%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:02:31 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 135 ( 25 unt; 12 def)
% Number of atoms : 370 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 385 ( 150 ~; 191 |; 19 &)
% ( 12 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 114 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
fof(f2,axiom,
! [X0,X1] :
( environment(X0)
=> ( ( in_environment(X0,initial_FM_EP(X0))
=> subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0)) )
& ( subpopulations(first_movers,efficient_producers,X0,X1)
=> greater_or_equal(X1,initial_FM_EP(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& greater_or_equal(X1,X2)
& greater_or_equal(X3,X1)
& subpopulations(first_movers,efficient_producers,X0,X3)
& greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
=> greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference) ).
fof(f4,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occurs) ).
fof(f5,axiom,
! [X0] :
( environment(X0)
=> greater_or_equal(initial_FM_EP(X0),start_time(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( environment(X0)
& greater_or_equal(X1,start_time(X0))
& greater(X2,X1)
& in_environment(X0,X2) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order) ).
fof(f8,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f9,axiom,
! [X0] :
( environment(X0)
=> greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8) ).
fof(f11,conjecture,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0)) )
& ( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ) )
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f21,plain,
! [X0,X1,X2] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater(X2,X1)
| ~ in_environment(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater(X2,X1)
| ~ in_environment(X0,X2) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f30,plain,
? [X0,X1] :
( ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f31,plain,
? [X0,X1] :
( ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
( ~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
& environment(sK0)
& subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1] :
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater(X2,X1)
| ~ in_environment(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X0] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f44,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f45,plain,
environment(sK0),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)),
inference(cnf_transformation,[],[f32]) ).
fof(f47,plain,
! [X0,X1] :
( environment(X0)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f48,plain,
! [X0] :
( in_environment(X0,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| environment(X0) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f49,plain,
! [X0,X1] :
( environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,initial_FM_EP(X0)) ),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| environment(X0)
| greater_or_equal(X1,X2)
| greater_or_equal(X3,X1)
| subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f51,plain,
! [X0,X1] :
( environment(X0)
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f52,plain,
! [X0] :
( ~ greater_or_equal(initial_FM_EP(X0),start_time(X0))
| environment(X0) ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f53,plain,
! [X2,X0,X1] :
( environment(X0)
| ~ in_environment(X0,X1)
| greater_or_equal(X1,start_time(X0))
| greater(X2,X1)
| in_environment(X0,X2) ),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f55,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 = X1
| greater_or_equal(X0,X1) ),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f56,plain,
! [X0] :
( ~ greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| environment(X0) ),
inference(consistent_polarity_flipping,[],[f42]) ).
fof(f58,plain,
greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f59,plain,
~ environment(sK0),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f60,plain,
~ subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f75,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ in_environment(sK0,X0) ),
inference(resolution,[],[f51,f59]) ).
fof(f76,plain,
~ in_environment(sK0,sK1),
inference(resolution,[],[f75,f60]) ).
fof(f78,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ greater_or_equal(X0,initial_FM_EP(sK0)) ),
inference(resolution,[],[f49,f59]) ).
fof(f79,plain,
~ greater_or_equal(sK1,initial_FM_EP(sK0)),
inference(resolution,[],[f78,f60]) ).
fof(f80,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(resolution,[],[f47,f59]) ).
fof(f89,plain,
! [X0,X1] :
( greater_or_equal(X0,start_time(sK0))
| ~ in_environment(sK0,X0)
| greater(X1,X0)
| in_environment(sK0,X1) ),
inference(resolution,[],[f53,f59]) ).
fof(f90,plain,
! [X0] :
( ~ in_environment(sK0,initial_FM_EP(sK0))
| greater(X0,initial_FM_EP(sK0))
| in_environment(sK0,X0)
| environment(sK0) ),
inference(resolution,[],[f89,f52]) ).
fof(f92,definition,
( spl2_3
<=> environment(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f94,plain,
( environment(sK0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl2_4
<=> ! [X0] :
( greater(X0,initial_FM_EP(sK0))
| in_environment(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f97,plain,
( ! [X0] :
( greater(X0,initial_FM_EP(sK0))
| in_environment(sK0,X0) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl2_5
<=> in_environment(sK0,initial_FM_EP(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f101,plain,
( ~ in_environment(sK0,initial_FM_EP(sK0))
| spl2_5 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl2_3
| spl2_4
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f90,f99,f96,f92]) ).
fof(f103,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,initial_FM_EP(sK0))
| environment(sK0)
| spl2_5 ),
inference(resolution,[],[f101,f48]) ).
fof(f105,definition,
( spl2_6
<=> subpopulations(first_movers,efficient_producers,sK0,initial_FM_EP(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f107,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,initial_FM_EP(sK0))
| spl2_6 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl2_3
| ~ spl2_6
| spl2_5 ),
inference(avatar_split_clause,[],[f103,f99,f105,f92]) ).
fof(f109,plain,
( ~ decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))))
| spl2_6 ),
inference(resolution,[],[f107,f80]) ).
fof(f110,plain,
( ~ greater_or_equal(initial_FM_EP(sK0),initial_FM_EP(sK0))
| spl2_6 ),
inference(resolution,[],[f107,f78]) ).
fof(f159,definition,
( spl2_10
<=> ! [X2,X0,X1] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| greater_or_equal(X2,X0)
| greater_or_equal(X0,initial_FM_EP(sK0))
| environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f160,plain,
( ! [X2,X0,X1] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| greater_or_equal(X2,X0)
| greater_or_equal(X0,initial_FM_EP(sK0))
| environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X2) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f169,definition,
( spl2_11
<=> greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f170,plain,
( greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0)))
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f171,plain,
( ~ greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0)))
| spl2_11 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f181,plain,
( ! [X2,X0,X1] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| environment(X1)
| greater_or_equal(X0,initial_FM_EP(sK0))
| greater_or_equal(X2,X0)
| subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) )
| spl2_11 ),
inference(resolution,[],[f171,f50]) ).
fof(f185,plain,
( spl2_10
| spl2_11 ),
inference(avatar_split_clause,[],[f181,f169,f159]) ).
fof(f207,plain,
( ! [X0,X1] :
( ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| greater_or_equal(X0,initial_FM_EP(sK0))
| greater_or_equal(initial_FM_EP(sK0),initial_FM_EP(sK0))
| environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X0) )
| spl2_6
| ~ spl2_10 ),
inference(resolution,[],[f160,f109]) ).
fof(f231,definition,
( spl2_19
<=> greater_or_equal(initial_FM_EP(sK0),initial_FM_EP(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_19])],[avatar_definition]) ).
fof(f235,definition,
( spl2_20
<=> ! [X0,X1] :
( ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X0)
| greater_or_equal(X0,initial_FM_EP(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f236,plain,
( ! [X0,X1] :
( greater_or_equal(X0,initial_FM_EP(sK0))
| environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X0)
| ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)) )
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f255,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f94,f59]) ).
fof(f256,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f255]) ).
fof(f257,plain,
( spl2_19
| spl2_20
| spl2_6
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f207,f159,f105,f235,f231]) ).
fof(f258,plain,
( ~ spl2_19
| spl2_6 ),
inference(avatar_split_clause,[],[f110,f105,f231]) ).
fof(f280,plain,
( ! [X0] :
( environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)) )
| ~ spl2_20 ),
inference(resolution,[],[f236,f79]) ).
fof(f282,definition,
( spl2_24
<=> greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_24])],[avatar_definition]) ).
fof(f284,plain,
( ~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
| spl2_24 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f286,definition,
( spl2_25
<=> ! [X0] :
( environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_25])],[avatar_definition]) ).
fof(f287,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK1)
| environment(X0) )
| ~ spl2_25 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( ~ spl2_24
| spl2_25
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f280,f235,f286,f282]) ).
fof(f289,plain,
( $false
| spl2_24 ),
inference(resolution,[],[f284,f58]) ).
fof(f295,plain,
spl2_24,
inference(avatar_contradiction_clause,[],[f289]) ).
fof(f296,plain,
( environment(sK0)
| ~ spl2_25 ),
inference(resolution,[],[f287,f60]) ).
fof(f297,plain,
( spl2_3
| ~ spl2_25 ),
inference(avatar_split_clause,[],[f296,f286,f92]) ).
fof(f305,plain,
( ! [X0] :
( greater_or_equal(X0,initial_FM_EP(sK0))
| initial_FM_EP(sK0) = X0
| in_environment(sK0,X0) )
| ~ spl2_4 ),
inference(resolution,[],[f97,f55]) ).
fof(f327,plain,
( environment(sK0)
| ~ spl2_11 ),
inference(resolution,[],[f170,f56]) ).
fof(f341,plain,
( spl2_3
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f327,f169,f92]) ).
fof(f348,plain,
( sK1 = initial_FM_EP(sK0)
| in_environment(sK0,sK1)
| ~ spl2_4 ),
inference(resolution,[],[f305,f79]) ).
fof(f350,definition,
( spl2_32
<=> in_environment(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_32])],[avatar_definition]) ).
fof(f352,plain,
( in_environment(sK0,sK1)
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f354,definition,
( spl2_33
<=> sK1 = initial_FM_EP(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_33])],[avatar_definition]) ).
fof(f356,plain,
( sK1 = initial_FM_EP(sK0)
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f357,plain,
( spl2_32
| spl2_33
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f348,f96,f354,f350]) ).
fof(f390,plain,
( ~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
| environment(sK0)
| ~ spl2_33 ),
inference(superposition,[],[f56,f356]) ).
fof(f397,plain,
( spl2_3
| ~ spl2_24
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f390,f354,f282,f92]) ).
fof(f408,plain,
( $false
| ~ spl2_32 ),
inference(resolution,[],[f352,f76]) ).
fof(f409,plain,
~ spl2_32,
inference(avatar_contradiction_clause,[],[f408]) ).
cnf(s2,plain,
( spl2_3
| spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f102]) ).
cnf(s3,plain,
( spl2_3
| spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f108]) ).
cnf(s7,plain,
( spl2_10
| spl2_11 ),
inference(sat_conversion,[],[f185]) ).
cnf(s19,plain,
~ spl2_3,
inference(sat_conversion,[],[f256]) ).
cnf(s20,plain,
( spl2_6
| ~ spl2_10
| spl2_19
| spl2_20 ),
inference(sat_conversion,[],[f257]) ).
cnf(s21,plain,
( spl2_6
| ~ spl2_19 ),
inference(sat_conversion,[],[f258]) ).
cnf(s25,plain,
( ~ spl2_20
| ~ spl2_24
| spl2_25 ),
inference(sat_conversion,[],[f288]) ).
cnf(s26,plain,
spl2_24,
inference(sat_conversion,[],[f295]) ).
cnf(s27,plain,
( spl2_3
| ~ spl2_25 ),
inference(sat_conversion,[],[f297]) ).
cnf(s33,plain,
( spl2_3
| ~ spl2_11 ),
inference(sat_conversion,[],[f341]) ).
cnf(s34,plain,
( ~ spl2_4
| spl2_32
| spl2_33 ),
inference(sat_conversion,[],[f357]) ).
cnf(s36,plain,
( spl2_3
| ~ spl2_24
| ~ spl2_33 ),
inference(sat_conversion,[],[f397]) ).
cnf(s43,plain,
~ spl2_32,
inference(sat_conversion,[],[f409]) ).
cnf(s45,plain,
( ~ spl2_4
| spl2_33 ),
inference(rat,[],[s34,s43]) ).
cnf(s46,plain,
( ~ spl2_20
| spl2_25 ),
inference(rat,[],[s25,s26]) ).
cnf(s47,plain,
~ spl2_33,
inference(rat,[],[s36,s26,s19]) ).
cnf(s48,plain,
~ spl2_11,
inference(rat,[],[s33,s19]) ).
cnf(s49,plain,
~ spl2_25,
inference(rat,[],[s27,s19]) ).
cnf(s50,plain,
~ spl2_4,
inference(rat,[],[s45,s47]) ).
cnf(s51,plain,
~ spl2_20,
inference(rat,[],[s46,s49]) ).
cnf(s57,plain,
spl2_10,
inference(rat,[],[s7,s48]) ).
cnf(s60,plain,
( spl2_5
| ~ spl2_6 ),
inference(rat,[],[s3,s19]) ).
cnf(s61,plain,
~ spl2_5,
inference(rat,[],[s2,s50,s19]) ).
cnf(s62,plain,
~ spl2_6,
inference(rat,[],[s60,s61]) ).
cnf(s64,plain,
~ spl2_19,
inference(rat,[],[s21,s62]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s20,s51,s57,s64,s62]) ).
fof(f410,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n019.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 17:16:48 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.47 % (3284243)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3284261)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3545688558:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (3284255)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3284255)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1554947854:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3284261) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3284243-3284261"...
% 0.16/0.47 % (3284254)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3439724496_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3284258)dis+10_1_sil=32000:sp=arity:random_seed=1074966909:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3284256)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1462086187:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3284259)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3153230328:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3284260)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3022644526:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3284261)...printing done.
% 0.16/0.47 % (3284261)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3284261)------------------------------
% 0.16/0.47 % (3284261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3284261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3284261)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3284261)Termination reason: Refutation
% 0.16/0.47 % (3284261)Time elapsed: 0.008 s
% 0.16/0.47 % (3284261)Peak memory usage: 12 MB
% 0.16/0.47 % (3284261)Instructions burned: 17 (million)
% 0.16/0.47 % (3284243)Success in time 0.044 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------