TSTP Solution File: GEO187+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO187+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 : n025.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 11:14:32 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 77 ( 11 unt; 0 def)
% Number of atoms : 241 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 265 ( 101 ~; 111 |; 34 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 88 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1125,plain,
$false,
inference(avatar_sat_refutation,[],[f68,f183,f219,f288,f294,f359,f783,f808,f844,f1124]) ).
fof(f1124,plain,
( spl4_28
| ~ spl4_2
| ~ spl4_11
| spl4_22 ),
inference(avatar_split_clause,[],[f812,f614,f286,f65,f780]) ).
fof(f780,plain,
( spl4_28
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
fof(f65,plain,
( spl4_2
<=> apart_point_and_line(sK3,line_connecting(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f286,plain,
( spl4_11
<=> ! [X0] :
( apart_point_and_line(sK0,X0)
| ~ apart_point_and_line(sK3,X0)
| apart_point_and_line(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f614,plain,
( spl4_22
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f812,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_11
| spl4_22 ),
inference(resolution,[],[f616,f287]) ).
fof(f287,plain,
( ! [X0] :
( apart_point_and_line(sK1,X0)
| ~ apart_point_and_line(sK3,X0)
| apart_point_and_line(sK0,X0) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f616,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
| spl4_22 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f844,plain,
~ spl4_28,
inference(avatar_contradiction_clause,[],[f836]) ).
fof(f836,plain,
( $false
| ~ spl4_28 ),
inference(resolution,[],[f823,f41]) ).
fof(f41,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) )
& ~ apart_point_and_line(sK1,line_connecting(sK2,sK3))
& ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
& distinct_points(sK2,sK3)
& distinct_points(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f39]) ).
fof(f39,plain,
( ? [X0,X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) )
& ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( ( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) )
& ~ apart_point_and_line(sK1,line_connecting(sK2,sK3))
& ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
& distinct_points(sK2,sK3)
& distinct_points(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) )
& ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ( apart_point_and_line(X3,line_connecting(X0,X1))
| apart_point_and_line(X2,line_connecting(X0,X1)) )
& ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X0,X1,X2,X3] :
( ( ~ apart_point_and_line(X1,line_connecting(X2,X3))
& ~ apart_point_and_line(X0,line_connecting(X2,X3))
& distinct_points(X2,X3)
& distinct_points(X0,X1) )
=> ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ) ),
inference(rectify,[],[f16]) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X3,X4] :
( ( ~ apart_point_and_line(X1,line_connecting(X3,X4))
& ~ apart_point_and_line(X0,line_connecting(X3,X4))
& distinct_points(X3,X4)
& distinct_points(X0,X1) )
=> ( ~ apart_point_and_line(X4,line_connecting(X0,X1))
& ~ apart_point_and_line(X3,line_connecting(X0,X1)) ) ),
inference(negated_conjecture,[],[f15]) ).
fof(f15,conjecture,
! [X0,X1,X3,X4] :
( ( ~ apart_point_and_line(X1,line_connecting(X3,X4))
& ~ apart_point_and_line(X0,line_connecting(X3,X4))
& distinct_points(X3,X4)
& distinct_points(X0,X1) )
=> ( ~ apart_point_and_line(X4,line_connecting(X0,X1))
& ~ apart_point_and_line(X3,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f823,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_28 ),
inference(resolution,[],[f782,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
fof(f782,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f808,plain,
~ spl4_22,
inference(avatar_contradiction_clause,[],[f800]) ).
fof(f800,plain,
( $false
| ~ spl4_22 ),
inference(resolution,[],[f788,f41]) ).
fof(f788,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_22 ),
inference(resolution,[],[f615,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ~ 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/sandbox2/benchmark/theBenchmark.p',ci2) ).
fof(f615,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f783,plain,
( spl4_28
| ~ spl4_1
| ~ spl4_14
| spl4_22 ),
inference(avatar_split_clause,[],[f623,f614,f357,f61,f780]) ).
fof(f61,plain,
( spl4_1
<=> apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f357,plain,
( spl4_14
<=> ! [X0] :
( apart_point_and_line(sK0,X0)
| ~ apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f623,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_14
| spl4_22 ),
inference(resolution,[],[f616,f358]) ).
fof(f358,plain,
( ! [X0] :
( apart_point_and_line(sK1,X0)
| ~ apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X0) )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f359,plain,
( ~ spl4_10
| spl4_14
| ~ spl4_9 ),
inference(avatar_split_clause,[],[f243,f181,f357,f282]) ).
fof(f282,plain,
( spl4_10
<=> distinct_points(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f181,plain,
( spl4_9
<=> ! [X0] :
( apart_point_and_line(sK0,X0)
| ~ distinct_lines(X0,line_connecting(sK2,sK3))
| apart_point_and_line(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f243,plain,
( ! [X0] :
( apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| ~ apart_point_and_line(sK2,X0)
| ~ distinct_points(sK2,sK3) )
| ~ spl4_9 ),
inference(resolution,[],[f182,f76]) ).
fof(f76,plain,
! [X2,X0,X1] :
( distinct_lines(X0,line_connecting(X1,X2))
| ~ apart_point_and_line(X1,X0)
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f57,f51]) ).
fof(f57,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f33,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/sandbox2/benchmark/theBenchmark.p',ceq2) ).
fof(f182,plain,
( ! [X0] :
( ~ distinct_lines(X0,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0) )
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f294,plain,
spl4_10,
inference(avatar_contradiction_clause,[],[f289]) ).
fof(f289,plain,
( $false
| spl4_10 ),
inference(resolution,[],[f284,f42]) ).
fof(f42,plain,
distinct_points(sK2,sK3),
inference(cnf_transformation,[],[f40]) ).
fof(f284,plain,
( ~ distinct_points(sK2,sK3)
| spl4_10 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f288,plain,
( ~ spl4_10
| spl4_11
| ~ spl4_9 ),
inference(avatar_split_clause,[],[f242,f181,f286,f282]) ).
fof(f242,plain,
( ! [X0] :
( apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| ~ apart_point_and_line(sK3,X0)
| ~ distinct_points(sK2,sK3) )
| ~ spl4_9 ),
inference(resolution,[],[f182,f77]) ).
fof(f77,plain,
! [X2,X0,X1] :
( distinct_lines(X0,line_connecting(X1,X2))
| ~ apart_point_and_line(X2,X0)
| ~ distinct_points(X1,X2) ),
inference(resolution,[],[f57,f52]) ).
fof(f219,plain,
spl4_8,
inference(avatar_contradiction_clause,[],[f214]) ).
fof(f214,plain,
( $false
| spl4_8 ),
inference(resolution,[],[f201,f41]) ).
fof(f201,plain,
( ~ distinct_points(sK0,sK1)
| spl4_8 ),
inference(resolution,[],[f200,f48]) ).
fof(f48,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(f200,plain,
( ! [X0] :
( distinct_points(X0,sK0)
| ~ distinct_points(X0,sK1) )
| spl4_8 ),
inference(resolution,[],[f179,f56]) ).
fof(f56,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X1,X2)
| distinct_points(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
fof(f179,plain,
( ~ distinct_points(sK1,sK0)
| spl4_8 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f177,plain,
( spl4_8
<=> distinct_points(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f183,plain,
( ~ spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f164,f181,f177]) ).
fof(f164,plain,
! [X0] :
( apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| ~ distinct_lines(X0,line_connecting(sK2,sK3))
| ~ distinct_points(sK1,sK0) ),
inference(resolution,[],[f90,f44]) ).
fof(f44,plain,
~ apart_point_and_line(sK1,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f40]) ).
fof(f90,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK2,sK3))
| apart_point_and_line(sK0,X0)
| apart_point_and_line(X1,X0)
| ~ distinct_lines(X0,line_connecting(sK2,sK3))
| ~ distinct_points(X1,sK0) ),
inference(resolution,[],[f59,f43]) ).
fof(f43,plain,
~ apart_point_and_line(sK0,line_connecting(sK2,sK3)),
inference(cnf_transformation,[],[f40]) ).
fof(f59,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,[],[f38]) ).
fof(f38,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,[],[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(ennf_transformation,[],[f18]) ).
fof(f18,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/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f68,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f45,f65,f61]) ).
fof(f45,plain,
( apart_point_and_line(sK3,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(cnf_transformation,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO187+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 05:56:41 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (12412)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (12413)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.38 % (12415)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)
% 0.22/0.38 % (12418)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.22/0.38 % (12416)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.38 % (12414)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (12419)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)
% 0.22/0.38 % (12417)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [1,1]
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% 0.22/0.40 TRYING [6]
% 0.22/0.40 TRYING [7,2]
% 0.22/0.40 TRYING [7,2]
% 0.22/0.40 % (12415)First to succeed.
% 0.22/0.40 % (12415)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (12415)------------------------------
% 0.22/0.40 % (12415)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40 % (12415)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (12415)Memory used [KB]: 1173
% 0.22/0.40 % (12415)Time elapsed: 0.025 s
% 0.22/0.40 % (12415)Instructions burned: 40 (million)
% 0.22/0.40 % (12415)------------------------------
% 0.22/0.40 % (12415)------------------------------
% 0.22/0.40 % (12412)Success in time 0.029 s
%------------------------------------------------------------------------------