TSTP Solution File: MGT024+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT024+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:42:44 EDT 2024
% Result : Theorem 0.16s 0.41s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 145 ( 20 unt; 0 def)
% Number of atoms : 569 ( 40 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 720 ( 296 ~; 319 |; 63 &)
% ( 29 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 30 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 119 ( 113 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f200,plain,
$false,
inference(avatar_sat_refutation,[],[f52,f57,f62,f71,f80,f89,f93,f97,f101,f105,f112,f116,f121,f125,f129,f133,f137,f141,f145,f149,f158,f163,f174,f179,f181,f182,f183,f186,f193,f194,f197,f198,f199]) ).
fof(f199,plain,
( ~ spl3_1
| spl3_9
| ~ spl3_26
| spl3_27
| spl3_7
| ~ spl3_3
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f153,f147,f59,f77,f171,f167,f86,f49]) ).
fof(f49,plain,
( spl3_1
<=> environment(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f86,plain,
( spl3_9
<=> greater(zero,growth_rate(first_movers,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f167,plain,
( spl3_26
<=> constant(number_of_organizations(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f171,plain,
( spl3_27
<=> sP0(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f77,plain,
( spl3_7
<=> greater(zero,growth_rate(efficient_producers,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f59,plain,
( spl3_3
<=> subpopulations(first_movers,efficient_producers,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f147,plain,
( spl3_23
<=> ! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f153,plain,
( greater(zero,growth_rate(efficient_producers,sK2))
| sP0(sK2)
| ~ constant(number_of_organizations(sK1,sK2))
| greater(zero,growth_rate(first_movers,sK2))
| ~ environment(sK1)
| ~ spl3_3
| ~ spl3_23 ),
inference(resolution,[],[f148,f61]) ).
fof(f61,plain,
( subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f148,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0) )
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f198,plain,
( spl3_29
| ~ spl3_4
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f196,f73,f64,f190]) ).
fof(f190,plain,
( spl3_29
<=> greater(zero,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f64,plain,
( spl3_4
<=> zero = growth_rate(first_movers,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f73,plain,
( spl3_6
<=> greater(growth_rate(first_movers,sK2),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f196,plain,
( greater(zero,zero)
| ~ spl3_4
| ~ spl3_6 ),
inference(superposition,[],[f74,f65]) ).
fof(f65,plain,
( zero = growth_rate(first_movers,sK2)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f74,plain,
( greater(growth_rate(first_movers,sK2),zero)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f197,plain,
( ~ spl3_29
| ~ spl3_4
| spl3_9 ),
inference(avatar_split_clause,[],[f195,f86,f64,f190]) ).
fof(f195,plain,
( ~ greater(zero,zero)
| ~ spl3_4
| spl3_9 ),
inference(superposition,[],[f88,f65]) ).
fof(f88,plain,
( ~ greater(zero,growth_rate(first_movers,sK2))
| spl3_9 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f194,plain,
( spl3_4
| ~ spl3_10
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f185,f171,f91,f64]) ).
fof(f91,plain,
( spl3_10
<=> ! [X0] :
( zero = growth_rate(first_movers,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f185,plain,
( zero = growth_rate(first_movers,sK2)
| ~ spl3_10
| ~ spl3_27 ),
inference(resolution,[],[f173,f92]) ).
fof(f92,plain,
( ! [X0] :
( ~ sP0(X0)
| zero = growth_rate(first_movers,X0) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f173,plain,
( sP0(sK2)
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f193,plain,
( spl3_29
| ~ spl3_5
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f187,f82,f68,f190]) ).
fof(f68,plain,
( spl3_5
<=> zero = growth_rate(efficient_producers,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f82,plain,
( spl3_8
<=> greater(growth_rate(efficient_producers,sK2),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f187,plain,
( greater(zero,zero)
| ~ spl3_5
| ~ spl3_8 ),
inference(superposition,[],[f83,f69]) ).
fof(f69,plain,
( zero = growth_rate(efficient_producers,sK2)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f83,plain,
( greater(growth_rate(efficient_producers,sK2),zero)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f186,plain,
( spl3_5
| ~ spl3_11
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f184,f171,f95,f68]) ).
fof(f95,plain,
( spl3_11
<=> ! [X0] :
( zero = growth_rate(efficient_producers,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f184,plain,
( zero = growth_rate(efficient_producers,sK2)
| ~ spl3_11
| ~ spl3_27 ),
inference(resolution,[],[f173,f96]) ).
fof(f96,plain,
( ! [X0] :
( ~ sP0(X0)
| zero = growth_rate(efficient_producers,X0) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f183,plain,
( ~ spl3_1
| spl3_9
| ~ spl3_26
| spl3_27
| spl3_6
| ~ spl3_3
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f152,f143,f59,f73,f171,f167,f86,f49]) ).
fof(f143,plain,
( spl3_22
<=> ! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f152,plain,
( greater(growth_rate(first_movers,sK2),zero)
| sP0(sK2)
| ~ constant(number_of_organizations(sK1,sK2))
| greater(zero,growth_rate(first_movers,sK2))
| ~ environment(sK1)
| ~ spl3_3
| ~ spl3_22 ),
inference(resolution,[],[f144,f61]) ).
fof(f144,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(growth_rate(first_movers,X1),zero)
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0) )
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f182,plain,
( ~ spl3_1
| spl3_8
| ~ spl3_26
| spl3_27
| spl3_7
| ~ spl3_3
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f151,f139,f59,f77,f171,f167,f82,f49]) ).
fof(f139,plain,
( spl3_21
<=> ! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f151,plain,
( greater(zero,growth_rate(efficient_producers,sK2))
| sP0(sK2)
| ~ constant(number_of_organizations(sK1,sK2))
| greater(growth_rate(efficient_producers,sK2),zero)
| ~ environment(sK1)
| ~ spl3_3
| ~ spl3_21 ),
inference(resolution,[],[f140,f61]) ).
fof(f140,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,growth_rate(efficient_producers,X1))
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ~ environment(X0) )
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f181,plain,
( ~ spl3_1
| ~ spl3_14
| spl3_26
| ~ spl3_17
| ~ spl3_28 ),
inference(avatar_split_clause,[],[f180,f176,f123,f167,f109,f49]) ).
fof(f109,plain,
( spl3_14
<=> in_environment(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f123,plain,
( spl3_17
<=> ! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f176,plain,
( spl3_28
<=> constant(resources(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f180,plain,
( constant(number_of_organizations(sK1,sK2))
| ~ in_environment(sK1,sK2)
| ~ environment(sK1)
| ~ spl3_17
| ~ spl3_28 ),
inference(resolution,[],[f178,f124]) ).
fof(f124,plain,
( ! [X0,X1] :
( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f178,plain,
( constant(resources(sK1,sK2))
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f179,plain,
( ~ spl3_1
| ~ spl3_14
| spl3_28
| spl3_24
| ~ spl3_19
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f164,f160,f131,f155,f176,f109,f49]) ).
fof(f155,plain,
( spl3_24
<=> greater(equilibrium(sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f131,plain,
( spl3_19
<=> ! [X0,X1] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f160,plain,
( spl3_25
<=> greater(number_of_organizations(sK1,sK2),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f164,plain,
( greater(equilibrium(sK1),sK2)
| constant(resources(sK1,sK2))
| ~ in_environment(sK1,sK2)
| ~ environment(sK1)
| ~ spl3_19
| ~ spl3_25 ),
inference(resolution,[],[f162,f132]) ).
fof(f132,plain,
( ! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) )
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f162,plain,
( greater(number_of_organizations(sK1,sK2),zero)
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f174,plain,
( ~ spl3_1
| spl3_8
| ~ spl3_26
| spl3_27
| spl3_6
| ~ spl3_3
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f150,f135,f59,f73,f171,f167,f82,f49]) ).
fof(f135,plain,
( spl3_20
<=> ! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f150,plain,
( greater(growth_rate(first_movers,sK2),zero)
| sP0(sK2)
| ~ constant(number_of_organizations(sK1,sK2))
| greater(growth_rate(efficient_producers,sK2),zero)
| ~ environment(sK1)
| ~ spl3_3
| ~ spl3_20 ),
inference(resolution,[],[f136,f61]) ).
fof(f136,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(growth_rate(first_movers,X1),zero)
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ~ environment(X0) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f163,plain,
( ~ spl3_1
| spl3_25
| ~ spl3_3
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f117,f114,f59,f160,f49]) ).
fof(f114,plain,
( spl3_15
<=> ! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f117,plain,
( greater(number_of_organizations(sK1,sK2),zero)
| ~ environment(sK1)
| ~ spl3_3
| ~ spl3_15 ),
inference(resolution,[],[f115,f61]) ).
fof(f115,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f158,plain,
( ~ spl3_1
| ~ spl3_24
| ~ spl3_2
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f106,f99,f54,f155,f49]) ).
fof(f54,plain,
( spl3_2
<=> greater_or_equal(sK2,equilibrium(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f99,plain,
( spl3_12
<=> ! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f106,plain,
( ~ greater(equilibrium(sK1),sK2)
| ~ environment(sK1)
| ~ spl3_2
| ~ spl3_12 ),
inference(resolution,[],[f100,f56]) ).
fof(f56,plain,
( greater_or_equal(sK2,equilibrium(sK1))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f100,plain,
( ! [X0,X1] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ greater(equilibrium(X0),X1)
| ~ environment(X0) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f149,plain,
spl3_23,
inference(avatar_split_clause,[],[f44,f147]) ).
fof(f44,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(definition_folding,[],[f16,f23]) ).
fof(f23,plain,
! [X1] :
( ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) )
| ~ sP0(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f16,plain,
! [X0,X1] :
( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) )
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) )
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( constant(number_of_organizations(X0,X1))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7) ).
fof(f145,plain,
spl3_22,
inference(avatar_split_clause,[],[f43,f143]) ).
fof(f43,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f141,plain,
spl3_21,
inference(avatar_split_clause,[],[f42,f139]) ).
fof(f42,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f137,plain,
spl3_20,
inference(avatar_split_clause,[],[f41,f135]) ).
fof(f41,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| sP0(X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f133,plain,
spl3_19,
inference(avatar_split_clause,[],[f36,f131]) ).
fof(f36,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( ( ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) )
& ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) ) )
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ( ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) )
& ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) ) )
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( greater(number_of_organizations(X0,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> ( ( ~ greater(equilibrium(X0),X1)
=> constant(resources(X0,X1)) )
& ( greater(equilibrium(X0),X1)
=> decreases(resources(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f129,plain,
spl3_18,
inference(avatar_split_clause,[],[f35,f127]) ).
fof(f127,plain,
( spl3_18
<=> ! [X0,X1] :
( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f35,plain,
! [X0,X1] :
( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f125,plain,
spl3_17,
inference(avatar_split_clause,[],[f38,f123]) ).
fof(f38,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( ( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1)) )
& ( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1)) ) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ( ( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1)) )
& ( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1)) ) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( ( constant(resources(X0,X1))
=> constant(number_of_organizations(X0,X1)) )
& ( decreases(resources(X0,X1))
=> ~ decreases(number_of_organizations(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(f121,plain,
spl3_16,
inference(avatar_split_clause,[],[f37,f119]) ).
fof(f119,plain,
( spl3_16
<=> ! [X0,X1] :
( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f37,plain,
! [X0,X1] :
( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f116,plain,
spl3_15,
inference(avatar_split_clause,[],[f47,f114]) ).
fof(f47,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
fof(f112,plain,
( ~ spl3_1
| spl3_14
| ~ spl3_3
| ~ spl3_13 ),
inference(avatar_split_clause,[],[f107,f103,f59,f109,f49]) ).
fof(f103,plain,
( spl3_13
<=> ! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f107,plain,
( in_environment(sK1,sK2)
| ~ environment(sK1)
| ~ spl3_3
| ~ spl3_13 ),
inference(resolution,[],[f104,f61]) ).
fof(f104,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1)
| ~ environment(X0) )
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f105,plain,
spl3_13,
inference(avatar_split_clause,[],[f46,f103]) ).
fof(f46,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f101,plain,
spl3_12,
inference(avatar_split_clause,[],[f45,f99]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ( greater_or_equal(X1,equilibrium(X0))
& environment(X0) )
=> ~ greater(equilibrium(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium) ).
fof(f97,plain,
spl3_11,
inference(avatar_split_clause,[],[f40,f95]) ).
fof(f40,plain,
! [X0] :
( zero = growth_rate(efficient_producers,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ( zero = growth_rate(efficient_producers,X0)
& zero = growth_rate(first_movers,X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X1] :
( ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) )
| ~ sP0(X1) ),
inference(nnf_transformation,[],[f23]) ).
fof(f93,plain,
spl3_10,
inference(avatar_split_clause,[],[f39,f91]) ).
fof(f39,plain,
! [X0] :
( zero = growth_rate(first_movers,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f89,plain,
( ~ spl3_8
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f34,f86,f82]) ).
fof(f34,plain,
( ~ greater(zero,growth_rate(first_movers,sK2))
| ~ greater(growth_rate(efficient_producers,sK2),zero) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
( ( ~ greater(zero,growth_rate(first_movers,sK2))
| ~ greater(growth_rate(efficient_producers,sK2),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK2))
| ~ greater(growth_rate(first_movers,sK2),zero) )
& ( zero != growth_rate(efficient_producers,sK2)
| zero != growth_rate(first_movers,sK2) )
& greater_or_equal(sK2,equilibrium(sK1))
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f10,f25]) ).
fof(f25,plain,
( ? [X0,X1] :
( ( ~ greater(zero,growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,X1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,X1))
| ~ greater(growth_rate(first_movers,X1),zero) )
& ( zero != growth_rate(efficient_producers,X1)
| zero != growth_rate(first_movers,X1) )
& greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( ~ greater(zero,growth_rate(first_movers,sK2))
| ~ greater(growth_rate(efficient_producers,sK2),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK2))
| ~ greater(growth_rate(first_movers,sK2),zero) )
& ( zero != growth_rate(efficient_producers,sK2)
| zero != growth_rate(first_movers,sK2) )
& greater_or_equal(sK2,equilibrium(sK1))
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0,X1] :
( ( ~ greater(zero,growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,X1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,X1))
| ~ greater(growth_rate(first_movers,X1),zero) )
& ( zero != growth_rate(efficient_producers,X1)
| zero != growth_rate(first_movers,X1) )
& greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(flattening,[],[f9]) ).
fof(f9,plain,
? [X0,X1] :
( ( ~ greater(zero,growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,X1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,X1))
| ~ greater(growth_rate(first_movers,X1),zero) )
& ( zero != growth_rate(efficient_producers,X1)
| zero != growth_rate(first_movers,X1) )
& greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) ) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( ( greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6) ).
fof(f80,plain,
( ~ spl3_6
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f33,f77,f73]) ).
fof(f33,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK2))
| ~ greater(growth_rate(first_movers,sK2),zero) ),
inference(cnf_transformation,[],[f26]) ).
fof(f71,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f32,f68,f64]) ).
fof(f32,plain,
( zero != growth_rate(efficient_producers,sK2)
| zero != growth_rate(first_movers,sK2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f62,plain,
spl3_3,
inference(avatar_split_clause,[],[f30,f59]) ).
fof(f30,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(cnf_transformation,[],[f26]) ).
fof(f57,plain,
spl3_2,
inference(avatar_split_clause,[],[f31,f54]) ).
fof(f31,plain,
greater_or_equal(sK2,equilibrium(sK1)),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
spl3_1,
inference(avatar_split_clause,[],[f29,f49]) ).
fof(f29,plain,
environment(sK1),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : MGT024+1 : TPTP v8.2.0. Released v2.0.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37 % Computer : n020.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 00:18:38 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % (24705)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (24706)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 % (24709)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.40 TRYING [1]
% 0.16/0.40 TRYING [2]
% 0.16/0.40 TRYING [1]
% 0.16/0.40 TRYING [2]
% 0.16/0.40 % (24710)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.40 TRYING [3]
% 0.16/0.40 TRYING [3]
% 0.16/0.40 % (24712)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.40 % (24710)First to succeed.
% 0.16/0.41 % (24708)WARNING: value z3 for option sas not known
% 0.16/0.41 % (24708)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.41 % (24710)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24705"
% 0.16/0.41 % (24710)Refutation found. Thanks to Tanya!
% 0.16/0.41 % SZS status Theorem for theBenchmark
% 0.16/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.41 % (24710)------------------------------
% 0.16/0.41 % (24710)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.41 % (24710)Termination reason: Refutation
% 0.16/0.41
% 0.16/0.41 % (24710)Memory used [KB]: 872
% 0.16/0.41 % (24710)Time elapsed: 0.007 s
% 0.16/0.41 % (24710)Instructions burned: 10 (million)
% 0.16/0.41 % (24705)Success in time 0.033 s
%------------------------------------------------------------------------------