TSTP Solution File: MGT032+2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---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 : n008.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 : Thu Aug 31 09:17:37 EDT 2023
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 4 unt; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 206 ( 82 ~; 64 |; 46 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 (; 53 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,plain,
$false,
inference(resolution,[],[f45,f18]) ).
fof(f18,plain,
environment(sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
( ! [X1] :
( ( ~ selection_favors(efficient_producers,first_movers,sK1(X1))
& greater_or_equal(sK1(X1),X1)
& subpopulations(first_movers,efficient_producers,sK0,sK1(X1)) )
| ~ in_environment(sK0,X1) )
& stable(sK0)
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f14,f13]) ).
fof(f13,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) )
=> ( ! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,sK0,X2) )
| ~ in_environment(sK0,X1) )
& stable(sK0)
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,sK0,X2) )
=> ( ~ selection_favors(efficient_producers,first_movers,sK1(X1))
& greater_or_equal(sK1(X1),X1)
& subpopulations(first_movers,efficient_producers,sK0,sK1(X1)) ) ),
introduced(choice_axiom,[]) ).
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/sandbox/tmp/tmp.v01bF9uOd4/Vampire---4.8_26338',prove_t1) ).
fof(f45,plain,
~ environment(sK0),
inference(duplicate_literal_removal,[],[f44]) ).
fof(f44,plain,
( ~ environment(sK0)
| ~ environment(sK0) ),
inference(resolution,[],[f43,f28]) ).
fof(f28,plain,
( in_environment(sK0,sK2(sK0))
| ~ environment(sK0) ),
inference(resolution,[],[f23,f19]) ).
fof(f19,plain,
stable(sK0),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0] :
( ~ stable(X0)
| in_environment(X0,sK2(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK2(X0)) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f10,f16]) ).
fof(f16,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,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK2(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/sandbox/tmp/tmp.v01bF9uOd4/Vampire---4.8_26338',l1) ).
fof(f43,plain,
( ~ in_environment(sK0,sK2(sK0))
| ~ environment(sK0) ),
inference(resolution,[],[f42,f20]) ).
fof(f20,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK0,sK1(X1))
| ~ in_environment(sK0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f42,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1(sK2(sK0)))
| ~ environment(sK0) ),
inference(duplicate_literal_removal,[],[f41]) ).
fof(f41,plain,
( ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1(sK2(sK0)))
| ~ environment(sK0) ),
inference(resolution,[],[f37,f28]) ).
fof(f37,plain,
( ~ in_environment(sK0,sK2(sK0))
| ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1(sK2(sK0))) ),
inference(resolution,[],[f36,f32]) ).
fof(f32,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ in_environment(sK0,X0) ),
inference(duplicate_literal_removal,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ in_environment(sK0,X0)
| ~ in_environment(sK0,X0) ),
inference(resolution,[],[f30,f22]) ).
fof(f22,plain,
! [X1] :
( ~ selection_favors(efficient_producers,first_movers,sK1(X1))
| ~ in_environment(sK0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ in_environment(sK0,X0) ),
inference(resolution,[],[f29,f18]) ).
fof(f29,plain,
! [X0] :
( ~ environment(sK0)
| selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ in_environment(sK0,X0) ),
inference(resolution,[],[f20,f25]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,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/sandbox/tmp/tmp.v01bF9uOd4/Vampire---4.8_26338',mp1_high_growth_rates) ).
fof(f36,plain,
( greater(growth_rate(efficient_producers,sK1(sK2(sK0))),growth_rate(first_movers,sK1(sK2(sK0))))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1(sK2(sK0)))
| ~ environment(sK0) ),
inference(resolution,[],[f35,f28]) ).
fof(f35,plain,
( ~ in_environment(sK0,sK2(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1(sK2(sK0)))
| greater(growth_rate(efficient_producers,sK1(sK2(sK0))),growth_rate(first_movers,sK1(sK2(sK0)))) ),
inference(resolution,[],[f34,f21]) ).
fof(f21,plain,
! [X1] :
( greater_or_equal(sK1(X1),X1)
| ~ in_environment(sK0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X0] :
( ~ greater_or_equal(X0,sK2(sK0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(resolution,[],[f33,f18]) ).
fof(f33,plain,
! [X0] :
( ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK2(sK0)) ),
inference(resolution,[],[f24,f19]) ).
fof(f24,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ greater_or_equal(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17 % Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% 0.14/0.19 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.39 % Computer : n008.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8042.1875MB
% 0.15/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Mon Aug 28 06:37:47 EDT 2023
% 0.15/0.39 % CPUTime :
% 0.15/0.39 This is a FOF_THM_RFO_NEQ problem
% 0.15/0.40 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.v01bF9uOd4/Vampire---4.8_26338
% 0.15/0.40 % (26546)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.45 % (26553)dis+3_1024_av=off:fsr=off:gsp=on:lcm=predicate:nm=4:sos=all:sp=weighted_frequency_338 on Vampire---4 for (338ds/0Mi)
% 0.20/0.45 % (26553)First to succeed.
% 0.20/0.45 % (26553)Refutation found. Thanks to Tanya!
% 0.20/0.45 % SZS status Theorem for Vampire---4
% 0.20/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.45 % (26553)------------------------------
% 0.20/0.45 % (26553)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.45 % (26553)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.45 % (26553)Termination reason: Refutation
% 0.20/0.45
% 0.20/0.45 % (26553)Memory used [KB]: 895
% 0.20/0.45 % (26553)Time elapsed: 0.003 s
% 0.20/0.45 % (26553)------------------------------
% 0.20/0.45 % (26553)------------------------------
% 0.20/0.45 % (26546)Success in time 0.049 s
% 0.20/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------