TSTP Solution File: MGT023+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : MGT023+1 : 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 : n009.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 17:50:56 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 6 unt; 0 def)
% Number of atoms : 226 ( 18 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 297 ( 120 ~; 118 |; 46 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 56 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f73,plain,
$false,
inference(avatar_sat_refutation,[],[f63,f70,f72]) ).
fof(f72,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f71]) ).
fof(f71,plain,
( $false
| spl3_2 ),
inference(resolution,[],[f62,f20]) ).
fof(f20,plain,
stable(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ~ in_environment(sK0,critical_point(sK0))
& stable(sK0)
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f12]) ).
fof(f12,plain,
( ? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) )
=> ( ~ in_environment(sK0,critical_point(sK0))
& stable(sK0)
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,critical_point(X0)) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,critical_point(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(f62,plain,
( ~ stable(sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f60,plain,
( spl3_2
<=> stable(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f70,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f69]) ).
fof(f69,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f58,f19]) ).
fof(f19,plain,
environment(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f58,plain,
( ~ environment(sK0)
| spl3_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f56,plain,
( spl3_1
<=> environment(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f63,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f54,f60,f56]) ).
fof(f54,plain,
( ~ stable(sK0)
| ~ environment(sK0) ),
inference(resolution,[],[f52,f21]) ).
fof(f21,plain,
~ in_environment(sK0,critical_point(sK0)),
inference(cnf_transformation,[],[f13]) ).
fof(f52,plain,
! [X0] :
( in_environment(X0,critical_point(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ~ environment(X0)
| ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,critical_point(X0))
| ~ stable(X0) ),
inference(resolution,[],[f47,f23]) ).
fof(f23,plain,
! [X0] :
( in_environment(X0,sK1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK1(X0))
& ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f14]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) )
=> ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK1(X0))
& ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ) ),
inference(flattening,[],[f10]) ).
fof(f10,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
fof(f47,plain,
! [X1] :
( ~ in_environment(X1,sK1(X1))
| ~ stable(X1)
| in_environment(X1,critical_point(X1))
| ~ environment(X1) ),
inference(duplicate_literal_removal,[],[f39]) ).
fof(f39,plain,
! [X1] :
( ~ environment(X1)
| ~ in_environment(X1,sK1(X1))
| ~ stable(X1)
| ~ environment(X1)
| in_environment(X1,critical_point(X1))
| ~ stable(X1) ),
inference(superposition,[],[f23,f37]) ).
fof(f37,plain,
! [X0] :
( critical_point(X0) = sK1(X0)
| ~ in_environment(X0,sK1(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ~ stable(X0)
| ~ stable(X0)
| ~ environment(X0)
| critical_point(X0) = sK1(X0)
| ~ stable(X0)
| ~ environment(X0)
| ~ environment(X0)
| ~ in_environment(X0,sK1(X0))
| ~ environment(X0)
| critical_point(X0) = sK1(X0)
| ~ in_environment(X0,sK1(X0)) ),
inference(resolution,[],[f34,f29]) ).
fof(f29,plain,
! [X0,X1] :
( greater(sK2(X0,sK1(X1)),sK1(X1))
| ~ in_environment(X0,sK1(X1))
| ~ environment(X0)
| ~ environment(X1)
| critical_point(X0) = sK1(X1)
| ~ stable(X1) ),
inference(resolution,[],[f27,f22]) ).
fof(f22,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| greater(sK2(X0,X1),X1)
| critical_point(X0) = X1
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ( greater(sK2(X0,X1),X1)
& subpopulations(first_movers,efficient_producers,X0,sK2(X0,X1))
& ~ greater(growth_rate(efficient_producers,sK2(X0,X1)),growth_rate(first_movers,sK2(X0,X1))) )
| critical_point(X0) = X1
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f16,f17]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
=> ( greater(sK2(X0,X1),X1)
& subpopulations(first_movers,efficient_producers,X0,sK2(X0,X1))
& ~ greater(growth_rate(efficient_producers,sK2(X0,X1)),growth_rate(first_movers,sK2(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ? [X2] :
( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| critical_point(X0) = X1
| ~ environment(X0) ),
inference(rectify,[],[f7]) ).
fof(f7,plain,
! [X1,X0] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(X1,X0)
| ? [X2] :
( greater(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| critical_point(X1) = X0
| ~ environment(X1) ),
inference(flattening,[],[f6]) ).
fof(f6,plain,
! [X1,X0] :
( critical_point(X1) = X0
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2) )
| ~ in_environment(X1,X0)
| ~ environment(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,plain,
! [X1,X0] :
( ( ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
& ! [X2] :
( ( greater(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X1,X0)
& environment(X1) )
=> critical_point(X1) = X0 ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& environment(X0) )
=> critical_point(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f34,plain,
! [X0,X1] :
( ~ greater(sK2(X0,sK1(X1)),sK1(X0))
| ~ environment(X0)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X0,sK1(X1))
| critical_point(X0) = sK1(X1)
| ~ stable(X0) ),
inference(resolution,[],[f33,f22]) ).
fof(f33,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| critical_point(X0) = X1
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(sK2(X0,X1),sK1(X0))
| ~ in_environment(X0,X1) ),
inference(duplicate_literal_removal,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| critical_point(X0) = X1
| ~ environment(X0)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| critical_point(X0) = X1
| ~ stable(X0)
| ~ greater(sK2(X0,X1),sK1(X0)) ),
inference(resolution,[],[f31,f26]) ).
fof(f26,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sK2(X0,X1))
| critical_point(X0) = X1
| ~ environment(X0)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X3,X4,X5] :
( ~ subpopulations(first_movers,efficient_producers,X5,sK2(X4,X3))
| ~ environment(X4)
| ~ environment(X5)
| ~ stable(X5)
| ~ greater(sK2(X4,X3),sK1(X5))
| greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
| critical_point(X4) = X3
| ~ in_environment(X4,X3) ),
inference(resolution,[],[f25,f24]) ).
fof(f24,plain,
! [X2,X0] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sK1(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sK2(X0,X1)),growth_rate(first_movers,sK2(X0,X1)))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| critical_point(X0) = X1
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 03:11:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 % (29601)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)
% 0.19/0.44 % (29593)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)
% 0.19/0.44 % (29601)First to succeed.
% 0.19/0.45 % (29593)Also succeeded, but the first one will report.
% 0.19/0.45 % (29601)Refutation found. Thanks to Tanya!
% 0.19/0.45 % SZS status Theorem for theBenchmark
% 0.19/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.45 % (29601)------------------------------
% 0.19/0.45 % (29601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.45 % (29601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.45 % (29601)Termination reason: Refutation
% 0.19/0.45
% 0.19/0.45 % (29601)Memory used [KB]: 6012
% 0.19/0.45 % (29601)Time elapsed: 0.050 s
% 0.19/0.45 % (29601)Instructions burned: 2 (million)
% 0.19/0.45 % (29601)------------------------------
% 0.19/0.45 % (29601)------------------------------
% 0.19/0.45 % (29578)Success in time 0.119 s
%------------------------------------------------------------------------------