TSTP Solution File: MGT024+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n007.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 : Wed Aug 31 17:51:25 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 172 ( 12 unt; 0 def)
% Number of atoms : 628 ( 84 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 714 ( 258 ~; 355 |; 70 &)
% ( 13 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 14 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 80 ( 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f283,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f75,f84,f103,f127,f153,f171,f178,f200,f208,f225,f227,f244,f263,f264,f266,f268,f275,f282]) ).
fof(f282,plain,
( ~ spl5_11
| ~ spl5_12
| spl5_14 ),
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f281,plain,
( $false
| ~ spl5_11
| ~ spl5_12
| spl5_14 ),
inference(subsumption_resolution,[],[f280,f258]) ).
fof(f258,plain,
( ~ greater(zero,zero)
| spl5_14 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f257,plain,
( spl5_14
<=> greater(zero,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f280,plain,
( greater(zero,zero)
| ~ spl5_11
| ~ spl5_12 ),
inference(forward_demodulation,[],[f213,f217]) ).
fof(f217,plain,
( zero = growth_rate(efficient_producers,sK0)
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f215,plain,
( spl5_12
<=> zero = growth_rate(efficient_producers,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f213,plain,
( greater(growth_rate(efficient_producers,sK0),zero)
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f211,plain,
( spl5_11
<=> greater(growth_rate(efficient_producers,sK0),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f275,plain,
( ~ spl5_4
| spl5_12 ),
inference(avatar_contradiction_clause,[],[f274]) ).
fof(f274,plain,
( $false
| ~ spl5_4
| spl5_12 ),
inference(subsumption_resolution,[],[f273,f216]) ).
fof(f216,plain,
( zero != growth_rate(efficient_producers,sK0)
| spl5_12 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f273,plain,
( zero = growth_rate(efficient_producers,sK0)
| ~ spl5_4 ),
inference(forward_demodulation,[],[f52,f73]) ).
fof(f73,plain,
( zero = sF3
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f72,plain,
( spl5_4
<=> zero = sF3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f52,plain,
sF3 = growth_rate(efficient_producers,sK0),
introduced(function_definition,[]) ).
fof(f268,plain,
( ~ spl5_14
| ~ spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f267,f77,f72,f257]) ).
fof(f77,plain,
( spl5_5
<=> greater(zero,sF3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f267,plain,
( ~ greater(zero,zero)
| ~ spl5_4
| spl5_5 ),
inference(forward_demodulation,[],[f79,f73]) ).
fof(f79,plain,
( ~ greater(zero,sF3)
| spl5_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f266,plain,
( ~ spl5_14
| spl5_2
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f265,f72,f63,f257]) ).
fof(f63,plain,
( spl5_2
<=> greater(sF3,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f265,plain,
( ~ greater(zero,zero)
| spl5_2
| ~ spl5_4 ),
inference(backward_demodulation,[],[f65,f73]) ).
fof(f65,plain,
( ~ greater(sF3,zero)
| spl5_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f264,plain,
( spl5_4
| ~ spl5_12 ),
inference(avatar_split_clause,[],[f245,f215,f72]) ).
fof(f245,plain,
( zero = sF3
| ~ spl5_12 ),
inference(backward_demodulation,[],[f52,f217]) ).
fof(f263,plain,
( spl5_14
| ~ spl5_12
| ~ spl5_13 ),
inference(avatar_split_clause,[],[f248,f219,f215,f257]) ).
fof(f219,plain,
( spl5_13
<=> greater(zero,growth_rate(efficient_producers,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f248,plain,
( greater(zero,zero)
| ~ spl5_12
| ~ spl5_13 ),
inference(forward_demodulation,[],[f221,f217]) ).
fof(f221,plain,
( greater(zero,growth_rate(efficient_producers,sK0))
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f244,plain,
( spl5_12
| ~ spl5_3
| spl5_6
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f243,f197,f81,f68,f215]) ).
fof(f68,plain,
( spl5_3
<=> zero = sF2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f81,plain,
( spl5_6
<=> greater(sF2,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f197,plain,
( spl5_10
<=> constant(number_of_organizations(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f243,plain,
( zero = growth_rate(efficient_producers,sK0)
| ~ spl5_3
| spl5_6
| ~ spl5_10 ),
inference(subsumption_resolution,[],[f242,f231]) ).
fof(f231,plain,
( ~ greater(zero,zero)
| ~ spl5_3
| spl5_6 ),
inference(backward_demodulation,[],[f83,f69]) ).
fof(f69,plain,
( zero = sF2
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f83,plain,
( ~ greater(sF2,zero)
| spl5_6 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f242,plain,
( greater(zero,zero)
| zero = growth_rate(efficient_producers,sK0)
| ~ spl5_3
| spl5_6
| ~ spl5_10 ),
inference(forward_demodulation,[],[f241,f233]) ).
fof(f233,plain,
( zero = growth_rate(first_movers,sK0)
| ~ spl5_3 ),
inference(backward_demodulation,[],[f51,f69]) ).
fof(f51,plain,
growth_rate(first_movers,sK0) = sF2,
introduced(function_definition,[]) ).
fof(f241,plain,
( greater(growth_rate(first_movers,sK0),zero)
| zero = growth_rate(efficient_producers,sK0)
| ~ spl5_3
| spl5_6
| ~ spl5_10 ),
inference(subsumption_resolution,[],[f240,f231]) ).
fof(f240,plain,
( zero = growth_rate(efficient_producers,sK0)
| greater(growth_rate(first_movers,sK0),zero)
| greater(zero,zero)
| ~ spl5_3
| ~ spl5_10 ),
inference(forward_demodulation,[],[f239,f233]) ).
fof(f239,plain,
( greater(growth_rate(first_movers,sK0),zero)
| zero = growth_rate(efficient_producers,sK0)
| greater(zero,growth_rate(first_movers,sK0))
| ~ spl5_10 ),
inference(subsumption_resolution,[],[f238,f198]) ).
fof(f198,plain,
( constant(number_of_organizations(sK1,sK0))
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f238,plain,
( greater(zero,growth_rate(first_movers,sK0))
| greater(growth_rate(first_movers,sK0),zero)
| ~ constant(number_of_organizations(sK1,sK0))
| zero = growth_rate(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f133,f45]) ).
fof(f45,plain,
environment(sK1),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ( zero != growth_rate(first_movers,sK0)
| zero != growth_rate(efficient_producers,sK0) )
& greater_or_equal(sK0,equilibrium(sK1))
& ( ~ greater(growth_rate(efficient_producers,sK0),zero)
| ~ greater(zero,growth_rate(first_movers,sK0)) )
& ( ~ greater(growth_rate(first_movers,sK0),zero)
| ~ greater(zero,growth_rate(efficient_producers,sK0)) )
& environment(sK1)
& subpopulations(first_movers,efficient_producers,sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f27]) ).
fof(f27,plain,
( ? [X0,X1] :
( ( zero != growth_rate(first_movers,X0)
| zero != growth_rate(efficient_producers,X0) )
& greater_or_equal(X0,equilibrium(X1))
& ( ~ greater(growth_rate(efficient_producers,X0),zero)
| ~ greater(zero,growth_rate(first_movers,X0)) )
& ( ~ greater(growth_rate(first_movers,X0),zero)
| ~ greater(zero,growth_rate(efficient_producers,X0)) )
& environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X0) )
=> ( ( zero != growth_rate(first_movers,sK0)
| zero != growth_rate(efficient_producers,sK0) )
& greater_or_equal(sK0,equilibrium(sK1))
& ( ~ greater(growth_rate(efficient_producers,sK0),zero)
| ~ greater(zero,growth_rate(first_movers,sK0)) )
& ( ~ greater(growth_rate(first_movers,sK0),zero)
| ~ greater(zero,growth_rate(efficient_producers,sK0)) )
& environment(sK1)
& subpopulations(first_movers,efficient_producers,sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1] :
( ( zero != growth_rate(first_movers,X0)
| zero != growth_rate(efficient_producers,X0) )
& greater_or_equal(X0,equilibrium(X1))
& ( ~ greater(growth_rate(efficient_producers,X0),zero)
| ~ greater(zero,growth_rate(first_movers,X0)) )
& ( ~ greater(growth_rate(first_movers,X0),zero)
| ~ greater(zero,growth_rate(efficient_producers,X0)) )
& environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X0) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
? [X1,X0] :
( ( ~ greater(growth_rate(first_movers,X0),zero)
| ~ greater(zero,growth_rate(efficient_producers,X0)) )
& ( zero != growth_rate(first_movers,X0)
| zero != growth_rate(efficient_producers,X0) )
& ( ~ greater(growth_rate(efficient_producers,X0),zero)
| ~ greater(zero,growth_rate(first_movers,X0)) )
& subpopulations(first_movers,efficient_producers,X1,X0)
& environment(X1)
& greater_or_equal(X0,equilibrium(X1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
~ ! [X1,X0] :
( ( subpopulations(first_movers,efficient_producers,X1,X0)
& environment(X1)
& greater_or_equal(X0,equilibrium(X1)) )
=> ( ( greater(zero,growth_rate(efficient_producers,X0))
& greater(growth_rate(first_movers,X0),zero) )
| ( zero = growth_rate(first_movers,X0)
& zero = growth_rate(efficient_producers,X0) )
| ( greater(growth_rate(efficient_producers,X0),zero)
& greater(zero,growth_rate(first_movers,X0)) ) ) ),
inference(rectify,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X1,X0] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(X1,equilibrium(X0))
& environment(X0) )
=> ( ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( zero = growth_rate(first_movers,X1)
& zero = growth_rate(efficient_producers,X1) )
| ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) ) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X1,X0] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(X1,equilibrium(X0))
& environment(X0) )
=> ( ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( zero = growth_rate(first_movers,X1)
& zero = growth_rate(efficient_producers,X1) )
| ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6) ).
fof(f133,plain,
( ~ environment(sK1)
| greater(zero,growth_rate(first_movers,sK0))
| greater(growth_rate(first_movers,sK0),zero)
| zero = growth_rate(efficient_producers,sK0)
| ~ constant(number_of_organizations(sK1,sK0)) ),
inference(resolution,[],[f32,f44]) ).
fof(f44,plain,
subpopulations(first_movers,efficient_producers,sK1,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X0)
| greater(growth_rate(first_movers,X0),zero)
| greater(zero,growth_rate(first_movers,X0))
| zero = growth_rate(efficient_producers,X0)
| ~ constant(number_of_organizations(X1,X0))
| ~ environment(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( greater(zero,growth_rate(efficient_producers,X0))
& greater(growth_rate(first_movers,X0),zero) )
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ constant(number_of_organizations(X1,X0))
| ( greater(zero,growth_rate(first_movers,X0))
& greater(growth_rate(efficient_producers,X0),zero) )
| ( zero = growth_rate(first_movers,X0)
& zero = growth_rate(efficient_producers,X0) ) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( greater(zero,growth_rate(first_movers,X0))
& greater(growth_rate(efficient_producers,X0),zero) )
| ( zero = growth_rate(first_movers,X0)
& zero = growth_rate(efficient_producers,X0) )
| ( greater(zero,growth_rate(efficient_producers,X0))
& greater(growth_rate(first_movers,X0),zero) )
| ~ constant(number_of_organizations(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ( constant(number_of_organizations(X1,X0))
& subpopulations(first_movers,efficient_producers,X1,X0)
& environment(X1) )
=> ( ( greater(zero,growth_rate(first_movers,X0))
& greater(growth_rate(efficient_producers,X0),zero) )
| ( zero = growth_rate(first_movers,X0)
& zero = growth_rate(efficient_producers,X0) )
| ( greater(zero,growth_rate(efficient_producers,X0))
& greater(growth_rate(first_movers,X0),zero) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] :
( ( environment(X0)
& constant(number_of_organizations(X0,X1))
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ( ( greater(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) )
| ( zero = growth_rate(first_movers,X1)
& 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',l7) ).
fof(f227,plain,
( spl5_3
| spl5_13
| spl5_11
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f226,f197,f211,f219,f68]) ).
fof(f226,plain,
( ~ constant(number_of_organizations(sK1,sK0))
| greater(growth_rate(efficient_producers,sK0),zero)
| greater(zero,growth_rate(efficient_producers,sK0))
| zero = sF2 ),
inference(forward_demodulation,[],[f184,f51]) ).
fof(f184,plain,
( greater(growth_rate(efficient_producers,sK0),zero)
| greater(zero,growth_rate(efficient_producers,sK0))
| zero = growth_rate(first_movers,sK0)
| ~ constant(number_of_organizations(sK1,sK0)) ),
inference(subsumption_resolution,[],[f154,f45]) ).
fof(f154,plain,
( greater(zero,growth_rate(efficient_producers,sK0))
| ~ constant(number_of_organizations(sK1,sK0))
| zero = growth_rate(first_movers,sK0)
| ~ environment(sK1)
| greater(growth_rate(efficient_producers,sK0),zero) ),
inference(resolution,[],[f35,f44]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ constant(number_of_organizations(X1,X0))
| ~ environment(X1)
| zero = growth_rate(first_movers,X0)
| greater(growth_rate(efficient_producers,X0),zero)
| greater(zero,growth_rate(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f225,plain,
( spl5_13
| ~ spl5_10
| spl5_4
| spl5_1 ),
inference(avatar_split_clause,[],[f224,f59,f72,f197,f219]) ).
fof(f59,plain,
( spl5_1
<=> greater(zero,sF2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f224,plain,
( zero = sF3
| ~ constant(number_of_organizations(sK1,sK0))
| greater(zero,growth_rate(efficient_producers,sK0))
| spl5_1 ),
inference(subsumption_resolution,[],[f223,f61]) ).
fof(f61,plain,
( ~ greater(zero,sF2)
| spl5_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f223,plain,
( greater(zero,sF2)
| zero = sF3
| greater(zero,growth_rate(efficient_producers,sK0))
| ~ constant(number_of_organizations(sK1,sK0)) ),
inference(forward_demodulation,[],[f172,f51]) ).
fof(f172,plain,
( greater(zero,growth_rate(efficient_producers,sK0))
| greater(zero,growth_rate(first_movers,sK0))
| zero = sF3
| ~ constant(number_of_organizations(sK1,sK0)) ),
inference(forward_demodulation,[],[f163,f52]) ).
fof(f163,plain,
( zero = growth_rate(efficient_producers,sK0)
| greater(zero,growth_rate(first_movers,sK0))
| greater(zero,growth_rate(efficient_producers,sK0))
| ~ constant(number_of_organizations(sK1,sK0)) ),
inference(subsumption_resolution,[],[f162,f45]) ).
fof(f162,plain,
( zero = growth_rate(efficient_producers,sK0)
| ~ environment(sK1)
| greater(zero,growth_rate(efficient_producers,sK0))
| ~ constant(number_of_organizations(sK1,sK0))
| greater(zero,growth_rate(first_movers,sK0)) ),
inference(resolution,[],[f36,f44]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X0)
| greater(zero,growth_rate(efficient_producers,X0))
| zero = growth_rate(efficient_producers,X0)
| greater(zero,growth_rate(first_movers,X0))
| ~ constant(number_of_organizations(X1,X0))
| ~ environment(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f208,plain,
( spl5_10
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f205,f96,f197]) ).
fof(f96,plain,
( spl5_7
<=> constant(resources(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f205,plain,
( constant(number_of_organizations(sK1,sK0))
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f204,f86]) ).
fof(f86,plain,
in_environment(sK1,sK0),
inference(subsumption_resolution,[],[f85,f45]) ).
fof(f85,plain,
( in_environment(sK1,sK0)
| ~ environment(sK1) ),
inference(resolution,[],[f42,f44]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f16,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(f204,plain,
( ~ in_environment(sK1,sK0)
| constant(number_of_organizations(sK1,sK0))
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f203,f45]) ).
fof(f203,plain,
( ~ environment(sK1)
| ~ in_environment(sK1,sK0)
| constant(number_of_organizations(sK1,sK0))
| ~ spl5_7 ),
inference(resolution,[],[f98,f40]) ).
fof(f40,plain,
! [X0,X1] :
( ~ constant(resources(X1,X0))
| constant(number_of_organizations(X1,X0))
| ~ environment(X1)
| ~ in_environment(X1,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ~ environment(X1)
| ~ in_environment(X1,X0)
| ( ( ~ decreases(resources(X1,X0))
| ~ decreases(number_of_organizations(X1,X0)) )
& ( constant(number_of_organizations(X1,X0))
| ~ constant(resources(X1,X0)) ) ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X1,X0] :
( ( ( ~ decreases(resources(X1,X0))
| ~ decreases(number_of_organizations(X1,X0)) )
& ( constant(number_of_organizations(X1,X0))
| ~ constant(resources(X1,X0)) ) )
| ~ in_environment(X1,X0)
| ~ environment(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
! [X1,X0] :
( ( in_environment(X1,X0)
& environment(X1) )
=> ( ( constant(resources(X1,X0))
=> constant(number_of_organizations(X1,X0)) )
& ( decreases(resources(X1,X0))
=> ~ decreases(number_of_organizations(X1,X0)) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( ( decreases(resources(X0,X1))
=> ~ decreases(number_of_organizations(X0,X1)) )
& ( constant(resources(X0,X1))
=> constant(number_of_organizations(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(f98,plain,
( constant(resources(sK1,sK0))
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f200,plain,
( spl5_6
| ~ spl5_10
| spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f195,f68,f59,f197,f81]) ).
fof(f195,plain,
( ~ constant(number_of_organizations(sK1,sK0))
| greater(sF2,zero)
| spl5_1
| spl5_3 ),
inference(forward_demodulation,[],[f194,f51]) ).
fof(f194,plain,
( greater(growth_rate(first_movers,sK0),zero)
| ~ constant(number_of_organizations(sK1,sK0))
| spl5_1
| spl5_3 ),
inference(subsumption_resolution,[],[f193,f61]) ).
fof(f193,plain,
( greater(zero,sF2)
| ~ constant(number_of_organizations(sK1,sK0))
| greater(growth_rate(first_movers,sK0),zero)
| spl5_3 ),
inference(forward_demodulation,[],[f192,f51]) ).
fof(f192,plain,
( ~ constant(number_of_organizations(sK1,sK0))
| greater(zero,growth_rate(first_movers,sK0))
| greater(growth_rate(first_movers,sK0),zero)
| spl5_3 ),
inference(subsumption_resolution,[],[f191,f70]) ).
fof(f70,plain,
( zero != sF2
| spl5_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f191,plain,
( greater(zero,growth_rate(first_movers,sK0))
| greater(growth_rate(first_movers,sK0),zero)
| zero = sF2
| ~ constant(number_of_organizations(sK1,sK0)) ),
inference(forward_demodulation,[],[f190,f51]) ).
fof(f190,plain,
( ~ constant(number_of_organizations(sK1,sK0))
| zero = growth_rate(first_movers,sK0)
| greater(growth_rate(first_movers,sK0),zero)
| greater(zero,growth_rate(first_movers,sK0)) ),
inference(subsumption_resolution,[],[f139,f45]) ).
fof(f139,plain,
( greater(zero,growth_rate(first_movers,sK0))
| zero = growth_rate(first_movers,sK0)
| ~ environment(sK1)
| greater(growth_rate(first_movers,sK0),zero)
| ~ constant(number_of_organizations(sK1,sK0)) ),
inference(resolution,[],[f33,f44]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X0)
| greater(zero,growth_rate(first_movers,X0))
| ~ environment(X1)
| greater(growth_rate(first_movers,X0),zero)
| zero = growth_rate(first_movers,X0)
| ~ constant(number_of_organizations(X1,X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f178,plain,
~ spl5_8,
inference(avatar_split_clause,[],[f161,f100]) ).
fof(f100,plain,
( spl5_8
<=> greater(sF4,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f161,plain,
~ greater(sF4,sK0),
inference(resolution,[],[f88,f55]) ).
fof(f55,plain,
greater_or_equal(sK0,sF4),
inference(definition_folding,[],[f48,f54]) ).
fof(f54,plain,
equilibrium(sK1) = sF4,
introduced(function_definition,[]) ).
fof(f48,plain,
greater_or_equal(sK0,equilibrium(sK1)),
inference(cnf_transformation,[],[f28]) ).
fof(f88,plain,
! [X0] :
( ~ greater_or_equal(X0,sF4)
| ~ greater(sF4,X0) ),
inference(subsumption_resolution,[],[f87,f45]) ).
fof(f87,plain,
! [X0] :
( ~ greater_or_equal(X0,sF4)
| ~ environment(sK1)
| ~ greater(sF4,X0) ),
inference(superposition,[],[f43,f54]) ).
fof(f43,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,equilibrium(X1))
| ~ greater(equilibrium(X1),X0)
| ~ environment(X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,equilibrium(X1))
| ~ environment(X1)
| ~ greater(equilibrium(X1),X0) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
! [X1,X0] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ( greater_or_equal(X1,equilibrium(X0))
& environment(X0) )
=> ~ greater(equilibrium(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium) ).
fof(f171,plain,
( spl5_1
| spl5_4
| spl5_5
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f170,plain,
( $false
| spl5_1
| spl5_4
| spl5_5
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f169,f74]) ).
fof(f74,plain,
( zero != sF3
| spl5_4 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f169,plain,
( zero = sF3
| spl5_1
| spl5_5
| ~ spl5_7 ),
inference(backward_demodulation,[],[f52,f168]) ).
fof(f168,plain,
( zero = growth_rate(efficient_producers,sK0)
| spl5_1
| spl5_5
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f167,f79]) ).
fof(f167,plain,
( zero = growth_rate(efficient_producers,sK0)
| greater(zero,sF3)
| spl5_1
| ~ spl5_7 ),
inference(forward_demodulation,[],[f166,f52]) ).
fof(f166,plain,
( greater(zero,growth_rate(efficient_producers,sK0))
| zero = growth_rate(efficient_producers,sK0)
| spl5_1
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f165,f61]) ).
fof(f165,plain,
( greater(zero,sF2)
| greater(zero,growth_rate(efficient_producers,sK0))
| zero = growth_rate(efficient_producers,sK0)
| ~ spl5_7 ),
inference(forward_demodulation,[],[f164,f51]) ).
fof(f164,plain,
( greater(zero,growth_rate(first_movers,sK0))
| zero = growth_rate(efficient_producers,sK0)
| greater(zero,growth_rate(efficient_producers,sK0))
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f163,f106]) ).
fof(f106,plain,
( constant(number_of_organizations(sK1,sK0))
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f105,f45]) ).
fof(f105,plain,
( constant(number_of_organizations(sK1,sK0))
| ~ environment(sK1)
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f104,f86]) ).
fof(f104,plain,
( ~ in_environment(sK1,sK0)
| constant(number_of_organizations(sK1,sK0))
| ~ environment(sK1)
| ~ spl5_7 ),
inference(resolution,[],[f98,f40]) ).
fof(f153,plain,
( spl5_2
| spl5_4
| spl5_5
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f152,f96,f77,f72,f63]) ).
fof(f152,plain,
( greater(sF3,zero)
| spl5_4
| spl5_5
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f151,f79]) ).
fof(f151,plain,
( greater(sF3,zero)
| greater(zero,sF3)
| spl5_4
| ~ spl5_7 ),
inference(forward_demodulation,[],[f150,f52]) ).
fof(f150,plain,
( greater(sF3,zero)
| greater(zero,growth_rate(efficient_producers,sK0))
| spl5_4
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f149,f74]) ).
fof(f149,plain,
( zero = sF3
| greater(sF3,zero)
| greater(zero,growth_rate(efficient_producers,sK0))
| ~ spl5_7 ),
inference(forward_demodulation,[],[f148,f52]) ).
fof(f148,plain,
( zero = growth_rate(efficient_producers,sK0)
| greater(zero,growth_rate(efficient_producers,sK0))
| greater(sF3,zero)
| ~ spl5_7 ),
inference(forward_demodulation,[],[f147,f52]) ).
fof(f147,plain,
( greater(growth_rate(efficient_producers,sK0),zero)
| greater(zero,growth_rate(efficient_producers,sK0))
| zero = growth_rate(efficient_producers,sK0)
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f146,f45]) ).
fof(f146,plain,
( greater(growth_rate(efficient_producers,sK0),zero)
| greater(zero,growth_rate(efficient_producers,sK0))
| zero = growth_rate(efficient_producers,sK0)
| ~ environment(sK1)
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f145,f106]) ).
fof(f145,plain,
( ~ constant(number_of_organizations(sK1,sK0))
| zero = growth_rate(efficient_producers,sK0)
| greater(zero,growth_rate(efficient_producers,sK0))
| greater(growth_rate(efficient_producers,sK0),zero)
| ~ environment(sK1) ),
inference(resolution,[],[f34,f44]) ).
fof(f34,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X0)
| zero = growth_rate(efficient_producers,X0)
| ~ constant(number_of_organizations(X1,X0))
| greater(growth_rate(efficient_producers,X0),zero)
| greater(zero,growth_rate(efficient_producers,X0))
| ~ environment(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f127,plain,
( spl5_6
| spl5_2
| spl5_4
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f126,f96,f72,f63,f81]) ).
fof(f126,plain,
( greater(sF3,zero)
| greater(sF2,zero)
| spl5_4
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f125,f74]) ).
fof(f125,plain,
( zero = sF3
| greater(sF2,zero)
| greater(sF3,zero)
| ~ spl5_7 ),
inference(forward_demodulation,[],[f120,f52]) ).
fof(f120,plain,
( greater(sF3,zero)
| greater(sF2,zero)
| zero = growth_rate(efficient_producers,sK0)
| ~ spl5_7 ),
inference(forward_demodulation,[],[f119,f51]) ).
fof(f119,plain,
( greater(growth_rate(first_movers,sK0),zero)
| greater(sF3,zero)
| zero = growth_rate(efficient_producers,sK0)
| ~ spl5_7 ),
inference(forward_demodulation,[],[f118,f52]) ).
fof(f118,plain,
( greater(growth_rate(efficient_producers,sK0),zero)
| greater(growth_rate(first_movers,sK0),zero)
| zero = growth_rate(efficient_producers,sK0)
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f117,f45]) ).
fof(f117,plain,
( zero = growth_rate(efficient_producers,sK0)
| greater(growth_rate(efficient_producers,sK0),zero)
| ~ environment(sK1)
| greater(growth_rate(first_movers,sK0),zero)
| ~ spl5_7 ),
inference(subsumption_resolution,[],[f116,f106]) ).
fof(f116,plain,
( greater(growth_rate(efficient_producers,sK0),zero)
| ~ constant(number_of_organizations(sK1,sK0))
| greater(growth_rate(first_movers,sK0),zero)
| ~ environment(sK1)
| zero = growth_rate(efficient_producers,sK0) ),
inference(resolution,[],[f30,f44]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X0)
| zero = growth_rate(efficient_producers,X0)
| ~ constant(number_of_organizations(X1,X0))
| greater(growth_rate(efficient_producers,X0),zero)
| greater(growth_rate(first_movers,X0),zero)
| ~ environment(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f103,plain,
( spl5_7
| spl5_8 ),
inference(avatar_split_clause,[],[f94,f100,f96]) ).
fof(f94,plain,
( greater(sF4,sK0)
| constant(resources(sK1,sK0)) ),
inference(forward_demodulation,[],[f93,f54]) ).
fof(f93,plain,
( constant(resources(sK1,sK0))
| greater(equilibrium(sK1),sK0) ),
inference(subsumption_resolution,[],[f92,f86]) ).
fof(f92,plain,
( ~ in_environment(sK1,sK0)
| greater(equilibrium(sK1),sK0)
| constant(resources(sK1,sK0)) ),
inference(subsumption_resolution,[],[f91,f45]) ).
fof(f91,plain,
( greater(equilibrium(sK1),sK0)
| ~ environment(sK1)
| constant(resources(sK1,sK0))
| ~ in_environment(sK1,sK0) ),
inference(resolution,[],[f38,f90]) ).
fof(f90,plain,
greater(number_of_organizations(sK1,sK0),zero),
inference(subsumption_resolution,[],[f89,f45]) ).
fof(f89,plain,
( greater(number_of_organizations(sK1,sK0),zero)
| ~ environment(sK1) ),
inference(resolution,[],[f50,f44]) ).
fof(f50,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1)
| greater(number_of_organizations(X1,X0),zero) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| greater(number_of_organizations(X1,X0),zero) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(number_of_organizations(X0,X1),zero) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X1,X0] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ( 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(f38,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ( ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) )
& ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ) )
| ~ environment(X0) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ( ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) )
& ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ) )
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ( greater(number_of_organizations(X0,X1),zero)
& environment(X0)
& in_environment(X0,X1) )
=> ( ( greater(equilibrium(X0),X1)
=> decreases(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
=> constant(resources(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f84,plain,
( ~ spl5_5
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f57,f81,f77]) ).
fof(f57,plain,
( ~ greater(sF2,zero)
| ~ greater(zero,sF3) ),
inference(definition_folding,[],[f46,f52,f51]) ).
fof(f46,plain,
( ~ greater(growth_rate(first_movers,sK0),zero)
| ~ greater(zero,growth_rate(efficient_producers,sK0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f75,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f53,f72,f68]) ).
fof(f53,plain,
( zero != sF3
| zero != sF2 ),
inference(definition_folding,[],[f49,f52,f51]) ).
fof(f49,plain,
( zero != growth_rate(first_movers,sK0)
| zero != growth_rate(efficient_producers,sK0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f66,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f56,f63,f59]) ).
fof(f56,plain,
( ~ greater(sF3,zero)
| ~ greater(zero,sF2) ),
inference(definition_folding,[],[f47,f51,f52]) ).
fof(f47,plain,
( ~ greater(growth_rate(efficient_producers,sK0),zero)
| ~ greater(zero,growth_rate(first_movers,sK0)) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : MGT024+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 02:59:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.48 % (10003)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.49 % (9995)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.50 % (10003)First to succeed.
% 0.20/0.50 % (10012)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.51 % (9988)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (10003)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (10003)------------------------------
% 0.20/0.51 % (10003)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (10003)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (10003)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (10003)Memory used [KB]: 5500
% 0.20/0.51 % (10003)Time elapsed: 0.101 s
% 0.20/0.51 % (10003)Instructions burned: 9 (million)
% 0.20/0.51 % (10003)------------------------------
% 0.20/0.51 % (10003)------------------------------
% 0.20/0.51 % (9977)Success in time 0.152 s
%------------------------------------------------------------------------------