TSTP Solution File: GEO222+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO222+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 : n007.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 11:14:51 EDT 2024
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 16 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 150 ( 49 ~; 80 |; 10 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 111 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3114,plain,
$false,
inference(avatar_sat_refutation,[],[f365,f951,f3113]) ).
fof(f3113,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f3112]) ).
fof(f3112,plain,
( $false
| ~ spl2_5 ),
inference(subsumption_resolution,[],[f3109,f59]) ).
fof(f59,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f32,f57]) ).
fof(f57,plain,
( ? [X0,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0))
=> convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
? [X0,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
~ ! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(rectify,[],[f24]) ).
fof(f24,negated_conjecture,
~ ! [X8,X5] : ~ convergent_lines(X5,orthogonal_through_point(orthogonal_through_point(X5,X8),X8)),
inference(negated_conjecture,[],[f23]) ).
fof(f23,conjecture,
! [X8,X5] : ~ convergent_lines(X5,orthogonal_through_point(orthogonal_through_point(X5,X8),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f3109,plain,
( ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ spl2_5 ),
inference(resolution,[],[f950,f71]) ).
fof(f71,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,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(f950,plain,
( apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f948,plain,
( spl2_5
<=> apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f951,plain,
( spl2_2
| spl2_5 ),
inference(avatar_split_clause,[],[f946,f948,f198]) ).
fof(f198,plain,
( spl2_2
<=> ! [X0] :
( unorthogonal_lines(sK1,X0)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f946,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| unorthogonal_lines(sK1,X0)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(subsumption_resolution,[],[f873,f62]) ).
fof(f62,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(f873,plain,
! [X0] :
( apart_point_and_line(intersection_point(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| unorthogonal_lines(sK1,X0)
| convergent_lines(sK1,sK1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(resolution,[],[f229,f59]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X2)
| apart_point_and_line(intersection_point(X1,X2),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| unorthogonal_lines(X1,X0)
| convergent_lines(sK1,X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(resolution,[],[f150,f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,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(f150,plain,
! [X2,X0,X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| unorthogonal_lines(X2,X0)
| convergent_lines(sK1,X2) ),
inference(resolution,[],[f83,f87]) ).
fof(f87,plain,
! [X0] :
( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| convergent_lines(sK1,X0) ),
inference(resolution,[],[f75,f59]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f43,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(f83,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,[],[f54]) ).
fof(f54,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,[],[f53]) ).
fof(f53,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,[],[f30]) ).
fof(f30,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,[],[f22]) ).
fof(f22,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/sandbox/benchmark/theBenchmark.p',ouo1) ).
fof(f365,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f364,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f360,f62]) ).
fof(f360,plain,
( convergent_lines(sK1,sK1)
| ~ spl2_2 ),
inference(resolution,[],[f270,f63]) ).
fof(f63,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X8,X5] : ~ unorthogonal_lines(orthogonal_through_point(X5,X8),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f270,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(sK1,X0) )
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f267,f94]) ).
fof(f94,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[],[f91,f62]) ).
fof(f91,plain,
! [X2,X0,X1] :
( convergent_lines(orthogonal_through_point(X0,X1),X2)
| convergent_lines(X0,X2) ),
inference(resolution,[],[f76,f85]) ).
fof(f85,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f67,f63]) ).
fof(f67,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X5,X6] :
( unorthogonal_lines(X5,X6)
| convergent_lines(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f45]) ).
fof(f45,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/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f267,plain,
( ! [X0] :
( convergent_lines(sK1,X0)
| unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| ~ convergent_lines(sK1,orthogonal_through_point(sK1,sK0)) )
| ~ spl2_2 ),
inference(resolution,[],[f249,f81]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,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,[],[f51]) ).
fof(f51,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,[],[f29]) ).
fof(f29,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,[],[f19]) ).
fof(f19,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/sandbox/benchmark/theBenchmark.p',oac1) ).
fof(f249,plain,
( unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
| ~ spl2_2 ),
inference(resolution,[],[f199,f63]) ).
fof(f199,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| unorthogonal_lines(sK1,X0) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GEO222+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 05:32:47 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (7998)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (8000)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34 % (8002)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.34 % (8004)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.34 % (8001)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)
% 0.11/0.34 % (8005)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)
% 0.11/0.34 % (7999)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.34 % (8003)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [1,1]
% 0.11/0.34 TRYING [1,1]
% 0.11/0.34 TRYING [2,1]
% 0.11/0.34 TRYING [2,1]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [3,1]
% 0.11/0.34 TRYING [3,1]
% 0.11/0.34 TRYING [4,1]
% 0.11/0.34 TRYING [4,1]
% 0.11/0.34 TRYING [4]
% 0.11/0.34 TRYING [3,2]
% 0.11/0.34 TRYING [3,2]
% 0.11/0.34 TRYING [4]
% 0.11/0.34 TRYING [4,2]
% 0.11/0.34 TRYING [4,2]
% 0.11/0.35 TRYING [5,1]
% 0.11/0.35 TRYING [5,1]
% 0.11/0.35 TRYING [5]
% 0.11/0.35 TRYING [5]
% 0.11/0.35 TRYING [5,2]
% 0.11/0.35 TRYING [5,2]
% 0.16/0.35 TRYING [6,1]
% 0.16/0.35 TRYING [6,1]
% 0.16/0.36 TRYING [6]
% 0.16/0.36 TRYING [6,2]
% 0.16/0.36 TRYING [6,2]
% 0.16/0.36 TRYING [6]
% 0.16/0.36 TRYING [7,1]
% 0.16/0.36 TRYING [7,1]
% 0.16/0.37 TRYING [7,2]
% 0.16/0.37 TRYING [7,2]
% 0.16/0.37 TRYING [7]
% 0.16/0.38 TRYING [8,1]
% 0.16/0.38 TRYING [8,1]
% 0.16/0.39 TRYING [7]
% 0.16/0.39 TRYING [8,2]
% 0.16/0.39 TRYING [8,2]
% 0.16/0.41 TRYING [9,1]
% 0.16/0.41 TRYING [9,1]
% 0.16/0.41 TRYING [8]
% 0.16/0.42 TRYING [9,2]
% 0.16/0.42 TRYING [9,2]
% 0.16/0.43 TRYING [8]
% 0.16/0.44 TRYING [10,1]
% 0.16/0.44 TRYING [10,1]
% 0.16/0.47 TRYING [10,2]
% 0.16/0.47 TRYING [10,2]
% 0.16/0.47 TRYING [9]
% 0.16/0.48 % (8004)First to succeed.
% 0.16/0.48 % (8004)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (8004)------------------------------
% 0.16/0.48 % (8004)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.48 % (8004)Termination reason: Refutation
% 0.16/0.48
% 0.16/0.48 % (8004)Memory used [KB]: 1922
% 0.16/0.48 % (8004)Time elapsed: 0.142 s
% 0.16/0.48 % (8004)Instructions burned: 302 (million)
% 0.16/0.48 % (8004)------------------------------
% 0.16/0.48 % (8004)------------------------------
% 0.16/0.48 % (7998)Success in time 0.152 s
%------------------------------------------------------------------------------