TSTP Solution File: MGT032+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT032+2 : 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 : n002.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 19:44:46 EDT 2023
% Result : Theorem 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 186 ( 67 ~; 55 |; 50 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 79 (; 61 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45,plain,
$false,
inference(subsumption_resolution,[],[f44,f34]) ).
fof(f34,plain,
sP0(sK3(sK2),sK2),
inference(resolution,[],[f33,f28]) ).
fof(f28,plain,
! [X1] :
( ~ in_environment(sK2,X1)
| sP0(X1,sK2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ! [X1] :
( sP0(X1,sK2)
| ~ in_environment(sK2,X1) )
& stable(sK2)
& environment(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f14,f19]) ).
fof(f19,plain,
( ? [X0] :
( ! [X1] :
( sP0(X1,X0)
| ~ in_environment(X0,X1) )
& stable(X0)
& environment(X0) )
=> ( ! [X1] :
( sP0(X1,sK2)
| ~ in_environment(sK2,X1) )
& stable(sK2)
& environment(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0] :
( ! [X1] :
( sP0(X1,X0)
| ~ in_environment(X0,X1) )
& stable(X0)
& environment(X0) ),
inference(definition_folding,[],[f8,f13]) ).
fof(f13,plain,
! [X1,X0] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f8,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1) )
& stable(X0)
& environment(X0) ),
inference(flattening,[],[f7]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1) )
& stable(X0)
& environment(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,plain,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> selection_favors(efficient_producers,first_movers,X2) )
& in_environment(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( ! [X3] :
( ( greater_or_equal(X3,X4)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) )
& in_environment(X0,X4) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( ! [X3] :
( ( greater_or_equal(X3,X4)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) )
& in_environment(X0,X4) ) ),
file('/export/starexec/sandbox2/tmp/tmp.e4ygQD6FOb/Vampire---4.8_30725',prove_t1) ).
fof(f33,plain,
in_environment(sK2,sK3(sK2)),
inference(subsumption_resolution,[],[f32,f26]) ).
fof(f26,plain,
environment(sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
( in_environment(sK2,sK3(sK2))
| ~ environment(sK2) ),
inference(resolution,[],[f29,f27]) ).
fof(f27,plain,
stable(sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0] :
( ~ stable(X0)
| in_environment(X0,sK3(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK3(X0)) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f10,f21]) ).
fof(f21,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1) )
=> ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f9]) ).
fof(f9,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,plain,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( ! [X3] :
( ( greater_or_equal(X3,X4)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X0,X4) ) ),
file('/export/starexec/sandbox2/tmp/tmp.e4ygQD6FOb/Vampire---4.8_30725',l1) ).
fof(f44,plain,
~ sP0(sK3(sK2),sK2),
inference(resolution,[],[f43,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ~ selection_favors(efficient_producers,first_movers,sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( ~ selection_favors(efficient_producers,first_movers,sK1(X0,X1))
& greater_or_equal(sK1(X0,X1),X0)
& subpopulations(first_movers,efficient_producers,X1,sK1(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f17]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ~ selection_favors(efficient_producers,first_movers,sK1(X0,X1))
& greater_or_equal(sK1(X0,X1),X0)
& subpopulations(first_movers,efficient_producers,X1,sK1(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
! [X1,X0] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f13]) ).
fof(f43,plain,
selection_favors(efficient_producers,first_movers,sK1(sK3(sK2),sK2)),
inference(resolution,[],[f42,f38]) ).
fof(f38,plain,
( ~ greater(growth_rate(efficient_producers,sK1(sK3(sK2),sK2)),growth_rate(first_movers,sK1(sK3(sK2),sK2)))
| selection_favors(efficient_producers,first_movers,sK1(sK3(sK2),sK2)) ),
inference(subsumption_resolution,[],[f37,f26]) ).
fof(f37,plain,
( ~ greater(growth_rate(efficient_producers,sK1(sK3(sK2),sK2)),growth_rate(first_movers,sK1(sK3(sK2),sK2)))
| selection_favors(efficient_producers,first_movers,sK1(sK3(sK2),sK2))
| ~ environment(sK2) ),
inference(resolution,[],[f31,f36]) ).
fof(f36,plain,
subpopulations(first_movers,efficient_producers,sK2,sK1(sK3(sK2),sK2)),
inference(resolution,[],[f23,f34]) ).
fof(f23,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| subpopulations(first_movers,efficient_producers,X1,sK1(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| selection_favors(X2,X1,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( greater(growth_rate(X2,X3),growth_rate(X1,X3))
& subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.e4ygQD6FOb/Vampire---4.8_30725',mp1_high_growth_rates) ).
fof(f42,plain,
greater(growth_rate(efficient_producers,sK1(sK3(sK2),sK2)),growth_rate(first_movers,sK1(sK3(sK2),sK2))),
inference(subsumption_resolution,[],[f41,f26]) ).
fof(f41,plain,
( greater(growth_rate(efficient_producers,sK1(sK3(sK2),sK2)),growth_rate(first_movers,sK1(sK3(sK2),sK2)))
| ~ environment(sK2) ),
inference(subsumption_resolution,[],[f40,f27]) ).
fof(f40,plain,
( greater(growth_rate(efficient_producers,sK1(sK3(sK2),sK2)),growth_rate(first_movers,sK1(sK3(sK2),sK2)))
| ~ stable(sK2)
| ~ environment(sK2) ),
inference(subsumption_resolution,[],[f39,f35]) ).
fof(f35,plain,
greater_or_equal(sK1(sK3(sK2),sK2),sK3(sK2)),
inference(resolution,[],[f24,f34]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| greater_or_equal(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
( ~ greater_or_equal(sK1(sK3(sK2),sK2),sK3(sK2))
| greater(growth_rate(efficient_producers,sK1(sK3(sK2),sK2)),growth_rate(first_movers,sK1(sK3(sK2),sK2)))
| ~ stable(sK2)
| ~ environment(sK2) ),
inference(resolution,[],[f30,f36]) ).
fof(f30,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK3(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 30 17:16:36 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.18/0.41 % (30831)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.42 % (30837)dis+11_4:5_nm=4_216 on Vampire---4 for (216ds/0Mi)
% 0.18/0.42 % (30833)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on Vampire---4 for (569ds/0Mi)
% 0.18/0.42 % (30836)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on Vampire---4 for (396ds/0Mi)
% 0.18/0.42 % (30832)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on Vampire---4 for (1451ds/0Mi)
% 0.18/0.42 % (30838)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on Vampire---4 for (1451ds/0Mi)
% 0.18/0.42 % (30834)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on Vampire---4 for (476ds/0Mi)
% 0.18/0.42 % (30835)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on Vampire---4 for (470ds/0Mi)
% 0.18/0.42 Detected minimum model sizes of [1,1,1,1,1]
% 0.18/0.42 TRYING [1]
% 0.18/0.42 TRYING [1]
% 0.18/0.42 % (30836)First to succeed.
% 0.18/0.42 Detected maximum model sizes of [max,2,max,1,max]
% 0.18/0.42 Detected minimum model sizes of [1,1,1,1,1]
% 0.18/0.42 TRYING [1,1,1,1,1]
% 0.18/0.42 Detected maximum model sizes of [max,2,max,1,max]
% 0.18/0.42 TRYING [1,1,1,1,1]
% 0.18/0.42 TRYING [2]
% 0.18/0.42 TRYING [2]
% 0.18/0.42 TRYING [2,1,1,1,1]
% 0.18/0.42 TRYING [2,1,1,1,1]
% 0.18/0.42 TRYING [2,2,1,1,1]
% 0.18/0.42 TRYING [2,2,1,1,1]
% 0.18/0.42 TRYING [2,1,2,1,1]
% 0.18/0.42 TRYING [3]
% 0.18/0.42 TRYING [2,1,2,1,1]
% 0.18/0.42 TRYING [3]
% 0.18/0.42 % (30837)Also succeeded, but the first one will report.
% 0.18/0.42 TRYING [2,1,1,1,2]
% 0.18/0.42 TRYING [2,1,1,1,2]
% 0.18/0.42 TRYING [2,2,1,1,2]
% 0.18/0.42 TRYING [2,2,1,1,2]
% 0.18/0.42 % (30836)Refutation found. Thanks to Tanya!
% 0.18/0.42 % SZS status Theorem for Vampire---4
% 0.18/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.18/0.42 % (30836)------------------------------
% 0.18/0.42 % (30836)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.42 % (30836)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.42 % (30836)Termination reason: Refutation
% 0.18/0.42
% 0.18/0.42 % (30836)Memory used [KB]: 895
% 0.18/0.42 % (30836)Time elapsed: 0.004 s
% 0.18/0.42 % (30836)------------------------------
% 0.18/0.42 % (30836)------------------------------
% 0.18/0.42 % (30831)Success in time 0.071 s
% 0.18/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------