TSTP Solution File: MGT024+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : MGT024+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n032.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 00:42:10 EDT 2024
% Result : Theorem 0.68s 0.88s
% Output : Refutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 112 ( 6 unt; 0 def)
% Number of atoms : 517 ( 31 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 657 ( 252 ~; 326 |; 58 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 8 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 126 ( 120 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f147,plain,
$false,
inference(avatar_sat_refutation,[],[f65,f74,f83,f101,f106,f110,f116,f123,f125,f132,f139,f146]) ).
fof(f146,plain,
( spl3_7
| spl3_1
| spl3_3
| spl3_6 ),
inference(avatar_split_clause,[],[f145,f80,f67,f58,f98]) ).
fof(f98,plain,
( spl3_7
<=> ! [X0] :
( ~ constant(number_of_organizations(X0,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f58,plain,
( spl3_1
<=> greater(growth_rate(efficient_producers,sK1),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f67,plain,
( spl3_3
<=> greater(growth_rate(first_movers,sK1),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f80,plain,
( spl3_6
<=> sQ2_eqProxy(zero,growth_rate(efficient_producers,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f145,plain,
( ! [X0] :
( ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_1
| spl3_3
| spl3_6 ),
inference(subsumption_resolution,[],[f144,f60]) ).
fof(f60,plain,
( ~ greater(growth_rate(efficient_producers,sK1),zero)
| spl3_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f144,plain,
( ! [X0] :
( greater(growth_rate(efficient_producers,sK1),zero)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_3
| spl3_6 ),
inference(subsumption_resolution,[],[f140,f69]) ).
fof(f69,plain,
( ~ greater(growth_rate(first_movers,sK1),zero)
| spl3_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f140,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_6 ),
inference(resolution,[],[f82,f53]) ).
fof(f53,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f30,f46]) ).
fof(f46,plain,
! [X0,X1] :
( sQ2_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ2_eqProxy])]) ).
fof(f30,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,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,[],[f13]) ).
fof(f13,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/sandbox/benchmark/theBenchmark.p',l7) ).
fof(f82,plain,
( ~ sQ2_eqProxy(zero,growth_rate(efficient_producers,sK1))
| spl3_6 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f139,plain,
( spl3_7
| spl3_2
| spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f138,f76,f71,f62,f98]) ).
fof(f62,plain,
( spl3_2
<=> greater(zero,growth_rate(first_movers,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f71,plain,
( spl3_4
<=> greater(zero,growth_rate(efficient_producers,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f76,plain,
( spl3_5
<=> sQ2_eqProxy(zero,growth_rate(first_movers,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f138,plain,
( ! [X0] :
( ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_2
| spl3_4
| spl3_5 ),
inference(subsumption_resolution,[],[f137,f64]) ).
fof(f64,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| spl3_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f137,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_4
| spl3_5 ),
inference(subsumption_resolution,[],[f136,f73]) ).
fof(f73,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| spl3_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f136,plain,
( ! [X0] :
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_5 ),
inference(resolution,[],[f78,f48]) ).
fof(f48,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f35,f46]) ).
fof(f35,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(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(cnf_transformation,[],[f14]) ).
fof(f78,plain,
( ~ sQ2_eqProxy(zero,growth_rate(first_movers,sK1))
| spl3_5 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f132,plain,
( spl3_7
| spl3_1
| spl3_4
| spl3_6 ),
inference(avatar_split_clause,[],[f131,f80,f71,f58,f98]) ).
fof(f131,plain,
( ! [X0] :
( ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_1
| spl3_4
| spl3_6 ),
inference(subsumption_resolution,[],[f130,f60]) ).
fof(f130,plain,
( ! [X0] :
( greater(growth_rate(efficient_producers,sK1),zero)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_4
| spl3_6 ),
inference(subsumption_resolution,[],[f127,f73]) ).
fof(f127,plain,
( ! [X0] :
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_6 ),
inference(resolution,[],[f82,f51]) ).
fof(f51,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f32,f46]) ).
fof(f32,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f125,plain,
( spl3_7
| spl3_4
| spl3_1
| spl3_5 ),
inference(avatar_split_clause,[],[f124,f76,f58,f71,f98]) ).
fof(f124,plain,
( ! [X0] :
( greater(zero,growth_rate(efficient_producers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_1
| spl3_5 ),
inference(subsumption_resolution,[],[f117,f60]) ).
fof(f117,plain,
( ! [X0] :
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_5 ),
inference(resolution,[],[f52,f78]) ).
fof(f52,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f31,f46]) ).
fof(f31,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(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(cnf_transformation,[],[f14]) ).
fof(f123,plain,
( spl3_7
| spl3_3
| spl3_1
| spl3_5 ),
inference(avatar_split_clause,[],[f122,f76,f58,f67,f98]) ).
fof(f122,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK1),zero)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_1
| spl3_5 ),
inference(subsumption_resolution,[],[f118,f60]) ).
fof(f118,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero)
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_5 ),
inference(resolution,[],[f54,f78]) ).
fof(f54,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f29,f46]) ).
fof(f29,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f116,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f115]) ).
fof(f115,plain,
( $false
| ~ spl3_7 ),
inference(subsumption_resolution,[],[f114,f85]) ).
fof(f85,plain,
~ greater(equilibrium(sK0),sK1),
inference(subsumption_resolution,[],[f84,f37]) ).
fof(f37,plain,
environment(sK0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
( ( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) )
& ( zero != growth_rate(efficient_producers,sK1)
| zero != growth_rate(first_movers,sK1) )
& greater_or_equal(sK1,equilibrium(sK0))
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f23]) ).
fof(f23,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,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) )
& ( zero != growth_rate(efficient_producers,sK1)
| zero != growth_rate(first_movers,sK1) )
& greater_or_equal(sK1,equilibrium(sK0))
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
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) )
& greater_or_equal(X1,equilibrium(X0))
& 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) )
& 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/sandbox/benchmark/theBenchmark.p',prove_l6) ).
fof(f84,plain,
( ~ greater(equilibrium(sK0),sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f39,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ greater(equilibrium(X0),X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(flattening,[],[f21]) ).
fof(f21,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/sandbox/benchmark/theBenchmark.p',mp_equilibrium) ).
fof(f39,plain,
greater_or_equal(sK1,equilibrium(sK0)),
inference(cnf_transformation,[],[f24]) ).
fof(f114,plain,
( greater(equilibrium(sK0),sK1)
| ~ spl3_7 ),
inference(subsumption_resolution,[],[f113,f37]) ).
fof(f113,plain,
( ~ environment(sK0)
| greater(equilibrium(sK0),sK1)
| ~ spl3_7 ),
inference(resolution,[],[f112,f38]) ).
fof(f38,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f112,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| greater(equilibrium(X0),sK1) )
| ~ spl3_7 ),
inference(duplicate_literal_removal,[],[f111]) ).
fof(f111,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| greater(equilibrium(X0),sK1) )
| ~ spl3_7 ),
inference(resolution,[],[f99,f103]) ).
fof(f103,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(equilibrium(X0),X1) ),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution,[],[f94,f89]) ).
fof(f89,plain,
! [X0,X1] :
( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(duplicate_literal_removal,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(resolution,[],[f28,f44]) ).
fof(f44,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/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f28,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,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,[],[f11]) ).
fof(f11,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/sandbox/benchmark/theBenchmark.p',a6) ).
fof(f94,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(subsumption_resolution,[],[f93,f43]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f17]) ).
fof(f17,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/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
fof(f93,plain,
! [X0,X1] :
( greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| constant(resources(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| constant(resources(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(resolution,[],[f26,f44]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| constant(resources(X0,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f10,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,[],[f9]) ).
fof(f9,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/sandbox/benchmark/theBenchmark.p',a3) ).
fof(f99,plain,
( ! [X0] :
( ~ constant(number_of_organizations(X0,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f110,plain,
( spl3_7
| spl3_2
| spl3_3
| spl3_5 ),
inference(avatar_split_clause,[],[f109,f76,f67,f62,f98]) ).
fof(f109,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_3
| spl3_5 ),
inference(subsumption_resolution,[],[f108,f69]) ).
fof(f108,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_5 ),
inference(resolution,[],[f50,f78]) ).
fof(f50,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1))
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f33,f46]) ).
fof(f33,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f106,plain,
( spl3_7
| spl3_2
| spl3_3
| spl3_6 ),
inference(avatar_split_clause,[],[f105,f80,f67,f62,f98]) ).
fof(f105,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_3
| spl3_6 ),
inference(subsumption_resolution,[],[f104,f69]) ).
fof(f104,plain,
( ! [X0] :
( greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_6 ),
inference(resolution,[],[f49,f82]) ).
fof(f49,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1))
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f34,f46]) ).
fof(f34,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f101,plain,
( spl3_7
| spl3_2
| spl3_4
| spl3_6 ),
inference(avatar_split_clause,[],[f95,f80,f71,f62,f98]) ).
fof(f95,plain,
( ! [X0] :
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) )
| spl3_6 ),
inference(resolution,[],[f47,f82]) ).
fof(f47,plain,
! [X0,X1] :
( sQ2_eqProxy(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(equality_proxy_replacement,[],[f36,f46]) ).
fof(f36,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f83,plain,
( ~ spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f55,f80,f76]) ).
fof(f55,plain,
( ~ sQ2_eqProxy(zero,growth_rate(efficient_producers,sK1))
| ~ sQ2_eqProxy(zero,growth_rate(first_movers,sK1)) ),
inference(equality_proxy_replacement,[],[f40,f46,f46]) ).
fof(f40,plain,
( zero != growth_rate(efficient_producers,sK1)
| zero != growth_rate(first_movers,sK1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f74,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f41,f71,f67]) ).
fof(f41,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) ),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f42,f62,f58]) ).
fof(f42,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : MGT024+1 : TPTP v8.2.0. Released v2.0.0.
% 0.08/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n032.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 23:57:07 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/0.87 % (29185)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2994ds/45Mi)
% 0.68/0.87 % (29181)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2994ds/51Mi)
% 0.68/0.87 % (29182)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2994ds/78Mi)
% 0.68/0.87 % (29180)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2994ds/34Mi)
% 0.68/0.87 % (29183)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2994ds/33Mi)
% 0.68/0.87 % (29184)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2994ds/34Mi)
% 0.68/0.87 % (29186)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2994ds/83Mi)
% 0.68/0.87 % (29187)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2994ds/56Mi)
% 0.68/0.88 % (29184)Also succeeded, but the first one will report.
% 0.68/0.88 % (29187)First to succeed.
% 0.68/0.88 % (29181)Also succeeded, but the first one will report.
% 0.68/0.88 % (29180)Also succeeded, but the first one will report.
% 0.68/0.88 % (29183)Refutation not found, incomplete strategy% (29183)------------------------------
% 0.68/0.88 % (29183)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.68/0.88 % (29183)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.88 % (29185)Also succeeded, but the first one will report.
% 0.68/0.88
% 0.68/0.88 % (29183)Memory used [KB]: 1054
% 0.68/0.88 % (29183)Time elapsed: 0.006 s
% 0.68/0.88 % (29183)Instructions burned: 6 (million)
% 0.68/0.88 % (29183)------------------------------
% 0.68/0.88 % (29183)------------------------------
% 0.68/0.88 % (29182)Also succeeded, but the first one will report.
% 0.68/0.88 % (29186)Also succeeded, but the first one will report.
% 0.68/0.88 % (29187)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29179"
% 0.68/0.88 % (29187)Refutation found. Thanks to Tanya!
% 0.68/0.88 % SZS status Theorem for theBenchmark
% 0.68/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 0.68/0.88 % (29187)------------------------------
% 0.68/0.88 % (29187)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.68/0.88 % (29187)Termination reason: Refutation
% 0.68/0.88
% 0.68/0.88 % (29187)Memory used [KB]: 1011
% 0.68/0.88 % (29187)Time elapsed: 0.007 s
% 0.68/0.88 % (29187)Instructions burned: 9 (million)
% 0.68/0.88 % (29179)Success in time 0.514 s
% 0.68/0.88 % Vampire---4.8 exiting
%------------------------------------------------------------------------------