%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT035+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Theorem 2.90s 1.35s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 53
% Syntax : Number of formulae : 387 ( 24 unt; 45 def)
% Number of atoms : 1232 ( 67 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1501 ( 656 ~; 731 |; 54 &)
% ( 49 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 54 ( 52 usr; 46 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 167 ( 0 sgn 155 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( ( greater(X0,X1)
& greater(X1,X2) )
=> greater(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( in_environment(X0,X1)
& in_environment(X0,X2) )
=> ( greater(X2,X1)
| X2 = X1
| greater(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_environment) ).
fof(f3,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f4,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f5,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(X1,equilibrium(X0)) )
=> ( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6) ).
fof(f6,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f7,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& greater_or_equal(X1,equilibrium(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f8,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> outcompetes(efficient_producers,first_movers,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t4) ).
fof(f9,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> outcompetes(efficient_producers,first_movers,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( greater(X2,X1)
| X2 = X1
| greater(X1,X2)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1,X2] :
( greater(X2,X1)
| X2 = X1
| greater(X1,X2)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X2) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) )
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,equilibrium(X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f17,plain,
! [X0,X1] :
( ( growth_rate(first_movers,X1) = zero
& growth_rate(efficient_producers,X1) = zero )
| ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( greater(growth_rate(efficient_producers,X1),zero)
& greater(zero,growth_rate(first_movers,X1)) )
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,equilibrium(X0)) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& greater_or_equal(X1,equilibrium(X0)) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& greater_or_equal(X1,equilibrium(X0)) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ outcompetes(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f23,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ outcompetes(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(nnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ( in_environment(X0,sK0(X0))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0)) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f19]) ).
fof(f29,plain,
! [X0] :
( ( in_environment(X0,sK1(X0))
& greater_or_equal(sK1(X0),equilibrium(X0)) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f21]) ).
fof(f30,plain,
( ! [X1] :
( ~ in_environment(sK2,X1)
| ( ~ outcompetes(efficient_producers,first_movers,sK3(X1))
& subpopulations(first_movers,efficient_producers,sK2,sK3(X1))
& greater_or_equal(sK3(X1),X1) ) )
& environment(sK2)
& stable(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X2,sK3(X1))],[f23]) ).
fof(f31,plain,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f32,plain,
! [X2,X0,X1] :
( greater(X2,X1)
| X1 = X2
| greater(X1,X2)
| ~ in_environment(X0,X1)
| ~ in_environment(X0,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f33,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3))
| outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X0,X1] :
( greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,equilibrium(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,equilibrium(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f47,plain,
! [X2,X0] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0] :
( in_environment(X0,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0] :
( greater_or_equal(sK1(X0),equilibrium(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0] :
( in_environment(X0,sK1(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
stable(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
environment(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
! [X1] :
( greater_or_equal(sK3(X1),X1)
| ~ in_environment(sK2,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK2,sK3(X1))
| ~ in_environment(sK2,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X1] :
( ~ outcompetes(efficient_producers,first_movers,sK3(X1))
| ~ in_environment(sK2,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
! [X2,X0,X1] :
( outcompetes(X0,X2,X1)
| ~ greater(zero,growth_rate(X2,X1))
| ~ greater_or_equal(growth_rate(X0,X1),zero)
| ~ subpopulations(X2,X0,sK2,X1) ),
inference(resolution,[],[f36,f52]) ).
fof(f58,plain,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sK3(X0)))
| ~ greater_or_equal(growth_rate(efficient_producers,sK3(X0)),zero)
| ~ subpopulations(first_movers,efficient_producers,sK2,sK3(X0))
| ~ in_environment(sK2,X0) ),
inference(resolution,[],[f57,f55]) ).
fof(f59,plain,
! [X0] :
( ~ greater_or_equal(growth_rate(efficient_producers,sK3(X0)),zero)
| ~ greater(zero,growth_rate(first_movers,sK3(X0)))
| ~ in_environment(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f58,f54]) ).
fof(f61,plain,
! [X0] :
( ~ in_environment(sK2,X0)
| ~ greater(zero,growth_rate(first_movers,sK3(X0)))
| ~ greater(growth_rate(efficient_producers,sK3(X0)),zero) ),
inference(resolution,[],[f59,f35]) ).
fof(f69,definition,
( spl4_1
<=> greater(growth_rate(efficient_producers,sK3(sK1(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f71,plain,
( ~ greater(growth_rate(efficient_producers,sK3(sK1(sK2))),zero)
| spl4_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f73,definition,
( spl4_2
<=> greater(zero,growth_rate(first_movers,sK3(sK1(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f75,plain,
( ~ greater(zero,growth_rate(first_movers,sK3(sK1(sK2))))
| spl4_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f78,definition,
( spl4_3
<=> greater(growth_rate(efficient_producers,sK3(sK0(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f80,plain,
( ~ greater(growth_rate(efficient_producers,sK3(sK0(sK2))),zero)
| spl4_3 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl4_4
<=> greater(zero,growth_rate(first_movers,sK3(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f84,plain,
( ~ greater(zero,growth_rate(first_movers,sK3(sK0(sK2))))
| spl4_4 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f95,definition,
( spl4_6
<=> zero = growth_rate(efficient_producers,sK3(sK1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f97,plain,
( zero = growth_rate(efficient_producers,sK3(sK1(sK2)))
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f103,definition,
( spl4_8
<=> greater(zero,growth_rate(efficient_producers,sK3(sK1(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f104,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK3(sK1(sK2))))
| spl4_8 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f108,definition,
( spl4_9
<=> ! [X0] :
( ~ environment(X0)
| ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2))) ) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0] :
( ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2))) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl4_10
<=> greater(growth_rate(first_movers,sK3(sK1(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f117,plain,
( ! [X0] :
( ~ greater(X0,growth_rate(first_movers,sK3(sK1(sK2))))
| ~ greater(zero,X0) )
| spl4_2 ),
inference(resolution,[],[f75,f31]) ).
fof(f125,definition,
( spl4_12
<=> zero = growth_rate(first_movers,sK3(sK1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
fof(f127,plain,
( zero = growth_rate(first_movers,sK3(sK1(sK2)))
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f144,definition,
( spl4_15
<=> zero = growth_rate(first_movers,sK3(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_15])],[avatar_definition]) ).
fof(f146,plain,
( zero = growth_rate(first_movers,sK3(sK0(sK2)))
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f152,definition,
( spl4_17
<=> greater(growth_rate(first_movers,sK3(sK0(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl4_17])],[avatar_definition]) ).
fof(f154,plain,
( greater(growth_rate(first_movers,sK3(sK0(sK2))),zero)
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f157,definition,
( spl4_18
<=> ! [X0] :
( ~ environment(X0)
| ~ greater_or_equal(sK3(sK0(sK2)),equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2))) ) ),
introduced(definition,[new_symbols(definition,[spl4_18])],[avatar_definition]) ).
fof(f158,plain,
( ! [X0] :
( ~ greater_or_equal(sK3(sK0(sK2)),equilibrium(X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2))) )
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,definition,
( spl4_19
<=> zero = growth_rate(efficient_producers,sK3(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_19])],[avatar_definition]) ).
fof(f162,plain,
( zero = growth_rate(efficient_producers,sK3(sK0(sK2)))
| ~ spl4_19 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f174,plain,
( ! [X0] :
( ~ greater(zero,growth_rate(efficient_producers,sK3(sK1(sK2))))
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_2 ),
inference(resolution,[],[f117,f47]) ).
fof(f176,definition,
( spl4_20
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(sK3(sK1(sK2)),sK0(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl4_20])],[avatar_definition]) ).
fof(f177,plain,
( ! [X0] :
( ~ greater_or_equal(sK3(sK1(sK2)),sK0(X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2))) )
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f178,plain,
( spl4_20
| ~ spl4_8
| spl4_2 ),
inference(avatar_split_clause,[],[f174,f73,f103,f176]) ).
fof(f190,plain,
( ! [X0] :
( zero = growth_rate(efficient_producers,sK3(sK1(sK2)))
| greater(zero,growth_rate(first_movers,sK3(sK1(sK2))))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(X0)) )
| spl4_8 ),
inference(resolution,[],[f104,f39]) ).
fof(f200,plain,
( ! [X0] :
( zero = growth_rate(efficient_producers,sK3(sK1(sK2)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(X0)) )
| spl4_2
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f190,f75]) ).
fof(f202,plain,
( spl4_9
| spl4_6
| spl4_2
| spl4_8 ),
inference(avatar_split_clause,[],[f200,f103,f73,f95,f108]) ).
fof(f215,definition,
( spl4_24
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl4_24])],[avatar_definition]) ).
fof(f216,plain,
( ! [X0] :
( ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ environment(X0)
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0)) )
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,definition,
( spl4_25
<=> greater(zero,growth_rate(efficient_producers,sK3(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl4_25])],[avatar_definition]) ).
fof(f219,plain,
( greater(zero,growth_rate(efficient_producers,sK3(sK0(sK2))))
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f220,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK3(sK0(sK2))))
| spl4_25 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f232,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ environment(X0)
| ~ greater(sK3(sK1(sK2)),equilibrium(X0)) )
| ~ spl4_9 ),
inference(resolution,[],[f109,f35]) ).
fof(f238,plain,
( ! [X0] :
( zero = growth_rate(efficient_producers,sK3(sK0(sK2)))
| greater(zero,growth_rate(first_movers,sK3(sK0(sK2))))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),equilibrium(X0)) )
| spl4_25 ),
inference(resolution,[],[f220,f39]) ).
fof(f252,plain,
( ! [X0] :
( zero = growth_rate(efficient_producers,sK3(sK0(sK2)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),equilibrium(X0)) )
| spl4_4
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f238,f84]) ).
fof(f256,plain,
( spl4_18
| spl4_19
| spl4_4
| spl4_25 ),
inference(avatar_split_clause,[],[f252,f218,f82,f160,f157]) ).
fof(f273,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ environment(X0)
| ~ greater(sK3(sK0(sK2)),equilibrium(X0)) )
| ~ spl4_18 ),
inference(resolution,[],[f158,f35]) ).
fof(f348,plain,
( ~ environment(sK2)
| ~ greater(sK3(sK1(sK2)),equilibrium(sK2))
| ~ in_environment(sK2,sK1(sK2))
| ~ spl4_9 ),
inference(resolution,[],[f232,f54]) ).
fof(f349,plain,
( ~ greater(sK3(sK1(sK2)),equilibrium(sK2))
| ~ in_environment(sK2,sK1(sK2))
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f348,f52]) ).
fof(f351,definition,
( spl4_28
<=> in_environment(sK2,sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_28])],[avatar_definition]) ).
fof(f352,plain,
( in_environment(sK2,sK1(sK2))
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f353,plain,
( ~ in_environment(sK2,sK1(sK2))
| spl4_28 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f355,definition,
( spl4_29
<=> greater(sK3(sK1(sK2)),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_29])],[avatar_definition]) ).
fof(f356,plain,
( greater(sK3(sK1(sK2)),equilibrium(sK2))
| ~ spl4_29 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f357,plain,
( ~ greater(sK3(sK1(sK2)),equilibrium(sK2))
| spl4_29 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f359,plain,
( ~ environment(sK2)
| ~ stable(sK2)
| spl4_28 ),
inference(resolution,[],[f353,f50]) ).
fof(f360,plain,
( ~ stable(sK2)
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f359,f52]) ).
fof(f361,plain,
( $false
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f360,f51]) ).
fof(f362,plain,
spl4_28,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f366,definition,
( spl4_30
<=> in_environment(sK2,sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_30])],[avatar_definition]) ).
fof(f367,plain,
( in_environment(sK2,sK0(sK2))
| ~ spl4_30 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f368,plain,
( ~ in_environment(sK2,sK0(sK2))
| spl4_30 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f370,definition,
( spl4_31
<=> greater(sK3(sK0(sK2)),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_31])],[avatar_definition]) ).
fof(f372,plain,
( ~ greater(sK3(sK0(sK2)),equilibrium(sK2))
| spl4_31 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f374,plain,
( ~ greater(zero,growth_rate(first_movers,sK3(sK1(sK2))))
| ~ greater(growth_rate(efficient_producers,sK3(sK1(sK2))),zero)
| ~ spl4_28 ),
inference(resolution,[],[f352,f61]) ).
fof(f391,plain,
( ~ environment(sK2)
| ~ stable(sK2)
| spl4_30 ),
inference(resolution,[],[f368,f48]) ).
fof(f392,plain,
( ~ stable(sK2)
| spl4_30 ),
inference(forward_subsumption_resolution,[],[f391,f52]) ).
fof(f393,plain,
( $false
| spl4_30 ),
inference(forward_subsumption_resolution,[],[f392,f51]) ).
fof(f394,plain,
spl4_30,
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f411,plain,
( ~ greater(zero,growth_rate(first_movers,sK3(sK0(sK2))))
| ~ greater(growth_rate(efficient_producers,sK3(sK0(sK2))),zero)
| ~ spl4_30 ),
inference(resolution,[],[f367,f61]) ).
fof(f417,definition,
( spl4_38
<=> greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_38])],[avatar_definition]) ).
fof(f418,plain,
( greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2))
| ~ spl4_38 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f419,plain,
( ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2))
| spl4_38 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f421,definition,
( spl4_39
<=> sK3(sK1(sK2)) = equilibrium(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_39])],[avatar_definition]) ).
fof(f422,plain,
( sK3(sK1(sK2)) != equilibrium(sK2)
| spl4_39 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f423,plain,
( sK3(sK1(sK2)) = equilibrium(sK2)
| ~ spl4_39 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f455,plain,
( ~ spl4_3
| ~ spl4_4
| ~ spl4_30 ),
inference(avatar_split_clause,[],[f411,f366,f82,f78]) ).
fof(f458,plain,
( ! [X0] :
( ~ greater(growth_rate(efficient_producers,sK3(sK0(sK2))),X0)
| ~ greater(X0,zero) )
| spl4_3 ),
inference(resolution,[],[f80,f31]) ).
fof(f489,plain,
( ! [X0] :
( ~ greater(growth_rate(first_movers,sK3(sK0(sK2))),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_3 ),
inference(resolution,[],[f458,f47]) ).
fof(f495,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_3
| ~ spl4_17 ),
inference(forward_subsumption_resolution,[],[f489,f154]) ).
fof(f496,plain,
( spl4_24
| spl4_3
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f495,f152,f78,f215]) ).
fof(f500,plain,
( ! [X0] :
( ~ greater(X0,growth_rate(first_movers,sK3(sK0(sK2))))
| ~ greater(zero,X0) )
| spl4_4 ),
inference(resolution,[],[f84,f31]) ).
fof(f509,plain,
( ! [X0] :
( ~ greater(zero,growth_rate(efficient_producers,sK3(sK0(sK2))))
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_4 ),
inference(resolution,[],[f500,f47]) ).
fof(f513,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_4
| ~ spl4_25 ),
inference(forward_subsumption_resolution,[],[f509,f219]) ).
fof(f514,plain,
( spl4_24
| spl4_4
| ~ spl4_25 ),
inference(avatar_split_clause,[],[f513,f218,f82,f215]) ).
fof(f541,plain,
( ! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater(sK3(sK1(sK2)),sK0(X0)) )
| ~ spl4_20 ),
inference(resolution,[],[f177,f35]) ).
fof(f555,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK0(sK2)))
| ~ environment(sK2)
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(sK2))
| ~ spl4_24 ),
inference(resolution,[],[f216,f51]) ).
fof(f556,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(sK2))
| ~ spl4_24 ),
inference(forward_subsumption_resolution,[],[f555,f52]) ).
fof(f558,definition,
( spl4_53
<=> greater_or_equal(sK3(sK0(sK2)),sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_53])],[avatar_definition]) ).
fof(f560,plain,
( ~ greater_or_equal(sK3(sK0(sK2)),sK0(sK2))
| spl4_53 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f562,definition,
( spl4_54
<=> subpopulations(first_movers,efficient_producers,sK2,sK3(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_54])],[avatar_definition]) ).
fof(f563,plain,
( subpopulations(first_movers,efficient_producers,sK2,sK3(sK0(sK2)))
| ~ spl4_54 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f564,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK0(sK2)))
| spl4_54 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f565,plain,
( ~ spl4_53
| ~ spl4_54
| ~ spl4_24 ),
inference(avatar_split_clause,[],[f556,f215,f562,f558]) ).
fof(f566,plain,
( ~ in_environment(sK2,sK0(sK2))
| spl4_53 ),
inference(resolution,[],[f560,f53]) ).
fof(f568,plain,
( $false
| ~ spl4_30
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f566,f367]) ).
fof(f569,plain,
( ~ spl4_30
| spl4_53 ),
inference(avatar_contradiction_clause,[],[f568]) ).
fof(f574,plain,
( ~ in_environment(sK2,sK0(sK2))
| spl4_54 ),
inference(resolution,[],[f564,f54]) ).
fof(f575,plain,
( $false
| ~ spl4_30
| spl4_54 ),
inference(forward_subsumption_resolution,[],[f574,f367]) ).
fof(f576,plain,
( ~ spl4_30
| spl4_54 ),
inference(avatar_contradiction_clause,[],[f575]) ).
fof(f577,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK3(sK0(sK2))),zero)
| zero = growth_rate(first_movers,sK3(sK0(sK2)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),equilibrium(X0)) )
| spl4_3 ),
inference(resolution,[],[f80,f46]) ).
fof(f584,plain,
( spl4_18
| spl4_15
| spl4_17
| spl4_3 ),
inference(avatar_split_clause,[],[f577,f78,f152,f144,f157]) ).
fof(f587,plain,
( ! [X0] :
( ~ greater(sK3(sK0(sK2)),X0)
| ~ greater(X0,equilibrium(sK2)) )
| spl4_31 ),
inference(resolution,[],[f372,f31]) ).
fof(f813,plain,
( ! [X0] :
( ~ greater_or_equal(sK3(sK0(sK2)),X0)
| sK3(sK0(sK2)) = X0
| ~ greater(X0,equilibrium(sK2)) )
| spl4_31 ),
inference(resolution,[],[f587,f33]) ).
fof(f828,plain,
( ~ environment(sK2)
| ~ greater(sK3(sK0(sK2)),equilibrium(sK2))
| ~ spl4_18
| ~ spl4_54 ),
inference(resolution,[],[f273,f563]) ).
fof(f873,plain,
( sK0(sK2) = sK3(sK0(sK2))
| ~ greater(sK0(sK2),equilibrium(sK2))
| ~ in_environment(sK2,sK0(sK2))
| spl4_31 ),
inference(resolution,[],[f813,f53]) ).
fof(f878,definition,
( spl4_69
<=> greater(sK0(sK2),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_69])],[avatar_definition]) ).
fof(f880,plain,
( ~ greater(sK0(sK2),equilibrium(sK2))
| spl4_69 ),
inference(avatar_component_clause,[],[f878]) ).
fof(f882,definition,
( spl4_70
<=> sK0(sK2) = sK3(sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_70])],[avatar_definition]) ).
fof(f884,plain,
( sK0(sK2) = sK3(sK0(sK2))
| ~ spl4_70 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f886,plain,
( sK0(sK2) = sK3(sK0(sK2))
| ~ greater(sK0(sK2),equilibrium(sK2))
| ~ spl4_30
| spl4_31 ),
inference(forward_subsumption_resolution,[],[f873,f367]) ).
fof(f887,plain,
( ~ spl4_69
| spl4_70
| ~ spl4_30
| spl4_31 ),
inference(avatar_split_clause,[],[f886,f370,f366,f882,f878]) ).
fof(f888,plain,
( ~ environment(sK2)
| ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ greater(sK3(sK1(sK2)),sK0(sK2))
| ~ spl4_20 ),
inference(resolution,[],[f541,f51]) ).
fof(f889,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ greater(sK3(sK1(sK2)),sK0(sK2))
| ~ spl4_20 ),
inference(forward_subsumption_resolution,[],[f888,f52]) ).
fof(f891,definition,
( spl4_71
<=> greater(sK3(sK1(sK2)),sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_71])],[avatar_definition]) ).
fof(f893,plain,
( ~ greater(sK3(sK1(sK2)),sK0(sK2))
| spl4_71 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f895,definition,
( spl4_72
<=> subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_72])],[avatar_definition]) ).
fof(f896,plain,
( subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ spl4_72 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f897,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| spl4_72 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f899,plain,
( ! [X0] :
( ~ greater(sK0(sK2),X0)
| ~ greater(X0,equilibrium(sK2)) )
| spl4_69 ),
inference(resolution,[],[f880,f31]) ).
fof(f903,definition,
( spl4_73
<=> greater_or_equal(sK0(sK2),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_73])],[avatar_definition]) ).
fof(f907,definition,
( spl4_74
<=> sK0(sK2) = equilibrium(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_74])],[avatar_definition]) ).
fof(f909,plain,
( sK0(sK2) = equilibrium(sK2)
| ~ spl4_74 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f912,definition,
( spl4_75
<=> ! [X0] :
( ~ in_environment(X0,equilibrium(sK2))
| ~ in_environment(X0,sK0(sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl4_75])],[avatar_definition]) ).
fof(f913,plain,
( ! [X0] :
( ~ in_environment(X0,equilibrium(sK2))
| ~ in_environment(X0,sK0(sK2)) )
| ~ spl4_75 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f915,definition,
( spl4_76
<=> greater(equilibrium(sK2),sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_76])],[avatar_definition]) ).
fof(f954,plain,
( ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2))
| ~ stable(sK2)
| ~ environment(sK2)
| ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ spl4_20
| ~ spl4_74 ),
inference(superposition,[],[f177,f909]) ).
fof(f957,plain,
( ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2))
| ~ environment(sK2)
| ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ spl4_20
| ~ spl4_74 ),
inference(forward_subsumption_resolution,[],[f954,f51]) ).
fof(f959,plain,
( ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2))
| ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ spl4_20
| ~ spl4_74 ),
inference(forward_subsumption_resolution,[],[f957,f52]) ).
fof(f960,plain,
( ~ spl4_72
| ~ spl4_38
| ~ spl4_20
| ~ spl4_74 ),
inference(avatar_split_clause,[],[f959,f907,f176,f417,f895]) ).
fof(f999,plain,
( ~ greater(sK3(sK1(sK2)),equilibrium(sK2))
| spl4_71
| ~ spl4_74 ),
inference(forward_demodulation,[],[f893,f909]) ).
fof(f1000,plain,
( $false
| ~ spl4_29
| spl4_71
| ~ spl4_74 ),
inference(forward_subsumption_resolution,[],[f999,f356]) ).
fof(f1001,plain,
( ~ spl4_29
| spl4_71
| ~ spl4_74 ),
inference(avatar_contradiction_clause,[],[f1000]) ).
fof(f1010,definition,
( spl4_81
<=> greater_or_equal(sK3(equilibrium(sK2)),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_81])],[avatar_definition]) ).
fof(f1012,plain,
( ~ greater_or_equal(sK3(equilibrium(sK2)),equilibrium(sK2))
| spl4_81 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1028,plain,
( ~ in_environment(sK2,sK1(sK2))
| spl4_72 ),
inference(resolution,[],[f897,f54]) ).
fof(f1029,plain,
( $false
| ~ spl4_28
| spl4_72 ),
inference(forward_subsumption_resolution,[],[f1028,f352]) ).
fof(f1030,plain,
( ~ spl4_28
| spl4_72 ),
inference(avatar_contradiction_clause,[],[f1029]) ).
fof(f1036,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f374,f351,f73,f69]) ).
fof(f1106,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK3(sK1(sK2))),zero)
| zero = growth_rate(first_movers,sK3(sK1(sK2)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(X0)) )
| spl4_1 ),
inference(resolution,[],[f71,f46]) ).
fof(f1108,plain,
( ! [X0] :
( ~ greater(growth_rate(efficient_producers,sK3(sK1(sK2))),X0)
| ~ greater(X0,zero) )
| spl4_1 ),
inference(resolution,[],[f71,f31]) ).
fof(f1159,plain,
( ! [X0] :
( greater(growth_rate(efficient_producers,sK3(sK0(sK2))),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl4_15 ),
inference(superposition,[],[f47,f146]) ).
fof(f1164,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_3
| ~ spl4_15 ),
inference(forward_subsumption_resolution,[],[f1159,f80]) ).
fof(f1172,plain,
( spl4_24
| spl4_3
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f1164,f144,f78,f215]) ).
fof(f1220,plain,
( ! [X0] :
( ~ greater(growth_rate(first_movers,sK3(sK1(sK2))),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_1 ),
inference(resolution,[],[f1108,f47]) ).
fof(f1228,plain,
( ~ greater(sK3(sK1(sK2)),equilibrium(sK2))
| ~ spl4_9
| ~ spl4_28 ),
inference(forward_subsumption_resolution,[],[f349,f352]) ).
fof(f1230,plain,
( spl4_9
| spl4_12
| spl4_10
| spl4_1 ),
inference(avatar_split_clause,[],[f1106,f69,f111,f125,f108]) ).
fof(f1233,plain,
( spl4_20
| ~ spl4_10
| spl4_1 ),
inference(avatar_split_clause,[],[f1220,f69,f111,f176]) ).
fof(f1234,plain,
( ~ spl4_29
| ~ spl4_9
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f1228,f351,f108,f355]) ).
fof(f1246,plain,
( ~ environment(sK2)
| ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ spl4_9
| ~ spl4_38 ),
inference(resolution,[],[f109,f418]) ).
fof(f1248,plain,
( ~ subpopulations(first_movers,efficient_producers,sK2,sK3(sK1(sK2)))
| ~ spl4_9
| ~ spl4_38 ),
inference(forward_subsumption_resolution,[],[f1246,f52]) ).
fof(f1249,plain,
( ~ spl4_72
| ~ spl4_9
| ~ spl4_38 ),
inference(avatar_split_clause,[],[f1248,f417,f108,f895]) ).
fof(f1304,plain,
( ~ greater(equilibrium(sK2),sK0(sK2))
| ~ spl4_39
| spl4_71 ),
inference(forward_demodulation,[],[f893,f423]) ).
fof(f1313,plain,
( ~ spl4_76
| ~ spl4_39
| spl4_71 ),
inference(avatar_split_clause,[],[f1304,f891,f421,f915]) ).
fof(f1331,plain,
( ! [X0] :
( ~ greater(sK3(sK1(sK2)),X0)
| ~ greater(X0,sK0(sK2)) )
| spl4_71 ),
inference(resolution,[],[f893,f31]) ).
fof(f1339,definition,
( spl4_95
<=> sK0(sK2) = sK3(sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_95])],[avatar_definition]) ).
fof(f1341,plain,
( sK0(sK2) = sK3(sK1(sK2))
| ~ spl4_95 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f1344,definition,
( spl4_96
<=> ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ in_environment(X0,sK3(sK1(sK2))) ) ),
introduced(definition,[new_symbols(definition,[spl4_96])],[avatar_definition]) ).
fof(f1345,plain,
( ! [X0] :
( ~ in_environment(X0,sK3(sK1(sK2)))
| ~ in_environment(X0,sK0(sK2)) )
| ~ spl4_96 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f1347,definition,
( spl4_97
<=> greater(sK0(sK2),sK3(sK1(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_97])],[avatar_definition]) ).
fof(f1348,plain,
( ~ greater(sK0(sK2),sK3(sK1(sK2)))
| spl4_97 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f1349,plain,
( greater(sK0(sK2),sK3(sK1(sK2)))
| ~ spl4_97 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f1406,plain,
( ~ in_environment(sK2,equilibrium(sK2))
| spl4_81 ),
inference(resolution,[],[f1012,f53]) ).
fof(f1428,plain,
( ~ greater(sK3(sK1(sK2)),equilibrium(sK2))
| spl4_69
| ~ spl4_97 ),
inference(resolution,[],[f899,f1349]) ).
fof(f1431,plain,
( ! [X0] :
( ~ greater_or_equal(sK0(sK2),X0)
| sK0(sK2) = X0
| ~ greater(X0,equilibrium(sK2)) )
| spl4_69 ),
inference(resolution,[],[f899,f33]) ).
fof(f1434,plain,
( ~ spl4_29
| spl4_69
| ~ spl4_97 ),
inference(avatar_split_clause,[],[f1428,f1347,f878,f355]) ).
fof(f1435,plain,
( ! [X0] :
( ~ greater(sK3(sK1(sK2)),X0)
| ~ greater(X0,equilibrium(sK2)) )
| spl4_29 ),
inference(resolution,[],[f357,f31]) ).
fof(f1437,plain,
( sK3(sK1(sK2)) = equilibrium(sK2)
| ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2))
| spl4_29 ),
inference(resolution,[],[f357,f33]) ).
fof(f1438,plain,
( ~ greater_or_equal(sK3(sK1(sK2)),equilibrium(sK2))
| spl4_29
| spl4_39 ),
inference(forward_subsumption_resolution,[],[f1437,f422]) ).
fof(f1440,plain,
( ~ spl4_38
| spl4_29
| spl4_39 ),
inference(avatar_split_clause,[],[f1438,f421,f355,f417]) ).
fof(f1445,plain,
( ! [X0] :
( ~ greater_or_equal(sK3(sK1(sK2)),X0)
| sK3(sK1(sK2)) = X0
| ~ greater(X0,equilibrium(sK2)) )
| spl4_29 ),
inference(resolution,[],[f1435,f33]) ).
fof(f1448,plain,
( ! [X0] :
( ~ greater(X0,sK0(sK2))
| sK3(sK1(sK2)) = X0
| ~ greater_or_equal(sK3(sK1(sK2)),X0) )
| spl4_71 ),
inference(resolution,[],[f1331,f33]) ).
fof(f1558,plain,
( ~ greater(sK0(sK2),equilibrium(sK2))
| spl4_31
| ~ spl4_70 ),
inference(superposition,[],[f372,f884]) ).
fof(f1694,plain,
( sK1(sK2) = sK3(sK1(sK2))
| ~ greater(sK1(sK2),equilibrium(sK2))
| ~ in_environment(sK2,sK1(sK2))
| spl4_29 ),
inference(resolution,[],[f1445,f53]) ).
fof(f1697,plain,
( sK1(sK2) = sK3(sK1(sK2))
| ~ greater(sK1(sK2),equilibrium(sK2))
| ~ spl4_28
| spl4_29 ),
inference(forward_subsumption_resolution,[],[f1694,f352]) ).
fof(f1699,definition,
( spl4_110
<=> greater(sK1(sK2),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_110])],[avatar_definition]) ).
fof(f1700,plain,
( greater(sK1(sK2),equilibrium(sK2))
| ~ spl4_110 ),
inference(avatar_component_clause,[],[f1699]) ).
fof(f1701,plain,
( ~ greater(sK1(sK2),equilibrium(sK2))
| spl4_110 ),
inference(avatar_component_clause,[],[f1699]) ).
fof(f1703,definition,
( spl4_111
<=> sK1(sK2) = sK3(sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_111])],[avatar_definition]) ).
fof(f1704,plain,
( sK1(sK2) != sK3(sK1(sK2))
| spl4_111 ),
inference(avatar_component_clause,[],[f1703]) ).
fof(f1705,plain,
( sK1(sK2) = sK3(sK1(sK2))
| ~ spl4_111 ),
inference(avatar_component_clause,[],[f1703]) ).
fof(f1706,plain,
( ~ spl4_110
| spl4_111
| ~ spl4_28
| spl4_29 ),
inference(avatar_split_clause,[],[f1697,f355,f351,f1703,f1699]) ).
fof(f1711,definition,
( spl4_112
<=> greater_or_equal(sK1(sK2),equilibrium(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_112])],[avatar_definition]) ).
fof(f1712,plain,
( greater_or_equal(sK1(sK2),equilibrium(sK2))
| ~ spl4_112 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f1713,plain,
( ~ greater_or_equal(sK1(sK2),equilibrium(sK2))
| spl4_112 ),
inference(avatar_component_clause,[],[f1711]) ).
fof(f1715,definition,
( spl4_113
<=> sK1(sK2) = equilibrium(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_113])],[avatar_definition]) ).
fof(f1717,plain,
( sK1(sK2) = equilibrium(sK2)
| ~ spl4_113 ),
inference(avatar_component_clause,[],[f1715]) ).
fof(f1728,plain,
( ~ environment(sK2)
| ~ stable(sK2)
| spl4_112 ),
inference(resolution,[],[f1713,f49]) ).
fof(f1730,plain,
( ~ stable(sK2)
| spl4_112 ),
inference(forward_subsumption_resolution,[],[f1728,f52]) ).
fof(f1731,plain,
( $false
| spl4_112 ),
inference(forward_subsumption_resolution,[],[f1730,f51]) ).
fof(f1732,plain,
spl4_112,
inference(avatar_contradiction_clause,[],[f1731]) ).
fof(f1773,plain,
( ~ greater(sK1(sK2),equilibrium(sK2))
| spl4_29
| ~ spl4_111 ),
inference(superposition,[],[f357,f1705]) ).
fof(f1775,plain,
( ~ greater_or_equal(sK1(sK2),equilibrium(sK2))
| spl4_38
| ~ spl4_111 ),
inference(superposition,[],[f419,f1705]) ).
fof(f1812,plain,
( $false
| spl4_38
| ~ spl4_111
| ~ spl4_112 ),
inference(forward_subsumption_resolution,[],[f1775,f1712]) ).
fof(f1813,plain,
( spl4_38
| ~ spl4_111
| ~ spl4_112 ),
inference(avatar_contradiction_clause,[],[f1812]) ).
fof(f1814,plain,
( $false
| spl4_29
| ~ spl4_110
| ~ spl4_111 ),
inference(forward_subsumption_resolution,[],[f1773,f1700]) ).
fof(f1815,plain,
( spl4_29
| ~ spl4_110
| ~ spl4_111 ),
inference(avatar_contradiction_clause,[],[f1814]) ).
fof(f1832,plain,
( ! [X0] :
( ~ in_environment(X0,sK1(sK2))
| ~ in_environment(X0,sK0(sK2)) )
| ~ spl4_96
| ~ spl4_111 ),
inference(forward_demodulation,[],[f1345,f1705]) ).
fof(f1839,definition,
( spl4_123
<=> greater_or_equal(sK0(sK2),sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_123])],[avatar_definition]) ).
fof(f1840,plain,
( greater_or_equal(sK0(sK2),sK1(sK2))
| ~ spl4_123 ),
inference(avatar_component_clause,[],[f1839]) ).
fof(f1841,plain,
( ~ greater_or_equal(sK0(sK2),sK1(sK2))
| spl4_123 ),
inference(avatar_component_clause,[],[f1839]) ).
fof(f1843,definition,
( spl4_124
<=> sK0(sK2) = sK1(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_124])],[avatar_definition]) ).
fof(f1844,plain,
( sK0(sK2) != sK1(sK2)
| spl4_124 ),
inference(avatar_component_clause,[],[f1843]) ).
fof(f1845,plain,
( sK0(sK2) = sK1(sK2)
| ~ spl4_124 ),
inference(avatar_component_clause,[],[f1843]) ).
fof(f1848,definition,
( spl4_125
<=> ! [X0] :
( ~ in_environment(X0,sK1(sK2))
| ~ in_environment(X0,sK0(sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl4_125])],[avatar_definition]) ).
fof(f1849,plain,
( ! [X0] :
( ~ in_environment(X0,sK1(sK2))
| ~ in_environment(X0,sK0(sK2)) )
| ~ spl4_125 ),
inference(avatar_component_clause,[],[f1848]) ).
fof(f1851,definition,
( spl4_126
<=> greater(sK1(sK2),sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_126])],[avatar_definition]) ).
fof(f1852,plain,
( ~ greater(sK1(sK2),sK0(sK2))
| spl4_126 ),
inference(avatar_component_clause,[],[f1851]) ).
fof(f1853,plain,
( greater(sK1(sK2),sK0(sK2))
| ~ spl4_126 ),
inference(avatar_component_clause,[],[f1851]) ).
fof(f1868,plain,
( ! [X0] :
( sK0(sK2) = sK3(sK1(sK2))
| greater(sK3(sK1(sK2)),sK0(sK2))
| ~ in_environment(X0,sK3(sK1(sK2)))
| ~ in_environment(X0,sK0(sK2)) )
| spl4_97 ),
inference(resolution,[],[f1348,f32]) ).
fof(f1875,plain,
( ! [X0] :
( sK0(sK2) = sK3(sK1(sK2))
| ~ in_environment(X0,sK3(sK1(sK2)))
| ~ in_environment(X0,sK0(sK2)) )
| spl4_71
| spl4_97 ),
inference(forward_subsumption_resolution,[],[f1868,f893]) ).
fof(f1876,plain,
( spl4_96
| spl4_95
| spl4_71
| spl4_97 ),
inference(avatar_split_clause,[],[f1875,f1347,f891,f1339,f1344]) ).
fof(f2162,plain,
( sK1(sK2) = sK3(sK1(sK2))
| ~ greater_or_equal(sK3(sK1(sK2)),sK1(sK2))
| spl4_71
| ~ spl4_126 ),
inference(resolution,[],[f1853,f1448]) ).
fof(f2163,plain,
( ~ greater_or_equal(sK3(sK1(sK2)),sK1(sK2))
| spl4_71
| spl4_111
| ~ spl4_126 ),
inference(forward_subsumption_resolution,[],[f2162,f1704]) ).
fof(f2164,plain,
( ~ in_environment(sK2,sK1(sK2))
| spl4_71
| spl4_111
| ~ spl4_126 ),
inference(resolution,[],[f2163,f53]) ).
fof(f2166,plain,
( $false
| ~ spl4_28
| spl4_71
| spl4_111
| ~ spl4_126 ),
inference(forward_subsumption_resolution,[],[f2164,f352]) ).
fof(f2167,plain,
( ~ spl4_28
| spl4_71
| spl4_111
| ~ spl4_126 ),
inference(avatar_contradiction_clause,[],[f2166]) ).
fof(f2178,plain,
( spl4_125
| ~ spl4_96
| ~ spl4_111 ),
inference(avatar_split_clause,[],[f1832,f1703,f1344,f1848]) ).
fof(f2192,plain,
( ~ greater(sK0(sK2),sK1(sK2))
| spl4_123 ),
inference(resolution,[],[f1841,f35]) ).
fof(f2203,plain,
( greater(sK3(sK0(sK2)),equilibrium(sK2))
| ~ spl4_29
| ~ spl4_124 ),
inference(superposition,[],[f356,f1845]) ).
fof(f2271,plain,
( $false
| ~ spl4_29
| spl4_31
| ~ spl4_124 ),
inference(forward_subsumption_resolution,[],[f2203,f372]) ).
fof(f2272,plain,
( ~ spl4_29
| spl4_31
| ~ spl4_124 ),
inference(avatar_contradiction_clause,[],[f2271]) ).
fof(f2398,plain,
( ~ in_environment(sK2,sK0(sK2))
| ~ environment(sK2)
| ~ stable(sK2)
| ~ spl4_125 ),
inference(resolution,[],[f1849,f50]) ).
fof(f2402,plain,
( ~ environment(sK2)
| ~ stable(sK2)
| ~ spl4_125 ),
inference(forward_subsumption_resolution,[],[f2398,f48]) ).
fof(f2403,plain,
( ~ stable(sK2)
| ~ spl4_125 ),
inference(forward_subsumption_resolution,[],[f2402,f52]) ).
fof(f2404,plain,
( $false
| ~ spl4_125 ),
inference(forward_subsumption_resolution,[],[f2403,f51]) ).
fof(f2405,plain,
~ spl4_125,
inference(avatar_contradiction_clause,[],[f2404]) ).
fof(f2407,definition,
( spl4_146
<=> greater(sK0(sK2),sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_146])],[avatar_definition]) ).
fof(f2411,plain,
( ~ spl4_146
| spl4_123 ),
inference(avatar_split_clause,[],[f2192,f1839,f2407]) ).
fof(f2421,plain,
( greater(sK0(sK2),equilibrium(sK2))
| ~ spl4_29
| ~ spl4_95 ),
inference(superposition,[],[f356,f1341]) ).
fof(f2466,plain,
( $false
| ~ spl4_29
| spl4_69
| ~ spl4_95 ),
inference(forward_subsumption_resolution,[],[f2421,f880]) ).
fof(f2467,plain,
( ~ spl4_29
| spl4_69
| ~ spl4_95 ),
inference(avatar_contradiction_clause,[],[f2466]) ).
fof(f2475,plain,
( sK0(sK2) = sK1(sK2)
| ~ greater(sK1(sK2),equilibrium(sK2))
| spl4_69
| ~ spl4_123 ),
inference(resolution,[],[f1840,f1431]) ).
fof(f2476,plain,
( ~ greater(sK1(sK2),equilibrium(sK2))
| spl4_69
| ~ spl4_123
| spl4_124 ),
inference(forward_subsumption_resolution,[],[f2475,f1844]) ).
fof(f2554,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK3(sK0(sK2))))
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl4_19 ),
inference(superposition,[],[f47,f162]) ).
fof(f2559,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK0(sK2)))
| ~ greater_or_equal(sK3(sK0(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_4
| ~ spl4_19 ),
inference(forward_subsumption_resolution,[],[f2554,f84]) ).
fof(f2563,plain,
( spl4_24
| spl4_4
| ~ spl4_19 ),
inference(avatar_split_clause,[],[f2559,f160,f82,f215]) ).
fof(f2566,plain,
( ~ greater(sK3(sK0(sK2)),equilibrium(sK2))
| ~ spl4_18
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f828,f52]) ).
fof(f2595,plain,
( ~ spl4_31
| ~ spl4_18
| ~ spl4_54 ),
inference(avatar_split_clause,[],[f2566,f562,f157,f370]) ).
fof(f2599,plain,
( ~ spl4_69
| spl4_31
| ~ spl4_70 ),
inference(avatar_split_clause,[],[f1558,f882,f370,f878]) ).
fof(f2601,plain,
( ! [X0] :
( sK0(sK2) = equilibrium(sK2)
| greater(equilibrium(sK2),sK0(sK2))
| ~ in_environment(X0,equilibrium(sK2))
| ~ in_environment(X0,sK0(sK2)) )
| spl4_69 ),
inference(resolution,[],[f880,f32]) ).
fof(f2602,plain,
( sK0(sK2) = equilibrium(sK2)
| ~ greater_or_equal(sK0(sK2),equilibrium(sK2))
| spl4_69 ),
inference(resolution,[],[f880,f33]) ).
fof(f2627,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK3(sK1(sK2))))
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl4_6 ),
inference(superposition,[],[f47,f97]) ).
fof(f2656,plain,
( spl4_20
| spl4_2
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f2627,f95,f73,f176]) ).
fof(f2671,plain,
( ~ greater(sK3(sK1(sK2)),sK0(sK2))
| ~ spl4_20
| ~ spl4_72 ),
inference(forward_subsumption_resolution,[],[f889,f896]) ).
fof(f2674,plain,
( ~ spl4_110
| spl4_69
| ~ spl4_123
| spl4_124 ),
inference(avatar_split_clause,[],[f2476,f1843,f1839,f878,f1699]) ).
fof(f2680,plain,
( ~ spl4_71
| ~ spl4_20
| ~ spl4_72 ),
inference(avatar_split_clause,[],[f2671,f895,f176,f891]) ).
fof(f2684,plain,
( sK1(sK2) = equilibrium(sK2)
| ~ greater_or_equal(sK1(sK2),equilibrium(sK2))
| spl4_110 ),
inference(resolution,[],[f1701,f33]) ).
fof(f2685,plain,
( sK1(sK2) = equilibrium(sK2)
| spl4_110
| ~ spl4_112 ),
inference(forward_subsumption_resolution,[],[f2684,f1712]) ).
fof(f2686,plain,
( spl4_113
| spl4_110
| ~ spl4_112 ),
inference(avatar_split_clause,[],[f2685,f1711,f1699,f1715]) ).
fof(f2706,plain,
( ! [X0] :
( sK0(sK2) = sK1(sK2)
| greater(sK0(sK2),sK1(sK2))
| ~ in_environment(X0,sK0(sK2))
| ~ in_environment(X0,sK1(sK2)) )
| spl4_126 ),
inference(resolution,[],[f1852,f32]) ).
fof(f2709,plain,
( ! [X0] :
( greater(sK0(sK2),sK1(sK2))
| ~ in_environment(X0,sK0(sK2))
| ~ in_environment(X0,sK1(sK2)) )
| spl4_124
| spl4_126 ),
inference(forward_subsumption_resolution,[],[f2706,f1844]) ).
fof(f2710,plain,
( spl4_125
| spl4_146
| spl4_124
| spl4_126 ),
inference(avatar_split_clause,[],[f2709,f1851,f1843,f2407,f1848]) ).
fof(f2718,plain,
( ! [X0] :
( greater(growth_rate(efficient_producers,sK3(sK1(sK2))),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl4_12 ),
inference(superposition,[],[f47,f127]) ).
fof(f2722,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK3(sK1(sK2)))
| ~ greater_or_equal(sK3(sK1(sK2)),sK0(X0))
| ~ environment(X0)
| ~ stable(X0) )
| spl4_1
| ~ spl4_12 ),
inference(forward_subsumption_resolution,[],[f2718,f71]) ).
fof(f2723,plain,
( spl4_20
| spl4_1
| ~ spl4_12 ),
inference(avatar_split_clause,[],[f2722,f125,f69,f176]) ).
fof(f2733,plain,
( in_environment(sK2,equilibrium(sK2))
| ~ spl4_28
| ~ spl4_113 ),
inference(superposition,[],[f352,f1717]) ).
fof(f2757,plain,
( greater_or_equal(sK0(sK2),equilibrium(sK2))
| ~ spl4_113
| ~ spl4_123 ),
inference(superposition,[],[f1840,f1717]) ).
fof(f2825,plain,
( ~ greater_or_equal(sK3(equilibrium(sK2)),equilibrium(sK2))
| spl4_38
| ~ spl4_113 ),
inference(forward_demodulation,[],[f419,f1717]) ).
fof(f2846,plain,
( ~ spl4_73
| spl4_74
| spl4_69 ),
inference(avatar_split_clause,[],[f2602,f878,f907,f903]) ).
fof(f2848,plain,
( spl4_73
| ~ spl4_113
| ~ spl4_123 ),
inference(avatar_split_clause,[],[f2757,f1839,f1715,f903]) ).
fof(f2851,plain,
( ~ spl4_81
| spl4_38
| ~ spl4_113 ),
inference(avatar_split_clause,[],[f2825,f1715,f417,f1010]) ).
fof(f2918,plain,
( ~ in_environment(sK2,sK0(sK2))
| ~ spl4_28
| ~ spl4_75
| ~ spl4_113 ),
inference(resolution,[],[f2733,f913]) ).
fof(f2919,plain,
( $false
| ~ spl4_28
| ~ spl4_30
| ~ spl4_75
| ~ spl4_113 ),
inference(forward_subsumption_resolution,[],[f2918,f367]) ).
fof(f2920,plain,
( ~ spl4_28
| ~ spl4_30
| ~ spl4_75
| ~ spl4_113 ),
inference(avatar_contradiction_clause,[],[f2919]) ).
fof(f2924,plain,
( spl4_75
| spl4_76
| spl4_74
| spl4_69 ),
inference(avatar_split_clause,[],[f2601,f878,f907,f915,f912]) ).
fof(f2949,plain,
( $false
| ~ spl4_28
| spl4_81
| ~ spl4_113 ),
inference(forward_subsumption_resolution,[],[f1406,f2733]) ).
fof(f2950,plain,
( ~ spl4_28
| spl4_81
| ~ spl4_113 ),
inference(avatar_contradiction_clause,[],[f2949]) ).
cnf(s12,plain,
( spl4_2
| ~ spl4_8
| spl4_20 ),
inference(sat_conversion,[],[f178]) ).
cnf(s15,plain,
( spl4_2
| spl4_6
| spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f202]) ).
cnf(s23,plain,
( spl4_4
| spl4_18
| spl4_19
| spl4_25 ),
inference(sat_conversion,[],[f256]) ).
cnf(s26,plain,
spl4_28,
inference(sat_conversion,[],[f362]) ).
cnf(s29,plain,
spl4_30,
inference(sat_conversion,[],[f394]) ).
cnf(s40,plain,
( ~ spl4_3
| ~ spl4_4
| ~ spl4_30 ),
inference(sat_conversion,[],[f455]) ).
cnf(s45,plain,
( spl4_3
| ~ spl4_17
| spl4_24 ),
inference(sat_conversion,[],[f496]) ).
cnf(s49,plain,
( spl4_4
| spl4_24
| ~ spl4_25 ),
inference(sat_conversion,[],[f514]) ).
cnf(s53,plain,
( ~ spl4_24
| ~ spl4_53
| ~ spl4_54 ),
inference(sat_conversion,[],[f565]) ).
cnf(s54,plain,
( ~ spl4_30
| spl4_53 ),
inference(sat_conversion,[],[f569]) ).
cnf(s55,plain,
( ~ spl4_30
| spl4_54 ),
inference(sat_conversion,[],[f576]) ).
cnf(s59,plain,
( spl4_3
| spl4_15
| spl4_17
| spl4_18 ),
inference(sat_conversion,[],[f584]) ).
cnf(s95,plain,
( ~ spl4_30
| spl4_31
| ~ spl4_69
| spl4_70 ),
inference(sat_conversion,[],[f887]) ).
cnf(s99,plain,
( ~ spl4_20
| ~ spl4_38
| ~ spl4_72
| ~ spl4_74 ),
inference(sat_conversion,[],[f960]) ).
cnf(s103,plain,
( ~ spl4_29
| spl4_71
| ~ spl4_74 ),
inference(sat_conversion,[],[f1001]) ).
cnf(s107,plain,
( ~ spl4_28
| spl4_72 ),
inference(sat_conversion,[],[f1030]) ).
cnf(s110,plain,
( ~ spl4_1
| ~ spl4_2
| ~ spl4_28 ),
inference(sat_conversion,[],[f1036]) ).
cnf(s152,plain,
( spl4_3
| ~ spl4_15
| spl4_24 ),
inference(sat_conversion,[],[f1172]) ).
cnf(s174,plain,
( spl4_1
| spl4_9
| spl4_10
| spl4_12 ),
inference(sat_conversion,[],[f1230]) ).
cnf(s175,plain,
( spl4_1
| ~ spl4_10
| spl4_20 ),
inference(sat_conversion,[],[f1233]) ).
cnf(s176,plain,
( ~ spl4_9
| ~ spl4_28
| ~ spl4_29 ),
inference(sat_conversion,[],[f1234]) ).
cnf(s180,plain,
( ~ spl4_9
| ~ spl4_38
| ~ spl4_72 ),
inference(sat_conversion,[],[f1249]) ).
cnf(s195,plain,
( ~ spl4_39
| spl4_71
| ~ spl4_76 ),
inference(sat_conversion,[],[f1313]) ).
cnf(s213,plain,
( ~ spl4_29
| spl4_69
| ~ spl4_97 ),
inference(sat_conversion,[],[f1434]) ).
cnf(s214,plain,
( spl4_29
| ~ spl4_38
| spl4_39 ),
inference(sat_conversion,[],[f1440]) ).
cnf(s241,plain,
( ~ spl4_28
| spl4_29
| ~ spl4_110
| spl4_111 ),
inference(sat_conversion,[],[f1706]) ).
cnf(s244,plain,
spl4_112,
inference(sat_conversion,[],[f1732]) ).
cnf(s250,plain,
( spl4_38
| ~ spl4_111
| ~ spl4_112 ),
inference(sat_conversion,[],[f1813]) ).
cnf(s251,plain,
( spl4_29
| ~ spl4_110
| ~ spl4_111 ),
inference(sat_conversion,[],[f1815]) ).
cnf(s258,plain,
( spl4_71
| spl4_95
| spl4_96
| spl4_97 ),
inference(sat_conversion,[],[f1876]) ).
cnf(s299,plain,
( ~ spl4_28
| spl4_71
| spl4_111
| ~ spl4_126 ),
inference(sat_conversion,[],[f2167]) ).
cnf(s307,plain,
( ~ spl4_96
| ~ spl4_111
| spl4_125 ),
inference(sat_conversion,[],[f2178]) ).
cnf(s320,plain,
( ~ spl4_29
| spl4_31
| ~ spl4_124 ),
inference(sat_conversion,[],[f2272]) ).
cnf(s342,plain,
~ spl4_125,
inference(sat_conversion,[],[f2405]) ).
cnf(s344,plain,
( spl4_123
| ~ spl4_146 ),
inference(sat_conversion,[],[f2411]) ).
cnf(s349,plain,
( ~ spl4_29
| spl4_69
| ~ spl4_95 ),
inference(sat_conversion,[],[f2467]) ).
cnf(s393,plain,
( spl4_4
| ~ spl4_19
| spl4_24 ),
inference(sat_conversion,[],[f2563]) ).
cnf(s412,plain,
( ~ spl4_18
| ~ spl4_31
| ~ spl4_54 ),
inference(sat_conversion,[],[f2595]) ).
cnf(s420,plain,
( spl4_31
| ~ spl4_69
| ~ spl4_70 ),
inference(sat_conversion,[],[f2599]) ).
cnf(s432,plain,
( spl4_2
| ~ spl4_6
| spl4_20 ),
inference(sat_conversion,[],[f2656]) ).
cnf(s440,plain,
( spl4_69
| ~ spl4_110
| ~ spl4_123
| spl4_124 ),
inference(sat_conversion,[],[f2674]) ).
cnf(s442,plain,
( ~ spl4_20
| ~ spl4_71
| ~ spl4_72 ),
inference(sat_conversion,[],[f2680]) ).
cnf(s444,plain,
( spl4_110
| ~ spl4_112
| spl4_113 ),
inference(sat_conversion,[],[f2686]) ).
cnf(s451,plain,
( spl4_124
| spl4_125
| spl4_126
| spl4_146 ),
inference(sat_conversion,[],[f2710]) ).
cnf(s452,plain,
( spl4_1
| ~ spl4_12
| spl4_20 ),
inference(sat_conversion,[],[f2723]) ).
cnf(s473,plain,
( spl4_69
| ~ spl4_73
| spl4_74 ),
inference(sat_conversion,[],[f2846]) ).
cnf(s475,plain,
( spl4_73
| ~ spl4_113
| ~ spl4_123 ),
inference(sat_conversion,[],[f2848]) ).
cnf(s477,plain,
( spl4_38
| ~ spl4_81
| ~ spl4_113 ),
inference(sat_conversion,[],[f2851]) ).
cnf(s496,plain,
( ~ spl4_28
| ~ spl4_30
| ~ spl4_75
| ~ spl4_113 ),
inference(sat_conversion,[],[f2920]) ).
cnf(s499,plain,
( spl4_69
| spl4_74
| spl4_75
| spl4_76 ),
inference(sat_conversion,[],[f2924]) ).
cnf(s507,plain,
( ~ spl4_28
| spl4_81
| ~ spl4_113 ),
inference(sat_conversion,[],[f2950]) ).
cnf(s510,plain,
( ~ spl4_96
| ~ spl4_111 ),
inference(rat,[],[s307,s342]) ).
cnf(s513,plain,
spl4_54,
inference(rat,[],[s55,s29]) ).
cnf(s514,plain,
spl4_53,
inference(rat,[],[s54,s29]) ).
cnf(s515,plain,
~ spl4_24,
inference(rat,[],[s53,s513,s514]) ).
cnf(s517,plain,
spl4_72,
inference(rat,[],[s107,s26]) ).
cnf(s520,plain,
( spl4_38
| spl4_29 ),
inference(rat,[],[s477,s507,s444,s241,s250,s26,s244]) ).
cnf(s521,plain,
( ~ spl4_69
| spl4_31 ),
inference(rat,[],[s420,s95,s29]) ).
cnf(s522,plain,
( ~ spl4_110
| spl4_29 ),
inference(rat,[],[s251,s241,s26]) ).
cnf(s523,plain,
( spl4_29
| ~ spl4_20
| spl4_69 ),
inference(rat,[],[s522,s444,s496,s499,s195,s99,s214,s520,s442,s244,s29,s26,s517]) ).
cnf(s524,plain,
( spl4_124
| ~ spl4_20
| spl4_69 ),
inference(rat,[],[s444,s440,s475,s344,s451,s473,s103,s299,s510,s258,s213,s349,s523,s442,s244,s342,s517,s26]) ).
cnf(s525,plain,
( ~ spl4_20
| spl4_31 ),
inference(rat,[],[s320,s524,s523,s521]) ).
cnf(s526,plain,
~ spl4_9,
inference(rat,[],[s520,s176,s180,s26,s517]) ).
cnf(s528,plain,
( spl4_3
| spl4_18 ),
inference(rat,[],[s59,s45,s152,s515]) ).
cnf(s529,plain,
spl4_18,
inference(rat,[],[s23,s49,s393,s40,s528,s515,s29]) ).
cnf(s530,plain,
~ spl4_31,
inference(rat,[],[s412,s513,s529]) ).
cnf(s532,plain,
~ spl4_20,
inference(rat,[],[s525,s530]) ).
cnf(s533,plain,
spl4_1,
inference(rat,[],[s174,s175,s452,s526,s532]) ).
cnf(s534,plain,
~ spl4_2,
inference(rat,[],[s110,s26,s533]) ).
cnf(s538,plain,
~ spl4_6,
inference(rat,[],[s432,s532,s534]) ).
cnf(s539,plain,
~ spl4_8,
inference(rat,[],[s12,s532,s534]) ).
cnf(s541,plain,
$false,
inference(rat,[],[s15,s526,s534,s538,s539]) ).
fof(f2951,plain,
$false,
inference(avatar_sat_refutation,[],[s541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT035+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 17:21:52 UTC 2026
% 0.16/0.38 % CPUTime :
% 0.16/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.90/1.35 % (3769249)Detected formulas, will run a generic FOF schedule.
% 2.90/1.35 % (3769256)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1124732534:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.90/1.35 % (3769255)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2187781081:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.90/1.35 % (3769254)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=4120543925:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.90/1.35 % (3769259)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1375514258:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.90/1.35 % (3769257)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3208402073:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.90/1.35 % (3769258)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=123487794:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.90/1.35 % (3769260)dis-21_1_sil=8000:lcm=predicate:random_seed=1979317641:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.90/1.35 % (3769260)Instruction limit reached!
% 2.90/1.35 % (3769260)------------------------------
% 2.90/1.35 % (3769260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.35 % (3769260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.35 % (3769260)CaDiCaL version: 2.1.3
% 2.90/1.35 % (3769260)Termination reason: Instruction limit
% 2.90/1.35 % (3769260)Termination phase: Saturation
% 2.90/1.35 % (3769260)Time elapsed: 0.055 s
% 2.90/1.35 % (3769260)Peak memory usage: 88 MB
% 2.90/1.35 % (3769260)Instructions burned: 131 (million)
% 2.90/1.35 % (3769257)Instruction limit reached!
% 2.90/1.35 % (3769257)------------------------------
% 2.90/1.35 % (3769257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.35 % (3769257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.35 % (3769257)CaDiCaL version: 2.1.3
% 2.90/1.35 % (3769257)Termination reason: Instruction limit
% 2.90/1.35 % (3769257)Termination phase: Saturation
% 2.90/1.35 % (3769257)Time elapsed: 0.062 s
% 2.90/1.35 % (3769257)Peak memory usage: 89 MB
% 2.90/1.35 % (3769257)Instructions burned: 110 (million)
% 2.90/1.35 % (3769258)Instruction limit reached!
% 2.90/1.35 % (3769258)------------------------------
% 2.90/1.35 % (3769258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.35 % (3769258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.35 % (3769258)CaDiCaL version: 2.1.3
% 2.90/1.35 % (3769258)Termination reason: Instruction limit
% 2.90/1.35 % (3769258)Termination phase: Saturation
% 2.90/1.35 % (3769258)Time elapsed: 0.066 s
% 2.90/1.35 % (3769258)Peak memory usage: 88 MB
% 2.90/1.35 % (3769258)Instructions burned: 119 (million)
% 2.90/1.35 % (3769259)First to succeed.
% 2.90/1.35 % (3769259)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3769249"
% 2.90/1.35 % (3769269)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1189662801:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.90/1.35 % (3769270)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3453496219:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.90/1.35 % (3769268)lrs+10_1_sil=8000:sp=occurrence:random_seed=4289553536:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.90/1.35 % (3769269)Refutation not found, incomplete strategy
% 2.90/1.35 % (3769269)------------------------------
% 2.90/1.35 % (3769269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.35 % (3769269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.35 % (3769269)CaDiCaL version: 2.1.3
% 2.90/1.35 % (3769269)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.35 % (3769269)Time elapsed: 0.003 s
% 2.90/1.35 % (3769269)Peak memory usage: 88 MB
% 2.90/1.35 % (3769269)Instructions burned: 3 (million)
% 2.90/1.35 % (3769270)Also succeeded, but the first one will report.
% 2.90/1.35 % (3769259)Refutation found. Thanks to Tanya!
% 2.90/1.35 % SZS status Theorem for theBenchmark
% 2.90/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.44 % (3769259)------------------------------
% 3.98/1.44 % (3769259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.44 % (3769259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.44 % (3769259)CaDiCaL version: 2.1.3
% 3.98/1.44 % (3769259)Termination reason: Refutation
% 3.98/1.44 % (3769259)Time elapsed: 0.084 s
% 3.98/1.44 % (3769259)Peak memory usage: 91 MB
% 3.98/1.44 % (3769259)Instructions burned: 117 (million)
% 3.98/1.44 % (3769259)------------------------------
% 3.98/1.44 % (3769259)------------------------------
% 3.98/1.44 % (3769249)Success in time 0.491 s
% 3.98/1.44 % Vampire exiting
%------------------------------------------------------------------------------