TSTP Solution File: GEO205+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO205+1 : 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 : n017.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 11:14:42 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 82 ( 12 unt; 0 def)
% Number of atoms : 226 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 241 ( 97 ~; 111 |; 16 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 102 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f650,plain,
$false,
inference(avatar_sat_refutation,[],[f65,f83,f309,f481,f525,f613,f647,f649]) ).
fof(f649,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f648]) ).
fof(f648,plain,
( $false
| ~ spl3_7 ),
inference(resolution,[],[f612,f43]) ).
fof(f43,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(f612,plain,
( distinct_lines(sK1,sK1)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f610,plain,
( spl3_7
<=> distinct_lines(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f647,plain,
spl3_6,
inference(avatar_contradiction_clause,[],[f643]) ).
fof(f643,plain,
( $false
| spl3_6 ),
inference(resolution,[],[f608,f40]) ).
fof(f40,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
( ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) )
& ~ distinct_lines(sK1,sK2)
& convergent_lines(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f38]) ).
fof(f38,plain,
( ? [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
| ~ convergent_lines(X0,X2) )
& ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1) )
=> ( ( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) )
& ~ distinct_lines(sK1,sK2)
& convergent_lines(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
| ~ convergent_lines(X0,X2) )
& ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
| ~ convergent_lines(X0,X2) )
& ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1) )
=> ( ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2) ) ),
inference(negated_conjecture,[],[f15]) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( ~ distinct_lines(X1,X2)
& convergent_lines(X0,X1) )
=> ( ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2))
& convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f608,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_6 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f606,plain,
( spl3_6
<=> convergent_lines(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f613,plain,
( ~ spl3_6
| spl3_7
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f555,f298,f610,f606]) ).
fof(f298,plain,
( spl3_3
<=> apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f555,plain,
( distinct_lines(sK1,sK1)
| ~ convergent_lines(sK0,sK1)
| ~ spl3_3 ),
inference(resolution,[],[f300,f142]) ).
fof(f142,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),sK2)
| distinct_lines(sK1,X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f115,f69]) ).
fof(f69,plain,
~ distinct_lines(sK2,sK1),
inference(resolution,[],[f66,f43]) ).
fof(f66,plain,
! [X0] :
( distinct_lines(X0,sK2)
| ~ distinct_lines(X0,sK1) ),
inference(resolution,[],[f50,f41]) ).
fof(f41,plain,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f50,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f24,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/sandbox/benchmark/theBenchmark.p',apart5) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( distinct_lines(X3,X0)
| ~ convergent_lines(X2,X1)
| distinct_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X2,X1),X3) ),
inference(resolution,[],[f89,f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(intersection_point(X2,X1),X0)
| distinct_lines(X0,X1)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[],[f54,f48]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).
fof(f300,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f525,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f521,plain,
( $false
| ~ spl3_5 ),
inference(resolution,[],[f498,f40]) ).
fof(f498,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_5 ),
inference(resolution,[],[f308,f49]) ).
fof(f49,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
fof(f308,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f306,plain,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f481,plain,
( ~ spl3_1
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f477]) ).
fof(f477,plain,
( $false
| ~ spl3_1
| spl3_4 ),
inference(resolution,[],[f443,f59]) ).
fof(f59,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f58,plain,
( spl3_1
<=> convergent_lines(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f443,plain,
( ~ convergent_lines(sK0,sK2)
| spl3_4 ),
inference(resolution,[],[f410,f74]) ).
fof(f74,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f52,f45]) ).
fof(f45,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(f52,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f410,plain,
( ~ distinct_lines(sK2,sK0)
| spl3_4 ),
inference(resolution,[],[f335,f43]) ).
fof(f335,plain,
( ! [X0] :
( distinct_lines(X0,sK2)
| ~ distinct_lines(X0,sK0) )
| spl3_4 ),
inference(resolution,[],[f304,f50]) ).
fof(f304,plain,
( ~ distinct_lines(sK0,sK2)
| spl3_4 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f302,plain,
( spl3_4
<=> distinct_lines(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f309,plain,
( ~ spl3_1
| spl3_3
| ~ spl3_4
| spl3_5
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f285,f62,f306,f302,f298,f58]) ).
fof(f62,plain,
( spl3_2
<=> distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f285,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_lines(sK0,sK2)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ convergent_lines(sK0,sK2)
| ~ spl3_2 ),
inference(resolution,[],[f176,f64]) ).
fof(f64,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,intersection_point(X2,X1))
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X1)
| apart_point_and_line(X0,X1)
| ~ convergent_lines(X2,X1) ),
inference(duplicate_literal_removal,[],[f161]) ).
fof(f161,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X1)
| ~ distinct_points(X0,intersection_point(X2,X1))
| ~ convergent_lines(X2,X1)
| ~ convergent_lines(X2,X1) ),
inference(resolution,[],[f103,f49]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| ~ distinct_lines(X2,X1)
| ~ distinct_points(X3,intersection_point(X0,X1))
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f56,f48]) ).
fof(f56,plain,
! [X2,X3,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)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,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,[],[f36]) ).
fof(f36,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,[],[f17]) ).
fof(f17,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,[],[f11]) ).
fof(f11,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/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f83,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f80,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f76,f40]) ).
fof(f76,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_1 ),
inference(resolution,[],[f75,f41]) ).
fof(f75,plain,
( ! [X0] :
( distinct_lines(X0,sK2)
| ~ convergent_lines(sK0,X0) )
| spl3_1 ),
inference(resolution,[],[f52,f60]) ).
fof(f60,plain,
( ~ convergent_lines(sK0,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f65,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f42,f62,f58]) ).
fof(f42,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ convergent_lines(sK0,sK2) ),
inference(cnf_transformation,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO205+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Tue Apr 30 05:22:19 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (19709)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (19712)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)
% 0.20/0.37 % (19711)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.37 % (19710)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.20/0.37 % (19713)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.20/0.37 % (19715)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.20/0.37 % (19716)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)
% 0.20/0.37 % (19714)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.20/0.37 TRYING [1]
% 0.20/0.37 TRYING [2]
% 0.20/0.37 TRYING [1]
% 0.20/0.37 TRYING [2]
% 0.20/0.37 TRYING [3]
% 0.20/0.37 % (19712)First to succeed.
% 0.20/0.37 TRYING [1,1]
% 0.20/0.38 TRYING [3]
% 0.20/0.38 TRYING [2,2]
% 0.20/0.38 TRYING [1,1]
% 0.20/0.38 TRYING [2,2]
% 0.20/0.38 TRYING [2,3]
% 0.20/0.38 TRYING [4]
% 0.20/0.38 TRYING [2,3]
% 0.20/0.38 % (19712)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38 % (19712)------------------------------
% 0.20/0.38 % (19712)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.38 % (19712)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (19712)Memory used [KB]: 1028
% 0.20/0.38 % (19712)Time elapsed: 0.010 s
% 0.20/0.38 % (19712)Instructions burned: 32 (million)
% 0.20/0.38 % (19712)------------------------------
% 0.20/0.38 % (19712)------------------------------
% 0.20/0.38 % (19709)Success in time 0.017 s
%------------------------------------------------------------------------------