TSTP Solution File: MGT025+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT025+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n003.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 : Fri Sep 1 19:44:37 EDT 2023
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 135 ( 22 unt; 0 def)
% Number of atoms : 483 ( 62 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 510 ( 162 ~; 219 |; 107 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 144 (; 138 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f226,plain,
$false,
inference(subsumption_resolution,[],[f225,f183]) ).
fof(f183,plain,
greater(zero,zero),
inference(forward_demodulation,[],[f177,f163]) ).
fof(f163,plain,
zero = growth_rate(efficient_producers,sK5),
inference(unit_resulting_resolution,[],[f90,f161,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ constant(cardinality_at_time(X1,X0))
| zero = growth_rate(X1,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( ( greater(zero,growth_rate(X1,X0))
| ~ decreases(cardinality_at_time(X1,X0)) )
& ( greater(growth_rate(X1,X0),zero)
| ~ increases(cardinality_at_time(X1,X0)) )
& ( zero = growth_rate(X1,X0)
| ~ constant(cardinality_at_time(X1,X0)) ) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X2,X0] :
( ( ( greater(zero,growth_rate(X0,X2))
| ~ decreases(cardinality_at_time(X0,X2)) )
& ( greater(growth_rate(X0,X2),zero)
| ~ increases(cardinality_at_time(X0,X2)) )
& ( zero = growth_rate(X0,X2)
| ~ constant(cardinality_at_time(X0,X2)) ) )
| ~ sP0(X2,X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X2,X0] :
( ( ( greater(zero,growth_rate(X0,X2))
| ~ decreases(cardinality_at_time(X0,X2)) )
& ( greater(growth_rate(X0,X2),zero)
| ~ increases(cardinality_at_time(X0,X2)) )
& ( zero = growth_rate(X0,X2)
| ~ constant(cardinality_at_time(X0,X2)) ) )
| ~ sP0(X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f161,plain,
constant(cardinality_at_time(efficient_producers,sK5)),
inference(subsumption_resolution,[],[f160,f150]) ).
fof(f150,plain,
( greater(zero,growth_rate(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f148,f96]) ).
fof(f96,plain,
( ~ decreases(cardinality_at_time(efficient_producers,sK5))
| greater(zero,growth_rate(efficient_producers,sK5)) ),
inference(resolution,[],[f90,f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ decreases(cardinality_at_time(X1,X0))
| greater(zero,growth_rate(X1,X0)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f148,plain,
( decreases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(duplicate_literal_removal,[],[f147]) ).
fof(f147,plain,
( constant(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5))
| decreases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f142,f120]) ).
fof(f120,plain,
( greater(zero,growth_rate(first_movers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5))
| decreases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f118,f93]) ).
fof(f93,plain,
( ~ decreases(cardinality_at_time(first_movers,sK5))
| greater(zero,growth_rate(first_movers,sK5)) ),
inference(resolution,[],[f89,f63]) ).
fof(f89,plain,
sP0(sK5,first_movers),
inference(unit_resulting_resolution,[],[f49,f75,f78,f81,f64]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ subpopulation(X0,X1,X2)
| ~ greater(cardinality_at_time(X0,X2),zero)
| sP0(X2,X0)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( sP0(X2,X0)
| ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(definition_folding,[],[f27,f32]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ( greater(zero,growth_rate(X0,X2))
| ~ decreases(cardinality_at_time(X0,X2)) )
& ( greater(growth_rate(X0,X2),zero)
| ~ increases(cardinality_at_time(X0,X2)) )
& ( zero = growth_rate(X0,X2)
| ~ constant(cardinality_at_time(X0,X2)) ) )
| ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ( greater(zero,growth_rate(X0,X2))
| ~ decreases(cardinality_at_time(X0,X2)) )
& ( greater(growth_rate(X0,X2),zero)
| ~ increases(cardinality_at_time(X0,X2)) )
& ( zero = growth_rate(X0,X2)
| ~ constant(cardinality_at_time(X0,X2)) ) )
| ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( greater(cardinality_at_time(X0,X2),zero)
& subpopulation(X0,X1,X2)
& in_environment(X1,X2)
& environment(X1) )
=> ( ( decreases(cardinality_at_time(X0,X2))
=> greater(zero,growth_rate(X0,X2)) )
& ( increases(cardinality_at_time(X0,X2))
=> greater(growth_rate(X0,X2),zero) )
& ( constant(cardinality_at_time(X0,X2))
=> zero = growth_rate(X0,X2) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ( greater(cardinality_at_time(X1,X2),zero)
& subpopulation(X1,X0,X2)
& in_environment(X0,X2)
& environment(X0) )
=> ( ( decreases(cardinality_at_time(X1,X2))
=> greater(zero,growth_rate(X1,X2)) )
& ( increases(cardinality_at_time(X1,X2))
=> greater(growth_rate(X1,X2),zero) )
& ( constant(cardinality_at_time(X1,X2))
=> zero = growth_rate(X1,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxlWKvLHHF/Vampire---4.8_30823',mp_growth_rate) ).
fof(f81,plain,
greater(cardinality_at_time(first_movers,sK5),zero),
inference(unit_resulting_resolution,[],[f49,f50,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( greater(cardinality_at_time(efficient_producers,X1),zero)
& greater(cardinality_at_time(first_movers,X1),zero) )
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( greater(cardinality_at_time(efficient_producers,X1),zero)
& greater(cardinality_at_time(first_movers,X1),zero) )
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( greater(cardinality_at_time(efficient_producers,X1),zero)
& greater(cardinality_at_time(first_movers,X1),zero) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& environment(X0) )
=> ( greater(cardinality_at_time(efficient_producers,X2),zero)
& greater(cardinality_at_time(first_movers,X2),zero) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxlWKvLHHF/Vampire---4.8_30823',mp_non_zero_producers) ).
fof(f50,plain,
subpopulations(first_movers,efficient_producers,sK4,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ( ~ greater(zero,growth_rate(first_movers,sK5))
| ~ greater(growth_rate(efficient_producers,sK5),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK5))
| ~ greater(growth_rate(first_movers,sK5),zero) )
& ( zero != growth_rate(efficient_producers,sK5)
| zero != growth_rate(first_movers,sK5) )
& constant(number_of_organizations(sK4,sK5))
& subpopulations(first_movers,efficient_producers,sK4,sK5)
& environment(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f17,f39]) ).
fof(f39,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) )
=> ( ( ~ greater(zero,growth_rate(first_movers,sK5))
| ~ greater(growth_rate(efficient_producers,sK5),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK5))
| ~ greater(growth_rate(first_movers,sK5),zero) )
& ( zero != growth_rate(efficient_producers,sK5)
| zero != growth_rate(first_movers,sK5) )
& constant(number_of_organizations(sK4,sK5))
& subpopulations(first_movers,efficient_producers,sK4,sK5)
& environment(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f17,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,[],[f16]) ).
fof(f16,plain,
? [X0,X1] :
( ( ~ greater(zero,growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,X1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,X1))
| ~ greater(growth_rate(first_movers,X1),zero) )
& ( zero != growth_rate(efficient_producers,X1)
| zero != growth_rate(first_movers,X1) )
& constant(number_of_organizations(X0,X1))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
~ ! [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) ) ) ),
inference(rectify,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0,X2] :
( ( constant(number_of_organizations(X0,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) )
| ( greater(zero,growth_rate(efficient_producers,X2))
& greater(growth_rate(first_movers,X2),zero) )
| ( zero = growth_rate(efficient_producers,X2)
& zero = growth_rate(first_movers,X2) ) ) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0,X2] :
( ( constant(number_of_organizations(X0,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) )
| ( greater(zero,growth_rate(efficient_producers,X2))
& greater(growth_rate(first_movers,X2),zero) )
| ( zero = growth_rate(efficient_producers,X2)
& zero = growth_rate(first_movers,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxlWKvLHHF/Vampire---4.8_30823',prove_l7) ).
fof(f78,plain,
subpopulation(first_movers,sK4,sK5),
inference(unit_resulting_resolution,[],[f49,f75,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| subpopulation(first_movers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X2] :
( ( in_environment(X0,X2)
& environment(X0) )
=> ( subpopulation(efficient_producers,X0,X2)
& subpopulation(first_movers,X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxlWKvLHHF/Vampire---4.8_30823',mp_subpopulations) ).
fof(f75,plain,
in_environment(sK4,sK5),
inference(unit_resulting_resolution,[],[f49,f50,f58]) ).
fof(f58,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> in_environment(X0,X1) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& environment(X0) )
=> in_environment(X0,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.KxlWKvLHHF/Vampire---4.8_30823',mp_time_point_occur) ).
fof(f49,plain,
environment(sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f118,plain,
( decreases(cardinality_at_time(first_movers,sK5))
| decreases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f116,f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| constant(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ( constant(X0)
& constant(X1) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f47]) ).
fof(f47,plain,
! [X2,X1] :
( ( constant(X2)
& constant(X1) )
| ~ sP2(X2,X1) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X2,X1] :
( ( constant(X2)
& constant(X1) )
| ~ sP2(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f116,plain,
( sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| decreases(cardinality_at_time(first_movers,sK5))
| decreases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f110,f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| decreases(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( decreases(X0)
& increases(X1) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X2,X1] :
( ( decreases(X2)
& increases(X1) )
| ~ sP3(X2,X1) ),
inference(nnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X2,X1] :
( ( decreases(X2)
& increases(X1) )
| ~ sP3(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f110,plain,
( sP3(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| decreases(cardinality_at_time(first_movers,sK5))
| sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5)) ),
inference(trivial_inequality_removal,[],[f109]) ).
fof(f109,plain,
( number_of_organizations(sK4,sK5) != number_of_organizations(sK4,sK5)
| sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| decreases(cardinality_at_time(first_movers,sK5))
| sP3(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5)) ),
inference(superposition,[],[f85,f106]) ).
fof(f106,plain,
number_of_organizations(sK4,sK5) = sum(cardinality_at_time(first_movers,sK5),cardinality_at_time(efficient_producers,sK5)),
inference(trivial_inequality_removal,[],[f105]) ).
fof(f105,plain,
( number_of_organizations(sK4,sK5) = sum(cardinality_at_time(first_movers,sK5),cardinality_at_time(efficient_producers,sK5))
| efficient_producers != efficient_producers ),
inference(resolution,[],[f101,f66]) ).
fof(f66,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| efficient_producers != X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( first_movers != X0
& efficient_producers != X0
& greater(cardinality_at_time(X0,X1),zero) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X1,X2] :
( ( first_movers != X1
& efficient_producers != X1
& greater(cardinality_at_time(X1,X2),zero) )
| ~ sP1(X1,X2) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X1,X2] :
( ( first_movers != X1
& efficient_producers != X1
& greater(cardinality_at_time(X1,X2),zero) )
| ~ sP1(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f101,plain,
( sP1(efficient_producers,sK5)
| number_of_organizations(sK4,sK5) = sum(cardinality_at_time(first_movers,sK5),cardinality_at_time(efficient_producers,sK5)) ),
inference(subsumption_resolution,[],[f99,f49]) ).
fof(f99,plain,
( sP1(efficient_producers,sK5)
| number_of_organizations(sK4,sK5) = sum(cardinality_at_time(first_movers,sK5),cardinality_at_time(efficient_producers,sK5))
| ~ environment(sK4) ),
inference(resolution,[],[f68,f77]) ).
fof(f77,plain,
subpopulation(efficient_producers,sK4,sK5),
inference(unit_resulting_resolution,[],[f49,f75,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| subpopulation(efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ subpopulation(X1,X0,X2)
| sP1(X1,X2)
| number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| sP1(X1,X2)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(definition_folding,[],[f29,f34]) ).
fof(f29,plain,
! [X0,X1,X2] :
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ( first_movers != X1
& efficient_producers != X1
& greater(cardinality_at_time(X1,X2),zero) )
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ( first_movers != X1
& efficient_producers != X1
& greater(cardinality_at_time(X1,X2),zero) )
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( ( ( greater(cardinality_at_time(X1,X2),zero)
=> ( first_movers = X1
| efficient_producers = X1 ) )
& subpopulation(X1,X0,X2)
& environment(X0) )
=> number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.KxlWKvLHHF/Vampire---4.8_30823',mp_only_members) ).
fof(f85,plain,
! [X0,X1] :
( number_of_organizations(sK4,sK5) != sum(X1,X0)
| sP2(X0,X1)
| decreases(X1)
| sP3(X0,X1) ),
inference(resolution,[],[f73,f51]) ).
fof(f51,plain,
constant(number_of_organizations(sK4,sK5)),
inference(cnf_transformation,[],[f40]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ constant(X0)
| sP3(X2,X1)
| sP2(X2,X1)
| decreases(X1)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( increases(X2)
& decreases(X1) )
| sP3(X2,X1)
| sP2(X2,X1)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(definition_folding,[],[f31,f37,f36]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( increases(X2)
& decreases(X1) )
| ( decreases(X2)
& increases(X1) )
| ( constant(X2)
& constant(X1) )
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( increases(X2)
& decreases(X1) )
| ( decreases(X2)
& increases(X1) )
| ( constant(X2)
& constant(X1) )
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( constant(X0)
& sum(X1,X2) = X0 )
=> ( ( increases(X2)
& decreases(X1) )
| ( decreases(X2)
& increases(X1) )
| ( constant(X2)
& constant(X1) ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X4,X5] :
( ( constant(X3)
& sum(X4,X5) = X3 )
=> ( ( increases(X5)
& decreases(X4) )
| ( decreases(X5)
& increases(X4) )
| ( constant(X5)
& constant(X4) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KxlWKvLHHF/Vampire---4.8_30823',mp_abc_sum_increase) ).
fof(f142,plain,
( ~ greater(zero,growth_rate(first_movers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f140,f54]) ).
fof(f54,plain,
( ~ greater(growth_rate(efficient_producers,sK5),zero)
| ~ greater(zero,growth_rate(first_movers,sK5)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f140,plain,
( greater(growth_rate(efficient_producers,sK5),zero)
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f137,f97]) ).
fof(f97,plain,
( ~ increases(cardinality_at_time(efficient_producers,sK5))
| greater(growth_rate(efficient_producers,sK5),zero) ),
inference(resolution,[],[f90,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ increases(cardinality_at_time(X1,X0))
| greater(growth_rate(X1,X0),zero) ),
inference(cnf_transformation,[],[f42]) ).
fof(f137,plain,
( increases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(subsumption_resolution,[],[f136,f130]) ).
fof(f130,plain,
( greater(zero,growth_rate(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f128,f96]) ).
fof(f128,plain,
( decreases(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f126,f72]) ).
fof(f126,plain,
( sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| decreases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f111,f70]) ).
fof(f111,plain,
( sP3(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5)) ),
inference(trivial_inequality_removal,[],[f108]) ).
fof(f108,plain,
( number_of_organizations(sK4,sK5) != number_of_organizations(sK4,sK5)
| sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| sP3(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5)) ),
inference(superposition,[],[f86,f106]) ).
fof(f86,plain,
! [X0,X1] :
( number_of_organizations(sK4,sK5) != sum(X1,X0)
| sP2(X0,X1)
| increases(X0)
| sP3(X0,X1) ),
inference(resolution,[],[f74,f51]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ constant(X0)
| sP3(X2,X1)
| sP2(X2,X1)
| increases(X2)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f136,plain,
( constant(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| ~ greater(zero,growth_rate(efficient_producers,sK5)) ),
inference(resolution,[],[f134,f53]) ).
fof(f53,plain,
( ~ greater(growth_rate(first_movers,sK5),zero)
| ~ greater(zero,growth_rate(efficient_producers,sK5)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f134,plain,
( greater(growth_rate(first_movers,sK5),zero)
| constant(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f132,f94]) ).
fof(f94,plain,
( ~ increases(cardinality_at_time(first_movers,sK5))
| greater(growth_rate(first_movers,sK5),zero) ),
inference(resolution,[],[f89,f62]) ).
fof(f132,plain,
( increases(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f127,f72]) ).
fof(f127,plain,
( sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f111,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| increases(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f160,plain,
( constant(cardinality_at_time(efficient_producers,sK5))
| ~ greater(zero,growth_rate(efficient_producers,sK5)) ),
inference(resolution,[],[f151,f53]) ).
fof(f151,plain,
( greater(growth_rate(first_movers,sK5),zero)
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f149,f94]) ).
fof(f149,plain,
( increases(cardinality_at_time(first_movers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(duplicate_literal_removal,[],[f145]) ).
fof(f145,plain,
( constant(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f142,f124]) ).
fof(f124,plain,
( greater(zero,growth_rate(first_movers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f122,f93]) ).
fof(f122,plain,
( decreases(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(first_movers,sK5))
| constant(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f117,f72]) ).
fof(f117,plain,
( sP2(cardinality_at_time(efficient_producers,sK5),cardinality_at_time(first_movers,sK5))
| decreases(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f110,f69]) ).
fof(f90,plain,
sP0(sK5,efficient_producers),
inference(unit_resulting_resolution,[],[f49,f75,f77,f83,f64]) ).
fof(f83,plain,
greater(cardinality_at_time(efficient_producers,sK5),zero),
inference(unit_resulting_resolution,[],[f49,f50,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f177,plain,
greater(growth_rate(efficient_producers,sK5),zero),
inference(unit_resulting_resolution,[],[f175,f141]) ).
fof(f141,plain,
( greater(growth_rate(efficient_producers,sK5),zero)
| constant(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f139,f97]) ).
fof(f139,plain,
( increases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(first_movers,sK5)) ),
inference(subsumption_resolution,[],[f138,f131]) ).
fof(f131,plain,
( greater(zero,growth_rate(efficient_producers,sK5))
| constant(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f129,f96]) ).
fof(f129,plain,
( decreases(cardinality_at_time(efficient_producers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f126,f71]) ).
fof(f71,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| constant(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f138,plain,
( constant(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| ~ greater(zero,growth_rate(efficient_producers,sK5)) ),
inference(resolution,[],[f135,f53]) ).
fof(f135,plain,
( greater(growth_rate(first_movers,sK5),zero)
| constant(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5)) ),
inference(resolution,[],[f133,f94]) ).
fof(f133,plain,
( increases(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(efficient_producers,sK5))
| constant(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f127,f71]) ).
fof(f175,plain,
~ constant(cardinality_at_time(first_movers,sK5)),
inference(unit_resulting_resolution,[],[f89,f167,f61]) ).
fof(f167,plain,
zero != growth_rate(first_movers,sK5),
inference(unit_resulting_resolution,[],[f163,f52]) ).
fof(f52,plain,
( zero != growth_rate(first_movers,sK5)
| zero != growth_rate(efficient_producers,sK5) ),
inference(cnf_transformation,[],[f40]) ).
fof(f225,plain,
~ greater(zero,zero),
inference(forward_demodulation,[],[f223,f163]) ).
fof(f223,plain,
~ greater(zero,growth_rate(efficient_producers,sK5)),
inference(unit_resulting_resolution,[],[f197,f53]) ).
fof(f197,plain,
greater(growth_rate(first_movers,sK5),zero),
inference(unit_resulting_resolution,[],[f89,f180,f62]) ).
fof(f180,plain,
increases(cardinality_at_time(first_movers,sK5)),
inference(unit_resulting_resolution,[],[f175,f157]) ).
fof(f157,plain,
( increases(cardinality_at_time(first_movers,sK5))
| constant(cardinality_at_time(first_movers,sK5)) ),
inference(duplicate_literal_removal,[],[f152]) ).
fof(f152,plain,
( constant(cardinality_at_time(first_movers,sK5))
| constant(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f143,f125]) ).
fof(f125,plain,
( greater(zero,growth_rate(first_movers,sK5))
| constant(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f123,f93]) ).
fof(f123,plain,
( decreases(cardinality_at_time(first_movers,sK5))
| increases(cardinality_at_time(first_movers,sK5))
| constant(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f117,f71]) ).
fof(f143,plain,
( ~ greater(zero,growth_rate(first_movers,sK5))
| constant(cardinality_at_time(first_movers,sK5)) ),
inference(resolution,[],[f141,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : MGT025+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35 % Computer : n003.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 : Wed Aug 30 17:03:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % (30930)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (30934)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.20/0.42 % (30932)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.20/0.42 % (30933)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.20/0.42 % (30935)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.20/0.42 % (30936)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.20/0.42 % (30937)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.20/0.42 % (30931)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.20/0.42 TRYING [1]
% 0.20/0.42 TRYING [2]
% 0.20/0.43 TRYING [1]
% 0.20/0.43 TRYING [2]
% 0.20/0.43 TRYING [3]
% 0.20/0.43 % (30937)First to succeed.
% 0.20/0.43 TRYING [3]
% 0.20/0.43 % (30935)Also succeeded, but the first one will report.
% 0.20/0.43 TRYING [4]
% 0.20/0.43 % (30937)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for Vampire---4
% 0.20/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.43 % (30937)------------------------------
% 0.20/0.43 % (30937)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.43 % (30937)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.43 % (30937)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (30937)Memory used [KB]: 1023
% 0.20/0.43 % (30937)Time elapsed: 0.008 s
% 0.20/0.43 % (30937)------------------------------
% 0.20/0.43 % (30937)------------------------------
% 0.20/0.43 % (30930)Success in time 0.074 s
% 0.20/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------