TSTP Solution File: MGT032+2 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : MGT032+2 : 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_uns --cores 0 -t %d %s
% Computer : n024.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 17:51:00 EDT 2022
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 5 unt; 0 def)
% Number of atoms : 226 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 279 ( 110 ~; 100 |; 48 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 7 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 68 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f67,plain,
$false,
inference(avatar_sat_refutation,[],[f41,f43,f45,f51,f62,f64,f66]) ).
fof(f66,plain,
( ~ spl3_6
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f65,f55,f59]) ).
fof(f59,plain,
( spl3_6
<=> in_environment(sK0,sK2(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f55,plain,
( spl3_5
<=> selection_favors(efficient_producers,first_movers,sK1(sK2(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f65,plain,
( ~ in_environment(sK0,sK2(sK0))
| ~ spl3_5 ),
inference(resolution,[],[f57,f22]) ).
fof(f22,plain,
! [X1] :
( ~ selection_favors(efficient_producers,first_movers,sK1(X1))
| ~ in_environment(sK0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( stable(sK0)
& ! [X1] :
( ~ in_environment(sK0,X1)
| ( greater_or_equal(sK1(X1),X1)
& ~ selection_favors(efficient_producers,first_movers,sK1(X1))
& subpopulations(first_movers,efficient_producers,sK0,sK1(X1)) ) )
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f15,f14]) ).
fof(f14,plain,
( ? [X0] :
( stable(X0)
& ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( greater_or_equal(X2,X1)
& ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2) ) )
& environment(X0) )
=> ( stable(sK0)
& ! [X1] :
( ~ in_environment(sK0,X1)
| ? [X2] :
( greater_or_equal(X2,X1)
& ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,sK0,X2) ) )
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,sK0,X2) )
=> ( greater_or_equal(sK1(X1),X1)
& ~ selection_favors(efficient_producers,first_movers,sK1(X1))
& subpopulations(first_movers,efficient_producers,sK0,sK1(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0] :
( stable(X0)
& ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( greater_or_equal(X2,X1)
& ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2) ) )
& environment(X0) ),
inference(flattening,[],[f10]) ).
fof(f10,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,[],[f6]) ).
fof(f6,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] :
( in_environment(X0,X4)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& greater_or_equal(X3,X4) )
=> selection_favors(efficient_producers,first_movers,X3) ) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( in_environment(X0,X4)
& ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& greater_or_equal(X3,X4) )
=> selection_favors(efficient_producers,first_movers,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1) ).
fof(f57,plain,
( selection_favors(efficient_producers,first_movers,sK1(sK2(sK0)))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f64,plain,
( ~ spl3_3
| ~ spl3_1
| spl3_6 ),
inference(avatar_split_clause,[],[f63,f59,f31,f38]) ).
fof(f38,plain,
( spl3_3
<=> stable(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f31,plain,
( spl3_1
<=> environment(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f63,plain,
( ~ environment(sK0)
| ~ stable(sK0)
| spl3_6 ),
inference(resolution,[],[f61,f25]) ).
fof(f25,plain,
! [X0] :
( in_environment(X0,sK2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| ( ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK2(X0)) )
& in_environment(X0,sK2(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f9,f17]) ).
fof(f17,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1) )
& in_environment(X0,X1) )
=> ( ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK2(X0)) )
& in_environment(X0,sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| ? [X1] :
( ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1) )
& in_environment(X0,X1) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
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/benchmark/theBenchmark.p',l1) ).
fof(f61,plain,
( ~ in_environment(sK0,sK2(sK0))
| spl3_6 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( spl3_5
| ~ spl3_6
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f53,f49,f59,f55]) ).
fof(f49,plain,
( spl3_4
<=> ! [X0] :
( selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ greater_or_equal(sK1(X0),sK2(sK0))
| ~ in_environment(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f53,plain,
( ~ in_environment(sK0,sK2(sK0))
| selection_favors(efficient_producers,first_movers,sK1(sK2(sK0)))
| ~ spl3_4 ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f52,plain,
( ~ in_environment(sK0,sK2(sK0))
| ~ in_environment(sK0,sK2(sK0))
| selection_favors(efficient_producers,first_movers,sK1(sK2(sK0)))
| ~ spl3_4 ),
inference(resolution,[],[f50,f23]) ).
fof(f23,plain,
! [X1] :
( greater_or_equal(sK1(X1),X1)
| ~ in_environment(sK0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f50,plain,
( ! [X0] :
( ~ greater_or_equal(sK1(X0),sK2(sK0))
| selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ in_environment(sK0,X0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( ~ spl3_1
| spl3_4
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f47,f35,f49,f31]) ).
fof(f35,plain,
( spl3_2
<=> ! [X0,X1] :
( ~ in_environment(sK0,X0)
| ~ greater_or_equal(sK1(X0),sK2(sK0))
| selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f47,plain,
( ! [X0] :
( selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ environment(sK0)
| ~ in_environment(sK0,X0)
| ~ greater_or_equal(sK1(X0),sK2(sK0)) )
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f46]) ).
fof(f46,plain,
( ! [X0] :
( ~ in_environment(sK0,X0)
| ~ in_environment(sK0,X0)
| ~ greater_or_equal(sK1(X0),sK2(sK0))
| selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ environment(sK0) )
| ~ spl3_2 ),
inference(resolution,[],[f36,f21]) ).
fof(f21,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK0,sK1(X1))
| ~ in_environment(sK0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,sK1(X0))
| ~ greater_or_equal(sK1(X0),sK2(sK0))
| ~ in_environment(sK0,X0)
| ~ environment(X1)
| selection_favors(efficient_producers,first_movers,sK1(X0)) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f45,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f44,plain,
( $false
| spl3_3 ),
inference(resolution,[],[f40,f24]) ).
fof(f24,plain,
stable(sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
( ~ stable(sK0)
| spl3_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f43,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f42]) ).
fof(f42,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f33,f20]) ).
fof(f20,plain,
environment(sK0),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
( ~ environment(sK0)
| spl3_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f41,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f29,f38,f35,f31]) ).
fof(f29,plain,
! [X0,X1] :
( ~ stable(sK0)
| ~ in_environment(sK0,X0)
| ~ environment(sK0)
| ~ subpopulations(first_movers,efficient_producers,X1,sK1(X0))
| ~ environment(X1)
| selection_favors(efficient_producers,first_movers,sK1(X0))
| ~ greater_or_equal(sK1(X0),sK2(sK0)) ),
inference(resolution,[],[f28,f21]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X2,X0)
| ~ greater_or_equal(X0,sK2(X2))
| selection_favors(efficient_producers,first_movers,X0)
| ~ environment(X1)
| ~ stable(X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X2) ),
inference(resolution,[],[f27,f26]) ).
fof(f26,plain,
! [X2,X0] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ greater_or_equal(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X3,X1),growth_rate(X2,X1))
| selection_favors(X3,X2,X1)
| ~ environment(X0)
| ~ subpopulations(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( selection_favors(X3,X2,X1)
| ~ environment(X0)
| ~ subpopulations(X2,X3,X0,X1)
| ~ greater(growth_rate(X3,X1),growth_rate(X2,X1)) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
! [X3,X0,X1,X2] :
( selection_favors(X2,X1,X0)
| ~ environment(X3)
| ~ subpopulations(X1,X2,X3,X0)
| ~ greater(growth_rate(X2,X0),growth_rate(X1,X0)) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
! [X2,X1,X0,X3] :
( selection_favors(X2,X1,X0)
| ~ environment(X3)
| ~ greater(growth_rate(X2,X0),growth_rate(X1,X0))
| ~ subpopulations(X1,X2,X3,X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,plain,
! [X2,X1,X0,X3] :
( ( environment(X3)
& greater(growth_rate(X2,X0),growth_rate(X1,X0))
& subpopulations(X1,X2,X3,X0) )
=> selection_favors(X2,X1,X0) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X3,X1,X2,X0] :
( ( 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/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 03:18:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.52 % (31945)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.52 % (31945)First to succeed.
% 0.21/0.52 % (31937)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.52 % (31937)Also succeeded, but the first one will report.
% 0.21/0.52 % (31945)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (31945)------------------------------
% 0.21/0.52 % (31945)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (31945)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (31945)Termination reason: Refutation
% 0.21/0.52
% 0.21/0.52 % (31945)Memory used [KB]: 5884
% 0.21/0.52 % (31945)Time elapsed: 0.062 s
% 0.21/0.52 % (31945)Instructions burned: 1 (million)
% 0.21/0.52 % (31945)------------------------------
% 0.21/0.52 % (31945)------------------------------
% 0.21/0.52 % (31922)Success in time 0.171 s
%------------------------------------------------------------------------------