TSTP Solution File: GEO222+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n003.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 16:12:22 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 85 ( 26 unt; 0 def)
% Number of atoms : 212 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 196 ( 69 ~; 99 |; 12 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 149 ( 145 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f335,plain,
$false,
inference(avatar_sat_refutation,[],[f275,f280,f332]) ).
fof(f332,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f331,plain,
( $false
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f326,f102]) ).
fof(f102,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f326,plain,
( convergent_lines(sK0,sK0)
| ~ spl4_7 ),
inference(resolution,[],[f290,f109]) ).
fof(f109,plain,
~ unorthogonal_lines(sF2,sK0),
inference(superposition,[],[f100,f105]) ).
fof(f105,plain,
sF2 = orthogonal_through_point(sK0,sK1),
introduced(function_definition,[]) ).
fof(f100,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X1,X0] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X5,X8] : ~ unorthogonal_lines(orthogonal_through_point(X5,X8),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f290,plain,
( ! [X0] :
( unorthogonal_lines(sF2,X0)
| convergent_lines(sK0,X0) )
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f287,f123]) ).
fof(f123,plain,
convergent_lines(sK0,sF2),
inference(resolution,[],[f119,f102]) ).
fof(f119,plain,
! [X4] :
( convergent_lines(sF2,X4)
| convergent_lines(sK0,X4) ),
inference(resolution,[],[f90,f113]) ).
fof(f113,plain,
convergent_lines(sF2,sK0),
inference(resolution,[],[f89,f109]) ).
fof(f89,plain,
! [X0,X1] :
( unorthogonal_lines(X1,X0)
| convergent_lines(X1,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( convergent_lines(X1,X0)
| unorthogonal_lines(X1,X0) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X6,X5] :
( unorthogonal_lines(X5,X6)
| convergent_lines(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X2,X0)
| convergent_lines(X2,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( convergent_lines(X2,X1)
| convergent_lines(X0,X1)
| ~ convergent_lines(X2,X0) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X0)
| convergent_lines(X2,X0)
| ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X1,X2,X0] :
( convergent_lines(X1,X0)
| convergent_lines(X2,X0)
| ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X1,X2,X0] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X0)
| convergent_lines(X2,X0) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f287,plain,
( ! [X0] :
( convergent_lines(sK0,X0)
| unorthogonal_lines(sF2,X0)
| ~ convergent_lines(sK0,sF2) )
| ~ spl4_7 ),
inference(resolution,[],[f283,f85]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ~ unorthogonal_lines(X0,X1)
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ( convergent_lines(X2,X1)
& unorthogonal_lines(X2,X1) )
| ~ unorthogonal_lines(X2,X0)
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ~ convergent_lines(X2,X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( convergent_lines(X2,X1)
& unorthogonal_lines(X2,X1) )
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ~ unorthogonal_lines(X2,X0)
| ~ convergent_lines(X2,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X2,X0)
& convergent_lines(X2,X0) )
=> ( ( convergent_lines(X2,X1)
& unorthogonal_lines(X2,X1) )
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) ) ) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X6,X7,X5] :
( ( unorthogonal_lines(X5,X6)
& convergent_lines(X5,X6) )
=> ( ( convergent_lines(X6,X7)
& unorthogonal_lines(X6,X7) )
| ( unorthogonal_lines(X5,X7)
& convergent_lines(X5,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oac1) ).
fof(f283,plain,
( unorthogonal_lines(sK0,sF2)
| ~ spl4_7 ),
inference(resolution,[],[f278,f111]) ).
fof(f111,plain,
~ unorthogonal_lines(sF3,sF2),
inference(superposition,[],[f100,f106]) ).
fof(f106,plain,
orthogonal_through_point(sF2,sK1) = sF3,
introduced(function_definition,[]) ).
fof(f278,plain,
( ! [X1] :
( unorthogonal_lines(sF3,X1)
| unorthogonal_lines(sK0,X1) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f277,plain,
( spl4_7
<=> ! [X1] :
( unorthogonal_lines(sF3,X1)
| unorthogonal_lines(sK0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f280,plain,
( spl4_7
| spl4_2 ),
inference(avatar_split_clause,[],[f171,f164,f277]) ).
fof(f164,plain,
( spl4_2
<=> ! [X0] :
( apart_point_and_line(X0,sF3)
| apart_point_and_line(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f171,plain,
! [X6,X5] :
( apart_point_and_line(X5,sK0)
| apart_point_and_line(X5,sF3)
| unorthogonal_lines(sF3,X6)
| unorthogonal_lines(sK0,X6) ),
inference(resolution,[],[f97,f143]) ).
fof(f143,plain,
distinct_lines(sK0,sF3),
inference(resolution,[],[f141,f87]) ).
fof(f87,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f141,plain,
! [X0] :
( distinct_lines(sF3,X0)
| distinct_lines(sK0,X0) ),
inference(resolution,[],[f138,f79]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X1,X0)
| distinct_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ distinct_lines(X1,X0)
| distinct_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X1,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X0)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
fof(f138,plain,
distinct_lines(sF3,sK0),
inference(resolution,[],[f130,f102]) ).
fof(f130,plain,
! [X3] :
( convergent_lines(sK0,X3)
| distinct_lines(sF3,X3) ),
inference(resolution,[],[f99,f107]) ).
fof(f107,plain,
convergent_lines(sK0,sF3),
inference(definition_folding,[],[f93,f106,f105]) ).
fof(f93,plain,
convergent_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
convergent_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f57,f71]) ).
fof(f71,plain,
( ? [X0,X1] : convergent_lines(X0,orthogonal_through_point(orthogonal_through_point(X0,X1),X1))
=> convergent_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0,X1] : convergent_lines(X0,orthogonal_through_point(orthogonal_through_point(X0,X1),X1)),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
~ ! [X0,X1] : ~ convergent_lines(X0,orthogonal_through_point(orthogonal_through_point(X0,X1),X1)),
inference(rectify,[],[f24]) ).
fof(f24,negated_conjecture,
~ ! [X5,X8] : ~ convergent_lines(X5,orthogonal_through_point(orthogonal_through_point(X5,X8),X8)),
inference(negated_conjecture,[],[f23]) ).
fof(f23,conjecture,
! [X5,X8] : ~ convergent_lines(X5,orthogonal_through_point(orthogonal_through_point(X5,X8),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X0)
| distinct_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| ~ convergent_lines(X1,X0)
| distinct_lines(X0,X2) ),
inference(rectify,[],[f61]) ).
fof(f61,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X0,X2)
| distinct_lines(X2,X1) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X1,X2,X0] :
( convergent_lines(X0,X1)
| distinct_lines(X2,X1)
| ~ convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X1,X2,X0] :
( convergent_lines(X0,X2)
=> ( convergent_lines(X0,X1)
| distinct_lines(X2,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X2,X1] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f97,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X3,X2)
| unorthogonal_lines(X1,X0)
| apart_point_and_line(X3,X1)
| unorthogonal_lines(X2,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X3,X1)
| unorthogonal_lines(X2,X0)
| unorthogonal_lines(X1,X0)
| apart_point_and_line(X3,X2) ),
inference(rectify,[],[f54]) ).
fof(f54,plain,
! [X3,X0,X1,X2] :
( ~ distinct_lines(X0,X1)
| apart_point_and_line(X2,X0)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X0,X3)
| apart_point_and_line(X2,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X3,X0,X1,X2] :
( unorthogonal_lines(X1,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| unorthogonal_lines(X0,X3)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X3,X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( unorthogonal_lines(X1,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0)
| unorthogonal_lines(X0,X3) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X5,X6,X8,X7] :
( distinct_lines(X5,X6)
=> ( apart_point_and_line(X8,X6)
| unorthogonal_lines(X5,X7)
| apart_point_and_line(X8,X5)
| unorthogonal_lines(X6,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
fof(f275,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f274]) ).
fof(f274,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f273,f107]) ).
fof(f273,plain,
( ~ convergent_lines(sK0,sF3)
| ~ spl4_2 ),
inference(duplicate_literal_removal,[],[f270]) ).
fof(f270,plain,
( ~ convergent_lines(sK0,sF3)
| ~ convergent_lines(sK0,sF3)
| ~ spl4_2 ),
inference(resolution,[],[f191,f91]) ).
fof(f91,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
! [X1,X0] :
( ~ convergent_lines(X1,X0)
| ~ apart_point_and_line(intersection_point(X1,X0),X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X0] :
( convergent_lines(X1,X0)
=> ~ apart_point_and_line(intersection_point(X1,X0),X1) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
fof(f191,plain,
( ! [X4] :
( apart_point_and_line(intersection_point(X4,sF3),sK0)
| ~ convergent_lines(X4,sF3) )
| ~ spl4_2 ),
inference(resolution,[],[f165,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X1,X0] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).
fof(f165,plain,
( ! [X0] :
( apart_point_and_line(X0,sF3)
| apart_point_and_line(X0,sK0) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n003.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 : Mon Aug 29 21:31:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (690)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (699)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (699)First to succeed.
% 0.20/0.51 % (707)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.52 % (699)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (699)------------------------------
% 0.20/0.52 % (699)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (699)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (699)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (699)Memory used [KB]: 5500
% 0.20/0.52 % (699)Time elapsed: 0.098 s
% 0.20/0.52 % (699)Instructions burned: 11 (million)
% 0.20/0.52 % (699)------------------------------
% 0.20/0.52 % (699)------------------------------
% 0.20/0.52 % (685)Success in time 0.173 s
%------------------------------------------------------------------------------