TSTP Solution File: MGT036-2 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : MGT036-2 : TPTP v8.1.0. Released v2.4.0.
% 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 : n028.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 17:51:03 EDT 2022
% Result : Unsatisfiable 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 64 ( 7 unt; 0 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 284 ( 148 ~; 127 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 10 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 93 ( 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f165,plain,
$false,
inference(avatar_sat_refutation,[],[f37,f39,f60,f114,f125,f128,f137,f139,f144,f164]) ).
fof(f164,plain,
( ~ spl0_5
| spl0_10 ),
inference(avatar_split_clause,[],[f162,f76,f51]) ).
fof(f51,plain,
( spl0_5
<=> subpopulations(efficient_producers,first_movers,sk1,sk2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f76,plain,
( spl0_10
<=> greater(zero,growth_rate(efficient_producers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f162,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| spl0_10 ),
inference(resolution,[],[f160,f12]) ).
fof(f12,axiom,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_12) ).
fof(f160,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) )
| spl0_10 ),
inference(resolution,[],[f154,f14]) ).
fof(f14,axiom,
outcompetes(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_14) ).
fof(f154,plain,
( ! [X2,X3] :
( ~ outcompetes(X3,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,X3,X2,sk2)
| ~ environment(X2) )
| spl0_10 ),
inference(resolution,[],[f77,f9]) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X1,X3))
| ~ environment(X0)
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_9) ).
fof(f77,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| spl0_10 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f144,plain,
( ~ spl0_3
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f142,f135,f27]) ).
fof(f27,plain,
( spl0_3
<=> subpopulations(first_movers,efficient_producers,sk1,sk2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f135,plain,
( spl0_17
<=> ! [X1] :
( ~ environment(X1)
| ~ in_environment(X1,sk2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f142,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ spl0_17 ),
inference(resolution,[],[f141,f12]) ).
fof(f141,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2) )
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f140]) ).
fof(f140,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) )
| ~ spl0_17 ),
inference(resolution,[],[f136,f2]) ).
fof(f2,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_2) ).
fof(f136,plain,
( ! [X1] :
( ~ in_environment(X1,sk2)
| ~ environment(X1) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,plain,
( ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f138,f132,f76]) ).
fof(f132,plain,
( spl0_16
<=> ! [X0] :
( ~ greater(zero,growth_rate(X0,sk2))
| ~ greater(resilience(X0),resilience(first_movers)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f138,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ spl0_16 ),
inference(resolution,[],[f133,f10]) ).
fof(f10,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_10) ).
fof(f133,plain,
( ! [X0] :
( ~ greater(resilience(X0),resilience(first_movers))
| ~ greater(zero,growth_rate(X0,sk2)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f137,plain,
( spl0_16
| spl0_17
| spl0_15 ),
inference(avatar_split_clause,[],[f129,f122,f135,f132]) ).
fof(f122,plain,
( spl0_15
<=> greater(zero,growth_rate(first_movers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f129,plain,
( ! [X0,X1] :
( ~ environment(X1)
| ~ greater(zero,growth_rate(X0,sk2))
| ~ in_environment(X1,sk2)
| ~ greater(resilience(X0),resilience(first_movers)) )
| spl0_15 ),
inference(resolution,[],[f124,f11]) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X2,X1))
| ~ greater(resilience(X3),resilience(X2))
| ~ in_environment(X0,X1)
| ~ greater(zero,growth_rate(X3,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_11) ).
fof(f124,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| spl0_15 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f128,plain,
( ~ spl0_15
| spl0_14 ),
inference(avatar_split_clause,[],[f126,f118,f122]) ).
fof(f118,plain,
( spl0_14
<=> subpopulations(first_movers,first_movers,sk1,sk2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f126,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| spl0_14 ),
inference(resolution,[],[f120,f4]) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( subpopulations(X0,X1,X2,X3)
| ~ greater(zero,growth_rate(X0,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_4) ).
fof(f120,plain,
( ~ subpopulations(first_movers,first_movers,sk1,sk2)
| spl0_14 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f125,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f115,f112,f51,f122,f118]) ).
fof(f112,plain,
( spl0_13
<=> ! [X0,X1] :
( ~ outcompetes(X0,X1,sk2)
| ~ subpopulations(X1,X0,sk1,sk2)
| ~ greater(zero,growth_rate(X0,sk2))
| ~ subpopulations(X0,first_movers,sk1,sk2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f115,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(first_movers,sk2))
| ~ subpopulations(first_movers,first_movers,sk1,sk2)
| ~ spl0_13 ),
inference(resolution,[],[f113,f14]) ).
fof(f113,plain,
( ! [X0,X1] :
( ~ outcompetes(X0,X1,sk2)
| ~ subpopulations(X1,X0,sk1,sk2)
| ~ subpopulations(X0,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(X0,sk2)) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( ~ spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f109,f112,f51]) ).
fof(f109,plain,
! [X0,X1] :
( ~ outcompetes(X0,X1,sk2)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ subpopulations(X0,first_movers,sk1,sk2)
| ~ greater(zero,growth_rate(X0,sk2))
| ~ subpopulations(X1,X0,sk1,sk2) ),
inference(resolution,[],[f107,f14]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] :
( ~ outcompetes(X3,X4,X2)
| ~ subpopulations(X1,X3,sk1,X2)
| ~ greater(zero,growth_rate(X1,X2))
| ~ outcompetes(X1,X0,X2)
| ~ subpopulations(X0,X1,sk1,X2)
| ~ subpopulations(X4,X3,sk1,X2) ),
inference(resolution,[],[f106,f12]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ environment(X0)
| ~ subpopulations(X5,X1,sk1,X3)
| ~ subpopulations(X1,X2,sk1,X3)
| ~ subpopulations(X4,X2,X0,X3)
| ~ greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X1,X5,X3)
| ~ outcompetes(X2,X4,X3) ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f104,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ subpopulations(X4,X2,X0,X3)
| ~ outcompetes(X1,X5,X3)
| ~ subpopulations(X1,X2,sk1,X3)
| ~ subpopulations(X1,X2,sk1,X3)
| ~ environment(X0)
| ~ subpopulations(X5,X1,sk1,X3)
| ~ greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X4,X3) ),
inference(resolution,[],[f101,f12]) ).
fof(f101,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( ~ environment(X11)
| ~ environment(X13)
| ~ subpopulations(X7,X10,sk1,X9)
| ~ subpopulations(X7,X10,X11,X9)
| ~ outcompetes(X10,X12,X9)
| ~ outcompetes(X7,X8,X9)
| ~ subpopulations(X12,X10,X13,X9)
| ~ greater(zero,growth_rate(X7,X9))
| ~ subpopulations(X8,X7,sk1,X9) ),
inference(resolution,[],[f49,f8]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( greater_or_equal(growth_rate(X2,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ outcompetes(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_8) ).
fof(f49,plain,
! [X2,X3,X1,X4,X5] :
( ~ greater_or_equal(growth_rate(X4,X3),zero)
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X2,X4,sk1,X3)
| ~ greater(zero,growth_rate(X2,X3))
| ~ subpopulations(X2,X4,X5,X3)
| ~ subpopulations(X1,X2,sk1,X3)
| ~ environment(X5) ),
inference(resolution,[],[f46,f7]) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( outcompetes(X2,X1,X3)
| ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_7) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ outcompetes(X3,X1,X2)
| ~ subpopulations(X0,X1,sk1,X2)
| ~ subpopulations(X1,X3,sk1,X2)
| ~ outcompetes(X1,X0,X2) ),
inference(resolution,[],[f44,f12]) ).
fof(f44,plain,
! [X2,X3,X0,X1,X4] :
( ~ environment(X2)
| ~ subpopulations(X0,X1,X2,X3)
| ~ subpopulations(X1,X4,sk1,X3)
| ~ outcompetes(X1,X0,X3)
| ~ outcompetes(X4,X1,X3) ),
inference(resolution,[],[f41,f12]) ).
fof(f41,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ environment(X4)
| ~ subpopulations(X1,X0,X3,X2)
| ~ outcompetes(X0,X1,X2)
| ~ outcompetes(X5,X0,X2)
| ~ environment(X3)
| ~ subpopulations(X0,X5,X4,X2) ),
inference(resolution,[],[f40,f9]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X0,X1))
| ~ outcompetes(X0,X2,X1)
| ~ subpopulations(X2,X0,X3,X1)
| ~ environment(X3) ),
inference(resolution,[],[f5,f8]) ).
fof(f5,axiom,
! [X0,X1] :
( ~ greater_or_equal(growth_rate(X0,X1),zero)
| ~ greater(zero,growth_rate(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
fof(f60,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f59,f51,f31,f27]) ).
fof(f31,plain,
( spl0_4
<=> environment(sk1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f59,plain,
( ~ environment(sk1)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| spl0_5 ),
inference(resolution,[],[f53,f1]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
fof(f53,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| spl0_5 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f39,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f38,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f33,f12]) ).
fof(f33,plain,
( ~ environment(sk1)
| spl0_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f37,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f35]) ).
fof(f35,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f29,f13]) ).
fof(f13,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_13) ).
fof(f29,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| spl0_3 ),
inference(avatar_component_clause,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : MGT036-2 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 30 03:26:48 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.49 % (14901)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=97:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/97Mi)
% 0.17/0.49 % (14884)dis+1011_1:16_fsr=off:nwc=2.0:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.17/0.50 % (14884)First to succeed.
% 0.17/0.50 % (14902)lrs+1011_1:1_aac=none:bsr=unit_only:ep=R:sac=on:sos=all:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.17/0.50 % (14884)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (14884)------------------------------
% 0.17/0.50 % (14884)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.50 % (14884)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.50 % (14884)Termination reason: Refutation
% 0.17/0.50
% 0.17/0.50 % (14884)Memory used [KB]: 6012
% 0.17/0.50 % (14884)Time elapsed: 0.113 s
% 0.17/0.50 % (14884)Instructions burned: 6 (million)
% 0.17/0.50 % (14884)------------------------------
% 0.17/0.50 % (14884)------------------------------
% 0.17/0.50 % (14878)Success in time 0.175 s
%------------------------------------------------------------------------------