TSTP Solution File: GEO223+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO223+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 : n022.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 : Sun May 5 05:16:15 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 23 unt; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 44 ~; 72 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 103 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f366,plain,
$false,
inference(avatar_sat_refutation,[],[f155,f180,f201,f262,f365]) ).
fof(f365,plain,
~ spl2_6,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f364,plain,
( $false
| ~ spl2_6 ),
inference(subsumption_resolution,[],[f360,f61]) ).
fof(f61,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f360,plain,
( convergent_lines(parallel_through_point(sK1,sK0),sK1)
| ~ spl2_6 ),
inference(resolution,[],[f200,f60]) ).
fof(f60,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X8,X5] : ~ unorthogonal_lines(orthogonal_through_point(X5,X8),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
fof(f200,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(parallel_through_point(sK1,sK0),X0) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f199,plain,
( spl2_6
<=> ! [X0] :
( convergent_lines(parallel_through_point(sK1,sK0),X0)
| unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f262,plain,
spl2_4,
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f261,plain,
( $false
| spl2_4 ),
inference(subsumption_resolution,[],[f256,f59]) ).
fof(f59,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f256,plain,
( convergent_lines(sK1,sK1)
| spl2_4 ),
inference(resolution,[],[f226,f61]) ).
fof(f226,plain,
( ! [X0] :
( convergent_lines(parallel_through_point(sK1,sK0),X0)
| convergent_lines(sK1,X0) )
| spl2_4 ),
inference(resolution,[],[f209,f71]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).
fof(f209,plain,
( convergent_lines(sK1,parallel_through_point(sK1,sK0))
| spl2_4 ),
inference(resolution,[],[f193,f101]) ).
fof(f101,plain,
! [X2,X0,X1] :
( convergent_lines(X1,orthogonal_through_point(X0,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[],[f91,f59]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(orthogonal_through_point(X0,X2),X3)
| convergent_lines(X1,X3) ),
inference(resolution,[],[f89,f71]) ).
fof(f89,plain,
! [X2,X0,X1] :
( convergent_lines(orthogonal_through_point(X0,X1),X2)
| convergent_lines(X0,X2) ),
inference(resolution,[],[f71,f82]) ).
fof(f82,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f64,f60]) ).
fof(f64,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X5,X6] :
( unorthogonal_lines(X5,X6)
| convergent_lines(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
fof(f193,plain,
( ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| spl2_4 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f191,plain,
( spl2_4
<=> convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f201,plain,
( ~ spl2_4
| spl2_6
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f188,f153,f199,f191]) ).
fof(f153,plain,
( spl2_3
<=> ! [X0] :
( unorthogonal_lines(parallel_through_point(sK1,sK0),X0)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f188,plain,
( ! [X0] :
( convergent_lines(parallel_through_point(sK1,sK0),X0)
| unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)) )
| ~ spl2_3 ),
inference(resolution,[],[f183,f78]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) )
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) )
| ~ unorthogonal_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( unorthogonal_lines(X0,X1)
& convergent_lines(X0,X1) )
=> ( ( unorthogonal_lines(X1,X2)
& convergent_lines(X1,X2) )
| ( unorthogonal_lines(X0,X2)
& convergent_lines(X0,X2) ) ) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X5,X6,X7] :
( ( unorthogonal_lines(X5,X6)
& convergent_lines(X5,X6) )
=> ( ( unorthogonal_lines(X6,X7)
& convergent_lines(X6,X7) )
| ( unorthogonal_lines(X5,X7)
& convergent_lines(X5,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oac1) ).
fof(f183,plain,
( unorthogonal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| ~ spl2_3 ),
inference(resolution,[],[f154,f60]) ).
fof(f154,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| unorthogonal_lines(parallel_through_point(sK1,sK0),X0) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f180,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f179,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f174,f62]) ).
fof(f62,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f174,plain,
( apart_point_and_line(sK0,parallel_through_point(sK1,sK0))
| ~ spl2_2 ),
inference(resolution,[],[f125,f63]) ).
fof(f63,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X8,X5] : ~ apart_point_and_line(X8,orthogonal_through_point(X5,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
fof(f125,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X0,parallel_through_point(sK1,sK0)) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f124,plain,
( spl2_2
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X0,parallel_through_point(sK1,sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f155,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f144,f153,f124]) ).
fof(f144,plain,
! [X0,X1] :
( unorthogonal_lines(parallel_through_point(sK1,sK0),X0)
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X1,parallel_through_point(sK1,sK0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(resolution,[],[f80,f56]) ).
fof(f56,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f30,f54]) ).
fof(f54,plain,
( ? [X0,X1] : distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0))
=> distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0,X1] : distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
~ ! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(rectify,[],[f22]) ).
fof(f22,negated_conjecture,
~ ! [X8,X5] : ~ distinct_lines(parallel_through_point(X5,X8),orthogonal_through_point(orthogonal_through_point(X5,X8),X8)),
inference(negated_conjecture,[],[f21]) ).
fof(f21,conjecture,
! [X8,X5] : ~ distinct_lines(parallel_through_point(X5,X8),orthogonal_through_point(orthogonal_through_point(X5,X8),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| unorthogonal_lines(X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X8,X5,X6,X7] :
( distinct_lines(X5,X6)
=> ( unorthogonal_lines(X6,X7)
| unorthogonal_lines(X5,X7)
| apart_point_and_line(X8,X6)
| apart_point_and_line(X8,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ouo1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n022.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
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 22:00:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (7475)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (7478)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 % (7482)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)
% 0.14/0.37 % (7479)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 % (7480)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (7481)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (7477)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1,1]
% 0.14/0.38 % (7476)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38 TRYING [2,1]
% 0.14/0.38 TRYING [3,1]
% 0.14/0.38 TRYING [1,1]
% 0.14/0.38 TRYING [2,1]
% 0.14/0.38 TRYING [4,1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [3,1]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [4,1]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3,2]
% 0.14/0.38 TRYING [3,2]
% 0.14/0.38 TRYING [4,2]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [4,2]
% 0.14/0.38 TRYING [5,1]
% 0.14/0.38 TRYING [5]
% 0.14/0.38 % (7481)First to succeed.
% 0.14/0.39 TRYING [5,1]
% 0.14/0.39 % (7481)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7475"
% 0.14/0.39 TRYING [5,2]
% 0.14/0.39 % (7481)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 % (7481)------------------------------
% 0.14/0.39 % (7481)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (7481)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (7481)Memory used [KB]: 952
% 0.14/0.39 % (7481)Time elapsed: 0.012 s
% 0.14/0.39 % (7481)Instructions burned: 20 (million)
% 0.14/0.39 % (7475)Success in time 0.016 s
%------------------------------------------------------------------------------