X1)
| ~ greater_or_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_50) ).
fof(f19,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_51) ).
fof(f20,axiom,
! [X0,X1] :
( X0 != X1
| greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_52) ).
fof(f21,axiom,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates_53) ).
fof(f22,axiom,
! [X0,X1] :
( ~ environment(X0)
| X1 != critical_point(X0)
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_54) ).
fof(f23,plain,
! [X0,X1] :
( ~ environment(X0)
| critical_point(X0) != X1
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(reorient_equations,[],[f22]) ).
fof(f26,axiom,
! [X2,X3,X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10_56) ).
fof(f27,axiom,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12_57) ).
fof(f28,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_58) ).
fof(f29,negated_conjecture,
in_environment(sk1,critical_point(sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_59) ).
fof(f30,negated_conjecture,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_60) ).
fof(f31,negated_conjecture,
greater(critical_point(sk1),sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_61) ).
fof(f32,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_62) ).
fof(f33,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f20]) ).
fof(f34,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(equality_resolution,[],[f23]) ).
fof(f37,plain,
! [X0] :
( ~ greater(zero,difference(growth_rate(first_movers,critical_point(X0)),growth_rate(efficient_producers,critical_point(X0))))
| ~ environment(X0) ),
inference(resolution,[],[f7,f34]) ).
fof(f40,plain,
! [X2,X0,X1] :
( in_environment(sk1,X2)
| ~ in_environment(sk1,X1)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X2,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[],[f11,f28]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in_environment(sk1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ greater_or_equal(appear(efficient_producers,sk1),X1)
| ~ in_environment(sk1,X1)
| ~ environment(sk1)
| subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
inference(resolution,[],[f40,f4]) ).
fof(f43,plain,
! [X0,X1] :
( ~ in_environment(sk1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ greater_or_equal(appear(efficient_producers,sk1),X1)
| ~ in_environment(sk1,X1)
| subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
inference(forward_subsumption_resolution,[],[f42,f28]) ).
fof(f45,definition,
( spl0_1
<=> subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f49,definition,
( spl0_2
<=> ! [X1] :
( ~ greater_or_equal(appear(efficient_producers,sk1),X1)
| ~ in_environment(sk1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f50,plain,
( ! [X1] :
( ~ greater_or_equal(appear(efficient_producers,sk1),X1)
| ~ in_environment(sk1,X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,definition,
( spl0_3
<=> ! [X0] :
( ~ in_environment(sk1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f53,plain,
( ! [X0] :
( ~ in_environment(sk1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f54,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f43,f52,f49,f45]) ).
fof(f55,plain,
! [X2,X0,X1] :
( selection_favors(X1,X0,X2)
| ~ greater(growth_rate(X1,X2),growth_rate(X0,X2))
| ~ subpopulations(X0,X1,sk1,X2) ),
inference(resolution,[],[f1,f28]) ).
fof(f56,plain,
( ~ in_environment(sk1,appear(efficient_producers,sk1))
| ~ spl0_2 ),
inference(resolution,[],[f50,f33]) ).
fof(f59,plain,
! [X0] :
( ~ in_environment(sk1,critical_point(sk1))
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ greater(critical_point(sk1),X0)
| in_environment(sk1,X0) ),
inference(resolution,[],[f14,f28]) ).
fof(f60,plain,
! [X0] :
( in_environment(sk1,X0)
| ~ greater(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) ),
inference(forward_subsumption_resolution,[],[f59,f29]) ).
fof(f64,plain,
( ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| ~ greater_or_equal(appear(efficient_producers,sk1),appear(efficient_producers,sk1))
| ~ environment(sk1)
| subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
inference(resolution,[],[f60,f4]) ).
fof(f65,plain,
( ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| ~ environment(sk1)
| subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
inference(forward_subsumption_resolution,[],[f64,f33]) ).
fof(f67,plain,
( ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)) ),
inference(forward_subsumption_resolution,[],[f65,f28]) ).
fof(f69,definition,
( spl0_4
<=> greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f71,plain,
( ~ greater(critical_point(sk1),appear(efficient_producers,sk1))
| spl0_4 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f67,f69,f45]) ).
fof(f75,definition,
( spl0_5
<=> critical_point(sk1) = appear(efficient_producers,sk1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f77,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_6
<=> greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f80,plain,
( greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( ~ greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1))
| spl0_6 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ environment(sk1)
| spl0_6 ),
inference(resolution,[],[f81,f17]) ).
fof(f85,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f83,f28]) ).
fof(f86,plain,
( ~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(resolution,[],[f55,f32]) ).
fof(f88,definition,
( spl0_7
<=> subpopulations(efficient_producers,first_movers,sk1,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f90,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_8
<=> greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f94,plain,
( ~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))
| spl0_8 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f86,f92,f88]) ).
fof(f96,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ environment(sk1)
| spl0_7 ),
inference(resolution,[],[f90,f16]) ).
fof(f97,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f96,f28]) ).
fof(f99,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(sk2,X0)
| ~ greater_or_equal(X1,sk2)
| ~ environment(sk1) )
| spl0_7 ),
inference(resolution,[],[f97,f26]) ).
fof(f102,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(sk2,X0)
| ~ greater_or_equal(X1,sk2) )
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f99,f28]) ).
fof(f117,definition,
( spl0_12
<=> ! [X1] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(X1,sk2) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f118,plain,
( ! [X1] :
( ~ greater_or_equal(X1,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl0_13
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f121,plain,
( ! [X0] :
( ~ greater_or_equal(sk2,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( spl0_12
| spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f102,f88,f120,f117]) ).
fof(f124,plain,
( ~ greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| spl0_8 ),
inference(resolution,[],[f94,f9]) ).
fof(f135,plain,
( ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1)
| spl0_6 ),
inference(resolution,[],[f85,f3]) ).
fof(f140,plain,
( ~ environment(sk1)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f135,f29]) ).
fof(f149,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f140,f28]) ).
fof(f150,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f149]) ).
fof(f164,plain,
( ~ in_environment(sk1,critical_point(sk1))
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f56,f77]) ).
fof(f170,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f164,f29]) ).
fof(f171,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f175,plain,
( ! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ greater_or_equal(sk2,appear(efficient_producers,X0))
| ~ greater(X1,sk2)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ environment(X0) )
| spl0_8 ),
inference(resolution,[],[f124,f6]) ).
fof(f188,definition,
( spl0_22
<=> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f190,plain,
( ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| spl0_22 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f192,definition,
( spl0_23
<=> ! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(X1,sk2)
| ~ greater_or_equal(sk2,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f193,plain,
( ! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X1,sk2)
| ~ greater_or_equal(sk2,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f194,plain,
( ~ spl0_22
| spl0_23
| spl0_8 ),
inference(avatar_split_clause,[],[f175,f92,f192,f188]) ).
fof(f195,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))
| spl0_22 ),
inference(resolution,[],[f190,f5]) ).
fof(f197,definition,
( spl0_24
<=> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f199,plain,
( ~ decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))
| spl0_24 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,definition,
( spl0_25
<=> decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f203,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( ~ spl0_24
| spl0_25
| spl0_22 ),
inference(avatar_split_clause,[],[f195,f188,f201,f197]) ).
fof(f206,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) )
| spl0_24 ),
inference(resolution,[],[f199,f27]) ).
fof(f214,definition,
( spl0_27
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f215,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ spl0_27 ),
inference(resolution,[],[f215,f28]) ).
fof(f218,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(sk2,X0)
| ~ greater_or_equal(X1,sk2)
| ~ environment(sk1) )
| ~ spl0_27 ),
inference(resolution,[],[f217,f26]) ).
fof(f221,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(sk2,X0)
| ~ greater_or_equal(X1,sk2) )
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f218,f28]) ).
fof(f223,plain,
( spl0_12
| spl0_13
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f221,f214,f120,f117]) ).
fof(f234,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))
| ~ spl0_13 ),
inference(resolution,[],[f121,f30]) ).
fof(f242,plain,
( ! [X0] :
( ~ greater(X0,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) )
| ~ spl0_12 ),
inference(resolution,[],[f118,f19]) ).
fof(f244,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ spl0_12 ),
inference(resolution,[],[f242,f31]) ).
fof(f245,plain,
( ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1)
| ~ spl0_12 ),
inference(resolution,[],[f244,f3]) ).
fof(f250,plain,
( ~ environment(sk1)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f245,f29]) ).
fof(f253,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f250,f28]) ).
fof(f254,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f253]) ).
fof(f256,plain,
( spl0_27
| spl0_24 ),
inference(avatar_split_clause,[],[f206,f197,f214]) ).
fof(f293,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_25 ),
inference(resolution,[],[f203,f2]) ).
fof(f294,plain,
( spl0_27
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f293,f201,f214]) ).
fof(f297,plain,
( ! [X0] :
( ~ in_environment(sk1,X0)
| ~ greater(X0,sk2)
| ~ greater_or_equal(sk2,appear(efficient_producers,sk1))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) )
| ~ spl0_23 ),
inference(resolution,[],[f193,f28]) ).
fof(f298,plain,
( ! [X0] :
( ~ greater(X0,sk2)
| ~ in_environment(sk1,X0)
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) )
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f297,f30]) ).
fof(f301,plain,
( ~ in_environment(sk1,critical_point(sk1))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)
| ~ spl0_23 ),
inference(resolution,[],[f298,f31]) ).
fof(f302,plain,
( ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f301,f29]) ).
fof(f303,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,critical_point(sk1))
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))
| ~ environment(X0) )
| ~ spl0_23 ),
inference(resolution,[],[f302,f21]) ).
fof(f306,definition,
( spl0_34
<=> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f308,plain,
( greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f310,definition,
( spl0_35
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,critical_point(sk1))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f311,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,critical_point(sk1)) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( spl0_34
| spl0_35
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f303,f192,f310,f306]) ).
fof(f315,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ spl0_35 ),
inference(resolution,[],[f311,f28]) ).
fof(f327,plain,
( ~ in_environment(sk1,critical_point(sk1))
| ~ environment(sk1)
| ~ spl0_35 ),
inference(resolution,[],[f315,f3]) ).
fof(f332,plain,
( ~ environment(sk1)
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f327,f29]) ).
fof(f335,plain,
( $false
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f332,f28]) ).
fof(f336,plain,
~ spl0_35,
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f338,plain,
( ~ environment(sk1)
| ~ spl0_34 ),
inference(resolution,[],[f308,f37]) ).
fof(f339,plain,
( $false
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f338,f28]) ).
fof(f340,plain,
~ spl0_34,
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f341,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f234,f120,f45]) ).
fof(f343,plain,
( ~ greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1))
| critical_point(sk1) = appear(efficient_producers,sk1)
| spl0_4 ),
inference(resolution,[],[f71,f18]) ).
fof(f344,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f343,f80]) ).
fof(f345,plain,
( spl0_5
| spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f344,f79,f69,f75]) ).
fof(f371,plain,
( ~ greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1))
| ~ spl0_3 ),
inference(resolution,[],[f53,f29]) ).
fof(f377,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f371,f80]) ).
fof(f378,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f377]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f54]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f72]) ).
cnf(s4,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f95]) ).
cnf(s6,plain,
( spl0_7
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s9,plain,
spl0_6,
inference(sat_conversion,[],[f150]) ).
cnf(s11,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f171]) ).
cnf(s14,plain,
( spl0_8
| ~ spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f194]) ).
cnf(s15,plain,
( spl0_22
| ~ spl0_24
| spl0_25 ),
inference(sat_conversion,[],[f204]) ).
cnf(s18,plain,
( spl0_12
| spl0_13
| ~ spl0_27 ),
inference(sat_conversion,[],[f223]) ).
cnf(s22,plain,
~ spl0_12,
inference(sat_conversion,[],[f254]) ).
cnf(s24,plain,
( spl0_24
| spl0_27 ),
inference(sat_conversion,[],[f256]) ).
cnf(s31,plain,
( ~ spl0_25
| spl0_27 ),
inference(sat_conversion,[],[f294]) ).
cnf(s33,plain,
( ~ spl0_23
| spl0_34
| spl0_35 ),
inference(sat_conversion,[],[f312]) ).
cnf(s36,plain,
~ spl0_35,
inference(sat_conversion,[],[f336]) ).
cnf(s38,plain,
~ spl0_34,
inference(sat_conversion,[],[f340]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(sat_conversion,[],[f341]) ).
cnf(s43,plain,
( spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f345]) ).
cnf(s46,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(sat_conversion,[],[f378]) ).
cnf(s47,plain,
~ spl0_23,
inference(rat,[],[s33,s36,s38]) ).
cnf(s49,plain,
( spl0_13
| ~ spl0_27 ),
inference(rat,[],[s18,s22]) ).
cnf(s50,plain,
( spl0_8
| ~ spl0_22 ),
inference(rat,[],[s14,s47]) ).
cnf(s51,plain,
~ spl0_3,
inference(rat,[],[s46,s9]) ).
cnf(s52,plain,
( spl0_7
| spl0_13 ),
inference(rat,[],[s6,s22]) ).
cnf(s54,plain,
( spl0_1
| spl0_2 ),
inference(rat,[],[s1,s51]) ).
cnf(s55,plain,
spl0_1,
inference(rat,[],[s11,s43,s54,s2,s9]) ).
cnf(s56,plain,
~ spl0_13,
inference(rat,[],[s39,s55]) ).
cnf(s57,plain,
~ spl0_27,
inference(rat,[],[s49,s56]) ).
cnf(s58,plain,
spl0_7,
inference(rat,[],[s52,s56]) ).
cnf(s59,plain,
~ spl0_25,
inference(rat,[],[s31,s57]) ).
cnf(s60,plain,
spl0_24,
inference(rat,[],[s24,s57]) ).
cnf(s61,plain,
~ spl0_8,
inference(rat,[],[s4,s58]) ).
cnf(s62,plain,
spl0_22,
inference(rat,[],[s15,s59,s60]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s50,s62,s61]) ).
fof(f379,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 17:25:31 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.74/1.31 % (1882678)Input is clausal, will run a generic CNF schedule.
% 2.74/1.31 % (1882683)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=1030977773:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.31 % (1882685)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=942029052:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.31 % (1882686)lrs+10_1_sil=8000:sp=occurrence:random_seed=4257618220:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.31 % (1882687)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=679341075:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.31 % (1882684)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2467787287:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.31 % (1882689)dis-21_1_sil=8000:lcm=predicate:random_seed=1109536807: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)
% 2.74/1.31 % (1882688)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1290812923:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.31 % (1882688)First to succeed.
% 2.74/1.31 % (1882688)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1882678"
% 2.74/1.31 % (1882686)Also succeeded, but the first one will report.
% 2.74/1.31 % (1882687)Instruction limit reached!
% 2.74/1.31 % (1882687)------------------------------
% 2.74/1.31 % (1882687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.31 % (1882687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.31 % (1882687)CaDiCaL version: 2.1.3
% 2.74/1.31 % (1882687)Termination reason: Instruction limit
% 2.74/1.31 % (1882687)Termination phase: Saturation
% 2.74/1.31 % (1882687)Time elapsed: 0.076 s
% 2.74/1.31 % (1882687)Peak memory usage: 88 MB
% 2.74/1.31 % (1882687)Instructions burned: 115 (million)
% 2.74/1.31 % (1882689)Instruction limit reached!
% 2.74/1.31 % (1882689)------------------------------
% 2.74/1.31 % (1882689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.31 % (1882689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.31 % (1882689)CaDiCaL version: 2.1.3
% 2.74/1.31 % (1882689)Termination reason: Instruction limit
% 2.74/1.31 % (1882689)Termination phase: Saturation
% 2.74/1.31 % (1882689)Time elapsed: 0.074 s
% 2.74/1.31 % (1882689)Peak memory usage: 89 MB
% 2.74/1.31 % (1882689)Instructions burned: 118 (million)
% 2.74/1.31 % (1882697)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=3537081377:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.74/1.31 % (1882698)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4181957217:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.74/1.31 % (1882698)Refutation not found, incomplete strategy
% 2.74/1.31 % (1882698)------------------------------
% 2.74/1.31 % (1882698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.32 % (1882698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.32 % (1882698)CaDiCaL version: 2.1.3
% 2.74/1.32 % (1882698)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.32 % (1882698)Time elapsed: 0.005 s
% 2.74/1.32 % (1882698)Peak memory usage: 88 MB
% 2.74/1.32 % (1882698)Instructions burned: 6 (million)
% 2.74/1.32 % (1882688)Refutation found. Thanks to Tanya!
% 2.74/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.41 % (1882688)------------------------------
% 3.72/1.41 % (1882688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.41 % (1882688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.41 % (1882688)CaDiCaL version: 2.1.3
% 3.72/1.41 % (1882688)Termination reason: Refutation
% 3.72/1.41 % (1882688)Time elapsed: 0.013 s
% 3.72/1.41 % (1882688)Peak memory usage: 89 MB
% 3.72/1.41 % (1882688)Instructions burned: 15 (million)
% 3.72/1.41 % (1882688)------------------------------
% 3.72/1.41 % (1882688)------------------------------
% 3.72/1.41 % (1882678)Success in time 0.455 s
% 3.72/1.41 % Vampire exiting
%------------------------------------------------------------------------------