TSTP Solution File: MGT027+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : MGT027+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 : n011.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 17:51:26 EDT 2022
% Result : Theorem 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of formulae : 155 ( 14 unt; 0 def)
% Number of atoms : 558 ( 14 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 706 ( 303 ~; 305 |; 67 &)
% ( 11 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 10 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 149 ( 136 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f326,plain,
$false,
inference(avatar_sat_refutation,[],[f105,f122,f129,f139,f154,f189,f243,f301,f310,f321,f325]) ).
fof(f325,plain,
( ~ spl4_7
| spl4_8 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f324,plain,
( $false
| ~ spl4_7
| spl4_8 ),
inference(subsumption_resolution,[],[f323,f84]) ).
fof(f84,plain,
greater(cardinality_at_time(efficient_producers,sK0(sK2)),zero),
inference(subsumption_resolution,[],[f82,f67]) ).
fof(f67,plain,
greater_or_equal(sK0(sK2),sF3),
inference(resolution,[],[f66,f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( X0 != X1
& ~ greater(X0,X1) ) )
& ( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X1,X0] :
( ( greater_or_equal(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ greater_or_equal(X1,X0) ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X1,X0] :
( ( greater_or_equal(X1,X0)
| ( X0 != X1
& ~ greater(X1,X0) ) )
& ( X0 = X1
| greater(X1,X0)
| ~ greater_or_equal(X1,X0) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X1,X0] :
( greater_or_equal(X1,X0)
<=> ( X0 = X1
| greater(X1,X0) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X6,X5] :
( greater_or_equal(X5,X6)
<=> ( greater(X5,X6)
| X5 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f66,plain,
greater(sK0(sK2),sF3),
inference(forward_demodulation,[],[f65,f62]) ).
fof(f62,plain,
sF3 = appear(efficient_producers,sK2),
introduced(function_definition,[]) ).
fof(f65,plain,
greater(sK0(sK2),appear(efficient_producers,sK2)),
inference(subsumption_resolution,[],[f64,f59]) ).
fof(f59,plain,
stable(sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
( stable(sK2)
& environment(sK2)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f43]) ).
fof(f43,plain,
( ? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) ) )
=> ( stable(sK2)
& environment(sK2)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
? [X0] :
( ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) )
& stable(X0)
& environment(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( contracts_from(X1,first_movers)
& greater(X1,appear(efficient_producers,X0)) ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( contracts_from(X1,first_movers)
& greater(X1,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9) ).
fof(f64,plain,
( ~ stable(sK2)
| greater(sK0(sK2),appear(efficient_producers,sK2)) ),
inference(resolution,[],[f49,f58]) ).
fof(f58,plain,
environment(sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f49,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| greater(sK0(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ~ stable(X0)
| ( greater(sK0(X0),appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) )
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f36]) ).
fof(f36,plain,
! [X0] :
( ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) )
=> ( greater(sK0(X0),appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
( ~ stable(X0)
| ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ) )
| ~ environment(X0) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X0] :
( ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10) ).
fof(f82,plain,
( ~ greater_or_equal(sK0(sK2),sF3)
| greater(cardinality_at_time(efficient_producers,sK0(sK2)),zero) ),
inference(resolution,[],[f70,f80]) ).
fof(f80,plain,
in_environment(sK2,sK0(sK2)),
inference(subsumption_resolution,[],[f79,f58]) ).
fof(f79,plain,
( ~ environment(sK2)
| in_environment(sK2,sK0(sK2)) ),
inference(subsumption_resolution,[],[f78,f59]) ).
fof(f78,plain,
( ~ stable(sK2)
| in_environment(sK2,sK0(sK2))
| ~ environment(sK2) ),
inference(resolution,[],[f77,f74]) ).
fof(f74,plain,
in_environment(sK2,sF3),
inference(forward_demodulation,[],[f73,f62]) ).
fof(f73,plain,
in_environment(sK2,appear(efficient_producers,sK2)),
inference(subsumption_resolution,[],[f72,f59]) ).
fof(f72,plain,
( ~ stable(sK2)
| in_environment(sK2,appear(efficient_producers,sK2)) ),
inference(resolution,[],[f60,f58]) ).
fof(f60,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
fof(f77,plain,
! [X0] :
( ~ in_environment(X0,sF3)
| in_environment(X0,sK0(sK2))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[],[f50,f66]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ greater(X0,X1)
| ~ in_environment(X2,X1)
| ~ environment(X2)
| ~ stable(X2)
| in_environment(X2,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ stable(X2)
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ greater(X0,X1)
| in_environment(X2,X0) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X2,X0)
| in_environment(X1,X2) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X1,X0,X2] :
( in_environment(X1,X2)
| ~ greater(X2,X0)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ stable(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X1,X0,X2] :
( ( greater(X2,X0)
& environment(X1)
& in_environment(X1,X0)
& stable(X1) )
=> in_environment(X1,X2) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X0,X4] :
( ( greater(X4,X3)
& stable(X0)
& in_environment(X0,X3)
& environment(X0) )
=> in_environment(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments) ).
fof(f70,plain,
! [X0] :
( ~ in_environment(sK2,X0)
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,sF3) ),
inference(subsumption_resolution,[],[f69,f58]) ).
fof(f69,plain,
! [X0] :
( ~ in_environment(sK2,X0)
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ environment(sK2)
| ~ greater_or_equal(X0,sF3) ),
inference(superposition,[],[f51,f62]) ).
fof(f51,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,appear(efficient_producers,X1))
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(X1,X0)
| ~ environment(X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,X1))
| greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,appear(efficient_producers,X1))
| ~ in_environment(X1,X0)
| ~ environment(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ( greater_or_equal(X0,appear(efficient_producers,X1))
& in_environment(X1,X0)
& environment(X1) )
=> greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X2,X0] :
( ( greater_or_equal(X2,appear(efficient_producers,X0))
& in_environment(X0,X2)
& environment(X0) )
=> greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f323,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK0(sK2)),zero)
| ~ spl4_7
| spl4_8 ),
inference(forward_demodulation,[],[f150,f138]) ).
fof(f138,plain,
( sK1(sK0(sK2)) = sK0(sK2)
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f136,plain,
( spl4_7
<=> sK1(sK0(sK2)) = sK0(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f150,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| spl4_8 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f148,plain,
( spl4_8
<=> greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f321,plain,
~ spl4_17,
inference(avatar_contradiction_clause,[],[f320]) ).
fof(f320,plain,
( $false
| ~ spl4_17 ),
inference(subsumption_resolution,[],[f319,f58]) ).
fof(f319,plain,
( ~ environment(sK2)
| ~ spl4_17 ),
inference(subsumption_resolution,[],[f318,f59]) ).
fof(f318,plain,
( ~ stable(sK2)
| ~ environment(sK2)
| ~ spl4_17 ),
inference(resolution,[],[f296,f80]) ).
fof(f296,plain,
( ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f295,plain,
( spl4_17
<=> ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ environment(X0)
| ~ stable(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
fof(f310,plain,
( ~ spl4_7
| ~ spl4_9
| spl4_18 ),
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f309,plain,
( $false
| ~ spl4_7
| ~ spl4_9
| spl4_18 ),
inference(subsumption_resolution,[],[f308,f58]) ).
fof(f308,plain,
( ~ environment(sK2)
| ~ spl4_7
| ~ spl4_9
| spl4_18 ),
inference(subsumption_resolution,[],[f307,f300]) ).
fof(f300,plain,
( ~ greater(zero,growth_rate(first_movers,sK0(sK2)))
| spl4_18 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f298,plain,
( spl4_18
<=> greater(zero,growth_rate(first_movers,sK0(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
fof(f307,plain,
( ~ environment(sK2)
| greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ spl4_7
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f306,f61]) ).
fof(f61,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f306,plain,
( ~ greater_or_equal(sK0(sK2),sK0(sK2))
| ~ environment(sK2)
| greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ spl4_7
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f305,f59]) ).
fof(f305,plain,
( ~ stable(sK2)
| greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ greater_or_equal(sK0(sK2),sK0(sK2))
| ~ environment(sK2)
| ~ spl4_7
| ~ spl4_9 ),
inference(resolution,[],[f304,f48]) ).
fof(f48,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0)
| ~ stable(X0)
| greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f304,plain,
( subpopulations(first_movers,efficient_producers,sK2,sK0(sK2))
| ~ spl4_7
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f303,f58]) ).
fof(f303,plain,
( ~ environment(sK2)
| subpopulations(first_movers,efficient_producers,sK2,sK0(sK2))
| ~ spl4_7
| ~ spl4_9 ),
inference(resolution,[],[f270,f80]) ).
fof(f270,plain,
( ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK0(sK2)) )
| ~ spl4_7
| ~ spl4_9 ),
inference(forward_demodulation,[],[f250,f138]) ).
fof(f250,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sK0(sK2))
| subpopulations(first_movers,efficient_producers,X0,sK1(sK0(sK2))) )
| ~ spl4_7
| ~ spl4_9 ),
inference(backward_demodulation,[],[f153,f138]) ).
fof(f153,plain,
( ! [X0] :
( ~ in_environment(X0,sK1(sK0(sK2)))
| subpopulations(first_movers,efficient_producers,X0,sK1(sK0(sK2)))
| ~ environment(X0) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f152,plain,
( spl4_9
<=> ! [X0] :
( ~ in_environment(X0,sK1(sK0(sK2)))
| subpopulations(first_movers,efficient_producers,X0,sK1(sK0(sK2)))
| ~ environment(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f301,plain,
( spl4_17
| ~ spl4_18
| spl4_2
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f293,f136,f102,f298,f295]) ).
fof(f102,plain,
( spl4_2
<=> contracts_from(sK0(sK2),first_movers) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f293,plain,
( ! [X0] :
( ~ greater(zero,growth_rate(first_movers,sK0(sK2)))
| ~ in_environment(X0,sK0(sK2))
| ~ stable(X0)
| ~ environment(X0) )
| spl4_2
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f292,f103]) ).
fof(f103,plain,
( ~ contracts_from(sK0(sK2),first_movers)
| spl4_2 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f292,plain,
( ! [X0] :
( ~ greater(zero,growth_rate(first_movers,sK0(sK2)))
| contracts_from(sK0(sK2),first_movers)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,sK0(sK2)) )
| ~ spl4_7 ),
inference(superposition,[],[f55,f138]) ).
fof(f55,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(first_movers,sK1(X1)))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ stable(X0)
| contracts_from(X1,first_movers) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| contracts_from(X1,first_movers)
| ( ~ greater(zero,growth_rate(first_movers,sK1(X1)))
& greater_or_equal(sK1(X1),X1)
& greater(cardinality_at_time(first_movers,sK1(X1)),zero) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f39,f40]) ).
fof(f40,plain,
! [X1] :
( ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) )
=> ( ~ greater(zero,growth_rate(first_movers,sK1(X1)))
& greater_or_equal(sK1(X1),X1)
& greater(cardinality_at_time(first_movers,sK1(X1)),zero) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| contracts_from(X1,first_movers)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X0)
| contracts_from(X0,first_movers)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X0)
& greater(cardinality_at_time(first_movers,X2),zero) ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X1,X0] :
( contracts_from(X0,first_movers)
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X0) )
| ~ in_environment(X1,X0)
| ~ stable(X1)
| ~ environment(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X0] :
( ( ! [X2] :
( ( greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X0) )
=> greater(zero,growth_rate(first_movers,X2)) )
& in_environment(X1,X0)
& stable(X1)
& environment(X1) )
=> contracts_from(X0,first_movers) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ( in_environment(X0,X1)
& ! [X2] :
( ( greater(cardinality_at_time(first_movers,X2),zero)
& greater_or_equal(X2,X1) )
=> greater(zero,growth_rate(first_movers,X2)) )
& stable(X0)
& environment(X0) )
=> contracts_from(X1,first_movers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from) ).
fof(f243,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f242,plain,
( $false
| ~ spl4_1
| spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f241,f58]) ).
fof(f241,plain,
( ~ environment(sK2)
| ~ spl4_1
| spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f240,f59]) ).
fof(f240,plain,
( ~ stable(sK2)
| ~ environment(sK2)
| ~ spl4_1
| spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(resolution,[],[f211,f80]) ).
fof(f211,plain,
( ! [X0] :
( ~ in_environment(X0,sK0(sK2))
| ~ environment(X0)
| ~ stable(X0) )
| ~ spl4_1
| spl4_2
| ~ spl4_6
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f203,f103]) ).
fof(f203,plain,
( ! [X0] :
( contracts_from(sK0(sK2),first_movers)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,sK0(sK2)) )
| ~ spl4_1
| ~ spl4_6
| ~ spl4_9 ),
inference(resolution,[],[f202,f55]) ).
fof(f202,plain,
( greater(zero,growth_rate(first_movers,sK1(sK0(sK2))))
| ~ spl4_1
| ~ spl4_6
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f201,f58]) ).
fof(f201,plain,
( ~ environment(sK2)
| greater(zero,growth_rate(first_movers,sK1(sK0(sK2))))
| ~ spl4_1
| ~ spl4_6
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f200,f100]) ).
fof(f100,plain,
( greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f98,plain,
( spl4_1
<=> greater_or_equal(sK1(sK0(sK2)),sK0(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f200,plain,
( ~ greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| ~ environment(sK2)
| greater(zero,growth_rate(first_movers,sK1(sK0(sK2))))
| ~ spl4_6
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f199,f59]) ).
fof(f199,plain,
( ~ stable(sK2)
| greater(zero,growth_rate(first_movers,sK1(sK0(sK2))))
| ~ greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| ~ environment(sK2)
| ~ spl4_6
| ~ spl4_9 ),
inference(resolution,[],[f198,f48]) ).
fof(f198,plain,
( subpopulations(first_movers,efficient_producers,sK2,sK1(sK0(sK2)))
| ~ spl4_6
| ~ spl4_9 ),
inference(subsumption_resolution,[],[f197,f58]) ).
fof(f197,plain,
( ~ environment(sK2)
| subpopulations(first_movers,efficient_producers,sK2,sK1(sK0(sK2)))
| ~ spl4_6
| ~ spl4_9 ),
inference(resolution,[],[f153,f164]) ).
fof(f164,plain,
( in_environment(sK2,sK1(sK0(sK2)))
| ~ spl4_6 ),
inference(subsumption_resolution,[],[f163,f59]) ).
fof(f163,plain,
( in_environment(sK2,sK1(sK0(sK2)))
| ~ stable(sK2)
| ~ spl4_6 ),
inference(subsumption_resolution,[],[f162,f58]) ).
fof(f162,plain,
( ~ environment(sK2)
| ~ stable(sK2)
| in_environment(sK2,sK1(sK0(sK2)))
| ~ spl4_6 ),
inference(resolution,[],[f157,f74]) ).
fof(f157,plain,
( ! [X0] :
( ~ in_environment(X0,sF3)
| ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,sK1(sK0(sK2))) )
| ~ spl4_6 ),
inference(resolution,[],[f156,f50]) ).
fof(f156,plain,
( greater(sK1(sK0(sK2)),sF3)
| ~ spl4_6 ),
inference(resolution,[],[f141,f66]) ).
fof(f141,plain,
( ! [X1] :
( ~ greater(sK0(sK2),X1)
| greater(sK1(sK0(sK2)),X1) )
| ~ spl4_6 ),
inference(resolution,[],[f134,f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ greater(X0,X1)
| ~ greater(X1,X2)
| greater(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( greater(X0,X1)
& greater(X1,X2) )
=> greater(X0,X2) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X5,X6,X7] :
( ( greater(X5,X6)
& greater(X6,X7) )
=> greater(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f134,plain,
( greater(sK1(sK0(sK2)),sK0(sK2))
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f132,plain,
( spl4_6
<=> greater(sK1(sK0(sK2)),sK0(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f189,plain,
( spl4_8
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f168,f132,f148]) ).
fof(f168,plain,
( greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl4_6 ),
inference(subsumption_resolution,[],[f165,f159]) ).
fof(f159,plain,
( greater_or_equal(sK1(sK0(sK2)),sF3)
| ~ spl4_6 ),
inference(resolution,[],[f156,f46]) ).
fof(f165,plain,
( ~ greater_or_equal(sK1(sK0(sK2)),sF3)
| greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl4_6 ),
inference(resolution,[],[f164,f70]) ).
fof(f154,plain,
( ~ spl4_8
| spl4_9
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f143,f126,f152,f148]) ).
fof(f126,plain,
( spl4_5
<=> greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f143,plain,
( ! [X0] :
( ~ in_environment(X0,sK1(sK0(sK2)))
| ~ environment(X0)
| ~ greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| subpopulations(first_movers,efficient_producers,X0,sK1(sK0(sK2))) )
| ~ spl4_5 ),
inference(resolution,[],[f128,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( ~ environment(X1)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| subpopulations(first_movers,efficient_producers,X1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(X1,X0) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X1,X0] :
( subpopulations(first_movers,efficient_producers,X1,X0)
| ~ in_environment(X1,X0)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ environment(X1)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X0] :
( ( in_environment(X1,X0)
& greater(cardinality_at_time(first_movers,X0),zero)
& environment(X1)
& greater(cardinality_at_time(efficient_producers,X0),zero) )
=> subpopulations(first_movers,efficient_producers,X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X0] :
( ( in_environment(X0,X2)
& environment(X0)
& greater(cardinality_at_time(efficient_producers,X2),zero)
& greater(cardinality_at_time(first_movers,X2),zero) )
=> subpopulations(first_movers,efficient_producers,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f128,plain,
( greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f139,plain,
( spl4_6
| spl4_7
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f130,f98,f136,f132]) ).
fof(f130,plain,
( sK1(sK0(sK2)) = sK0(sK2)
| greater(sK1(sK0(sK2)),sK0(sK2))
| ~ spl4_1 ),
inference(resolution,[],[f100,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f129,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f124,f102,f126]) ).
fof(f124,plain,
( contracts_from(sK0(sK2),first_movers)
| greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero) ),
inference(subsumption_resolution,[],[f123,f59]) ).
fof(f123,plain,
( greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero)
| ~ stable(sK2)
| contracts_from(sK0(sK2),first_movers) ),
inference(subsumption_resolution,[],[f119,f58]) ).
fof(f119,plain,
( ~ environment(sK2)
| greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero)
| contracts_from(sK0(sK2),first_movers)
| ~ stable(sK2) ),
inference(resolution,[],[f53,f80]) ).
fof(f53,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sK1(X1)),zero)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f122,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f121]) ).
fof(f121,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f120,f66]) ).
fof(f120,plain,
( ~ greater(sK0(sK2),sF3)
| ~ spl4_2 ),
inference(resolution,[],[f104,f63]) ).
fof(f63,plain,
! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,sF3) ),
inference(definition_folding,[],[f57,f62]) ).
fof(f57,plain,
! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f104,plain,
( contracts_from(sK0(sK2),first_movers)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f96,f102,f98]) ).
fof(f96,plain,
( contracts_from(sK0(sK2),first_movers)
| greater_or_equal(sK1(sK0(sK2)),sK0(sK2)) ),
inference(subsumption_resolution,[],[f95,f59]) ).
fof(f95,plain,
( greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| contracts_from(sK0(sK2),first_movers)
| ~ stable(sK2) ),
inference(subsumption_resolution,[],[f94,f58]) ).
fof(f94,plain,
( greater_or_equal(sK1(sK0(sK2)),sK0(sK2))
| ~ environment(sK2)
| ~ stable(sK2)
| contracts_from(sK0(sK2),first_movers) ),
inference(resolution,[],[f54,f80]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| contracts_from(X1,first_movers)
| ~ stable(X0)
| greater_or_equal(sK1(X1),X1) ),
inference(cnf_transformation,[],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.36 % Computer : n011.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 : Tue Aug 30 03:12:40 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.51 % (7448)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 TRYING [1]
% 0.21/0.51 TRYING [2]
% 0.21/0.51 TRYING [3]
% 0.21/0.51 TRYING [4]
% 0.21/0.51 % (7442)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.52 TRYING [1]
% 0.21/0.52 TRYING [2]
% 0.21/0.52 TRYING [3]
% 0.21/0.52 TRYING [4]
% 0.21/0.52 % (7456)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)
% 0.21/0.52 % (7464)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.53 % (7446)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53 % (7458)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.53 % (7444)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.54 % (7462)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.54 % (7450)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.54 % (7450)Instruction limit reached!
% 0.21/0.54 % (7450)------------------------------
% 0.21/0.54 % (7450)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (7450)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (7450)Termination reason: Unknown
% 0.21/0.54 % (7450)Termination phase: Blocked clause elimination
% 0.21/0.54
% 0.21/0.54 % (7450)Memory used [KB]: 895
% 0.21/0.54 % (7450)Time elapsed: 0.002 s
% 0.21/0.54 % (7450)Instructions burned: 2 (million)
% 0.21/0.54 % (7450)------------------------------
% 0.21/0.54 % (7450)------------------------------
% 0.21/0.54 TRYING [5]
% 0.21/0.54 % (7454)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.54 % (7457)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.21/0.54 % (7471)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.54 % (7470)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.55 % (7445)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)
% 0.21/0.55 % (7471)First to succeed.
% 0.21/0.55 % (7447)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.55 % (7449)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.55 % (7460)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.55 % (7446)Also succeeded, but the first one will report.
% 0.21/0.55 % (7471)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Theorem for theBenchmark
% 0.21/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.55 % (7471)------------------------------
% 0.21/0.55 % (7471)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.55 % (7471)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.55 % (7471)Termination reason: Refutation
% 0.21/0.55
% 0.21/0.55 % (7471)Memory used [KB]: 5628
% 0.21/0.55 % (7471)Time elapsed: 0.138 s
% 0.21/0.55 % (7471)Instructions burned: 7 (million)
% 0.21/0.55 % (7471)------------------------------
% 0.21/0.55 % (7471)------------------------------
% 0.21/0.55 % (7439)Success in time 0.181 s
%------------------------------------------------------------------------------