TSTP Solution File: GEO203+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO203+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.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 : Tue Apr 30 11:14:41 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 14 unt; 0 def)
% Number of atoms : 188 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 185 ( 63 ~; 82 |; 26 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 74 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f632,plain,
$false,
inference(avatar_sat_refutation,[],[f246,f259,f483,f530,f631]) ).
fof(f631,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f630,plain,
( $false
| ~ spl3_7 ),
inference(subsumption_resolution,[],[f627,f37]) ).
fof(f37,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0)
& distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
& convergent_lines(sK0,sK2)
& convergent_lines(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f35]) ).
fof(f35,plain,
( ? [X0,X1,X2] :
( distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> ( distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0)
& distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
& convergent_lines(sK0,sK2)
& convergent_lines(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0,X1,X2] :
( distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0,X1,X2] :
( distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> ~ distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2)
& convergent_lines(X0,X1) )
=> ~ distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f627,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_7 ),
inference(resolution,[],[f534,f43]) ).
fof(f43,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f534,plain,
( ! [X0] :
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,X0))
| ~ convergent_lines(sK0,X0) )
| ~ spl3_7 ),
inference(resolution,[],[f151,f46]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1))
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).
fof(f151,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f149,plain,
( spl3_7
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f530,plain,
( spl3_4
| spl3_7
| spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f529,f145,f141,f149,f137]) ).
fof(f137,plain,
( spl3_4
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f141,plain,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f145,plain,
( spl3_6
<=> apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f529,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| spl3_5
| spl3_6 ),
inference(subsumption_resolution,[],[f528,f142]) ).
fof(f142,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| spl3_5 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f528,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| spl3_6 ),
inference(subsumption_resolution,[],[f193,f146]) ).
fof(f146,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| spl3_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f193,plain,
( apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
inference(resolution,[],[f105,f92]) ).
fof(f92,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| apart_point_and_line(intersection_point(sK0,sK1),X1)
| apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(intersection_point(sK0,sK2),X0)
| apart_point_and_line(intersection_point(sK0,sK2),X1) ),
inference(resolution,[],[f54,f39]) ).
fof(f39,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X3,X4] :
( ( distinct_lines(X3,X4)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X4)
| apart_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f105,plain,
distinct_lines(sK0,line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))),
inference(resolution,[],[f64,f42]) ).
fof(f42,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
fof(f64,plain,
! [X0] :
( distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),X0)
| distinct_lines(sK0,X0) ),
inference(resolution,[],[f48,f40]) ).
fof(f40,plain,
distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| distinct_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
fof(f483,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f482,plain,
( $false
| ~ spl3_4 ),
inference(subsumption_resolution,[],[f479,f38]) ).
fof(f38,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f479,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_4 ),
inference(resolution,[],[f173,f43]) ).
fof(f173,plain,
( ! [X0] :
( distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,X0))
| ~ convergent_lines(sK0,X0) )
| ~ spl3_4 ),
inference(resolution,[],[f139,f46]) ).
fof(f139,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f259,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f258,plain,
( $false
| ~ spl3_6 ),
inference(subsumption_resolution,[],[f257,f39]) ).
fof(f257,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_6 ),
inference(subsumption_resolution,[],[f252,f43]) ).
fof(f252,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK1))
| ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_6 ),
inference(resolution,[],[f147,f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X1)
& distinct_points(X2,X0) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X1)
& distinct_points(X2,X0) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X1)
& distinct_points(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).
fof(f147,plain,
( apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f246,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f245,plain,
( $false
| ~ spl3_5 ),
inference(subsumption_resolution,[],[f244,f39]) ).
fof(f244,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_5 ),
inference(subsumption_resolution,[],[f238,f43]) ).
fof(f238,plain,
( distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK2))
| ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_5 ),
inference(resolution,[],[f143,f53]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f143,plain,
( apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO203+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:29:49 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (5221)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (5224)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.37 % (5222)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 % (5225)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37 % (5223)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (5226)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37 % (5227)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37 % (5228)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [5]
% 0.14/0.38 TRYING [5]
% 0.14/0.38 TRYING [5]
% 0.14/0.38 TRYING [5]
% 0.14/0.39 TRYING [6]
% 0.14/0.39 % (5227)First to succeed.
% 0.14/0.39 TRYING [6]
% 0.14/0.39 TRYING [6]
% 0.14/0.39 % (5227)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (5227)------------------------------
% 0.14/0.39 % (5227)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39 % (5227)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (5227)Memory used [KB]: 956
% 0.14/0.39 % (5227)Time elapsed: 0.017 s
% 0.14/0.39 % (5227)Instructions burned: 28 (million)
% 0.14/0.39 % (5227)------------------------------
% 0.14/0.39 % (5227)------------------------------
% 0.14/0.39 % (5221)Success in time 0.022 s
%------------------------------------------------------------------------------