TSTP Solution File: GEO204+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : GEO204+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_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 16:09:11 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 6 unt; 0 def)
% Number of atoms : 217 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 232 ( 88 ~; 104 |; 20 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 94 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f459,plain,
$false,
inference(avatar_sat_refutation,[],[f84,f91,f156,f169,f174,f283,f423,f458]) ).
fof(f458,plain,
~ spl3_29,
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f456,plain,
( $false
| ~ spl3_29 ),
inference(resolution,[],[f422,f59]) ).
fof(f59,plain,
~ distinct_points(sK1,sK0),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( ( distinct_lines(line_connecting(sK2,sK1),line_connecting(sK2,sK0))
| ~ distinct_points(sK2,sK0) )
& distinct_points(sK2,sK1)
& ~ distinct_points(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f46,f47]) ).
fof(f47,plain,
( ? [X0,X1,X2] :
( ( distinct_lines(line_connecting(X2,X1),line_connecting(X2,X0))
| ~ distinct_points(X2,X0) )
& distinct_points(X2,X1)
& ~ distinct_points(X1,X0) )
=> ( ( distinct_lines(line_connecting(sK2,sK1),line_connecting(sK2,sK0))
| ~ distinct_points(sK2,sK0) )
& distinct_points(sK2,sK1)
& ~ distinct_points(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0,X1,X2] :
( ( distinct_lines(line_connecting(X2,X1),line_connecting(X2,X0))
| ~ distinct_points(X2,X0) )
& distinct_points(X2,X1)
& ~ distinct_points(X1,X0) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
? [X1,X2,X0] :
( ( distinct_lines(line_connecting(X0,X2),line_connecting(X0,X1))
| ~ distinct_points(X0,X1) )
& distinct_points(X0,X2)
& ~ distinct_points(X2,X1) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
? [X0,X2,X1] :
( ( distinct_lines(line_connecting(X0,X2),line_connecting(X0,X1))
| ~ distinct_points(X0,X1) )
& distinct_points(X0,X2)
& ~ distinct_points(X2,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X0,X2,X1] :
( ( distinct_points(X0,X2)
& ~ distinct_points(X2,X1) )
=> ( distinct_points(X0,X1)
& ~ distinct_lines(line_connecting(X0,X2),line_connecting(X0,X1)) ) ),
inference(rectify,[],[f16]) ).
fof(f16,negated_conjecture,
~ ! [X0,X2,X1] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2) ) ),
inference(negated_conjecture,[],[f15]) ).
fof(f15,conjecture,
! [X0,X2,X1] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2))
& distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f422,plain,
( distinct_points(sK1,sK0)
| ~ spl3_29 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f420,plain,
( spl3_29
<=> distinct_points(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f423,plain,
( ~ spl3_2
| spl3_29
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f411,f138,f420,f81]) ).
fof(f81,plain,
( spl3_2
<=> distinct_points(sK2,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f138,plain,
( spl3_3
<=> apart_point_and_line(sK1,line_connecting(sK2,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f411,plain,
( distinct_points(sK1,sK0)
| ~ distinct_points(sK2,sK0)
| ~ spl3_3 ),
inference(resolution,[],[f238,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X1,X0))
| ~ distinct_points(X1,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X1,X0))
| ~ distinct_points(X1,X0) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X1,X0] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
fof(f238,plain,
( ! [X1] :
( apart_point_and_line(X1,line_connecting(sK2,sK0))
| distinct_points(sK1,X1) )
| ~ spl3_3 ),
inference(resolution,[],[f140,f70]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X2)
| distinct_points(X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ apart_point_and_line(X1,X2)
| distinct_points(X1,X0)
| apart_point_and_line(X0,X2) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X1,X2,X0] :
( ~ apart_point_and_line(X2,X0)
| distinct_points(X2,X1)
| apart_point_and_line(X1,X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X2,X1,X0] :
( distinct_points(X2,X1)
| apart_point_and_line(X1,X0)
| ~ apart_point_and_line(X2,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X2,X1,X0] :
( apart_point_and_line(X2,X0)
=> ( distinct_points(X2,X1)
| apart_point_and_line(X1,X0) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X2,X0] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
fof(f140,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK0))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f283,plain,
( ~ spl3_5
| spl3_3
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f281,f154,f138,f145]) ).
fof(f145,plain,
( spl3_5
<=> distinct_points(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f154,plain,
( spl3_7
<=> ! [X1] :
( ~ distinct_points(sK2,X1)
| apart_point_and_line(X1,line_connecting(sK2,sK0))
| apart_point_and_line(X1,line_connecting(sK2,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f281,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK0))
| ~ distinct_points(sK2,sK1)
| ~ spl3_7 ),
inference(duplicate_literal_removal,[],[f275]) ).
fof(f275,plain,
( apart_point_and_line(sK1,line_connecting(sK2,sK0))
| ~ distinct_points(sK2,sK1)
| ~ distinct_points(sK2,sK1)
| ~ spl3_7 ),
inference(resolution,[],[f155,f62]) ).
fof(f155,plain,
( ! [X1] :
( apart_point_and_line(X1,line_connecting(sK2,sK1))
| ~ distinct_points(sK2,X1)
| apart_point_and_line(X1,line_connecting(sK2,sK0)) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f174,plain,
( ~ spl3_2
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f171,f150,f81]) ).
fof(f150,plain,
( spl3_6
<=> apart_point_and_line(sK2,line_connecting(sK2,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f171,plain,
( ~ distinct_points(sK2,sK0)
| ~ spl3_6 ),
inference(resolution,[],[f152,f66]) ).
fof(f66,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(rectify,[],[f35]) ).
fof(f35,plain,
! [X1,X0] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X1,line_connecting(X1,X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( distinct_points(X1,X0)
=> ~ apart_point_and_line(X1,line_connecting(X1,X0)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f152,plain,
( apart_point_and_line(sK2,line_connecting(sK2,sK0))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f169,plain,
spl3_5,
inference(avatar_contradiction_clause,[],[f157]) ).
fof(f157,plain,
( $false
| spl3_5 ),
inference(resolution,[],[f147,f60]) ).
fof(f60,plain,
distinct_points(sK2,sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f147,plain,
( ~ distinct_points(sK2,sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f156,plain,
( ~ spl3_5
| spl3_6
| spl3_7
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f130,f77,f154,f150,f145]) ).
fof(f77,plain,
( spl3_1
<=> distinct_lines(line_connecting(sK2,sK1),line_connecting(sK2,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f130,plain,
( ! [X1] :
( ~ distinct_points(sK2,X1)
| apart_point_and_line(sK2,line_connecting(sK2,sK0))
| ~ distinct_points(sK2,sK1)
| apart_point_and_line(X1,line_connecting(sK2,sK1))
| apart_point_and_line(X1,line_connecting(sK2,sK0)) )
| ~ spl3_1 ),
inference(resolution,[],[f115,f66]) ).
fof(f115,plain,
( ! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK2,sK1))
| ~ distinct_points(X1,X0)
| apart_point_and_line(X0,line_connecting(sK2,sK0))
| apart_point_and_line(X1,line_connecting(sK2,sK0))
| apart_point_and_line(X0,line_connecting(sK2,sK1)) )
| ~ spl3_1 ),
inference(resolution,[],[f65,f79]) ).
fof(f79,plain,
( distinct_lines(line_connecting(sK2,sK1),line_connecting(sK2,sK0))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X3,X1)
| ~ distinct_points(X0,X3)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X3,X2)
| ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_points(X0,X3)
| apart_point_and_line(X3,X1) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X1,X0)
| ~ distinct_lines(X3,X0)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X0)
| ~ distinct_points(X2,X1)
| apart_point_and_line(X1,X3) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X2,X1,X0,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X1,X0)
| apart_point_and_line(X2,X0)
| ~ distinct_lines(X3,X0)
| ~ distinct_points(X2,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X2,X1,X0,X3] :
( ( distinct_lines(X3,X0)
& distinct_points(X2,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X1,X0)
| apart_point_and_line(X2,X0) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X4,X1,X0,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X3,X4) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X0,X4)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f91,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f89]) ).
fof(f89,plain,
( $false
| spl3_2 ),
inference(resolution,[],[f86,f59]) ).
fof(f86,plain,
( distinct_points(sK1,sK0)
| spl3_2 ),
inference(resolution,[],[f85,f83]) ).
fof(f83,plain,
( ~ distinct_points(sK2,sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,plain,
! [X0] :
( distinct_points(sK2,X0)
| distinct_points(sK1,X0) ),
inference(resolution,[],[f73,f60]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ distinct_points(X2,X1)
| distinct_points(X2,X0)
| distinct_points(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( distinct_points(X1,X0)
| ~ distinct_points(X2,X1)
| distinct_points(X2,X0) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X0,X2,X1] :
( distinct_points(X2,X0)
| ~ distinct_points(X1,X2)
| distinct_points(X1,X0) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X1,X0)
| distinct_points(X2,X0)
| ~ distinct_points(X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X0)
| distinct_points(X2,X0) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
fof(f84,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f61,f81,f77]) ).
fof(f61,plain,
( ~ distinct_points(sK2,sK0)
| distinct_lines(line_connecting(sK2,sK1),line_connecting(sK2,sK0)) ),
inference(cnf_transformation,[],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO204+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 21:40:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (25743)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52 % (25759)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)
% 0.20/0.53 % (25759)First to succeed.
% 0.20/0.54 % (25743)Instruction limit reached!
% 0.20/0.54 % (25743)------------------------------
% 0.20/0.54 % (25743)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (25759)Refutation found. Thanks to Tanya!
% 0.20/0.54 % SZS status Theorem for theBenchmark
% 0.20/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54 % (25759)------------------------------
% 0.20/0.54 % (25759)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (25759)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (25759)Termination reason: Refutation
% 0.20/0.54
% 0.20/0.54 % (25759)Memory used [KB]: 6140
% 0.20/0.54 % (25759)Time elapsed: 0.102 s
% 0.20/0.54 % (25759)Instructions burned: 6 (million)
% 0.20/0.54 % (25759)------------------------------
% 0.20/0.54 % (25759)------------------------------
% 0.20/0.54 % (25736)Success in time 0.186 s
%------------------------------------------------------------------------------