TSTP Solution File: GEO172+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO172+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 11:14:25 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 20 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 175 ( 66 ~; 73 |; 21 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 118 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f831,plain,
$false,
inference(avatar_sat_refutation,[],[f777,f791,f830]) ).
fof(f830,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f825]) ).
fof(f825,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f815,f144]) ).
fof(f144,plain,
distinct_points(sK2,intersection_point(sK0,sK1)),
inference(resolution,[],[f118,f100]) ).
fof(f100,plain,
~ equal_points(sK2,intersection_point(sK0,sK1)),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( ~ equal_points(sK2,intersection_point(sK0,sK1))
& incident_point_and_line(sK2,sK1)
& incident_point_and_line(sK2,sK0)
& convergent_lines(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f54,f95]) ).
fof(f95,plain,
( ? [X0,X1,X2] :
( ~ equal_points(X2,intersection_point(X0,X1))
& incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> ( ~ equal_points(sK2,intersection_point(sK0,sK1))
& incident_point_and_line(sK2,sK1)
& incident_point_and_line(sK2,sK0)
& convergent_lines(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
? [X0,X1,X2] :
( ~ equal_points(X2,intersection_point(X0,X1))
& incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
? [X0,X1,X2] :
( ~ equal_points(X2,intersection_point(X0,X1))
& incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> equal_points(X2,intersection_point(X0,X1)) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( incident_point_and_line(X2,X1)
& incident_point_and_line(X2,X0)
& convergent_lines(X0,X1) )
=> equal_points(X2,intersection_point(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f118,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f815,plain,
( ! [X0,X1] : ~ distinct_points(X0,X1)
| ~ spl4_2 ),
inference(resolution,[],[f802,f796]) ).
fof(f796,plain,
( ! [X0] : ~ distinct_points(X0,sK2)
| ~ spl4_2 ),
inference(resolution,[],[f792,f222]) ).
fof(f222,plain,
! [X0,X1] : ~ apart_point_and_line(X0,X1),
inference(resolution,[],[f160,f187]) ).
fof(f187,plain,
! [X0,X1] : ~ distinct_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[],[f183,f111]) ).
fof(f111,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f183,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[],[f168,f143]) ).
fof(f143,plain,
! [X0,X1] : ~ distinct_lines(parallel_through_point(X0,X1),X0),
inference(resolution,[],[f111,f107]) ).
fof(f107,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f168,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f126,f103]) ).
fof(f103,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(f126,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f81]) ).
fof(f81,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/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f160,plain,
! [X2,X0,X1] :
( distinct_lines(X0,parallel_through_point(X1,X2))
| ~ apart_point_and_line(X2,X0) ),
inference(resolution,[],[f125,f106]) ).
fof(f106,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
fof(f125,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
| distinct_lines(X1,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f79,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(f792,plain,
( ! [X0] :
( apart_point_and_line(X0,sK0)
| ~ distinct_points(X0,sK2) )
| ~ spl4_2 ),
inference(resolution,[],[f776,f222]) ).
fof(f776,plain,
( ! [X0] :
( apart_point_and_line(X0,sK1)
| ~ distinct_points(X0,sK2)
| apart_point_and_line(X0,sK0) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f775,plain,
( spl4_2
<=> ! [X0] :
( apart_point_and_line(X0,sK0)
| ~ distinct_points(X0,sK2)
| apart_point_and_line(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f802,plain,
( ! [X0,X1] :
( distinct_points(X0,sK2)
| ~ distinct_points(X0,X1) )
| ~ spl4_2 ),
inference(resolution,[],[f796,f121]) ).
fof(f121,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f71,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(f791,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f783]) ).
fof(f783,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f781,f97]) ).
fof(f97,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f96]) ).
fof(f781,plain,
( ~ convergent_lines(sK0,sK1)
| spl4_1 ),
inference(resolution,[],[f773,f168]) ).
fof(f773,plain,
( ~ distinct_lines(sK1,sK0)
| spl4_1 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f771,plain,
( spl4_1
<=> distinct_lines(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f777,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f713,f775,f771]) ).
fof(f713,plain,
! [X0] :
( apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1)
| ~ distinct_lines(sK1,sK0)
| ~ distinct_points(X0,sK2) ),
inference(resolution,[],[f261,f146]) ).
fof(f146,plain,
~ apart_point_and_line(sK2,sK1),
inference(resolution,[],[f119,f99]) ).
fof(f99,plain,
incident_point_and_line(sK2,sK1),
inference(cnf_transformation,[],[f96]) ).
fof(f119,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
=> ~ apart_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(f261,plain,
! [X0,X1] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X1,X0)
| ~ distinct_lines(X0,sK0)
| ~ distinct_points(X1,sK2) ),
inference(resolution,[],[f138,f145]) ).
fof(f145,plain,
~ apart_point_and_line(sK2,sK0),
inference(resolution,[],[f119,f98]) ).
fof(f98,plain,
incident_point_and_line(sK2,sK0),
inference(cnf_transformation,[],[f96]) ).
fof(f138,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,[],[f94]) ).
fof(f94,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,[],[f93]) ).
fof(f93,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,[],[f50]) ).
fof(f50,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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO172+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.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 05:58:10 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (30824)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (30829)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 % (30830)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 % (30828)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (30832)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37 % (30831)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37 % (30833)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 % (30827)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 TRYING [1,2]
% 0.14/0.37 TRYING [1,2]
% 0.14/0.37 TRYING [2,2]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [2,2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [2,3]
% 0.14/0.38 TRYING [2,3]
% 0.14/0.38 TRYING [2,4]
% 0.14/0.38 TRYING [2,4]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [4]
% 0.14/0.38 TRYING [2,5]
% 0.14/0.38 TRYING [2,5]
% 0.14/0.38 TRYING [2,6]
% 0.14/0.38 TRYING [2,6]
% 0.14/0.38 TRYING [5]
% 0.14/0.38 % (30829)First to succeed.
% 0.14/0.38 TRYING [2,7]
% 0.14/0.38 TRYING [2,7]
% 0.14/0.39 TRYING [5]
% 0.14/0.39 % (30829)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 % (30829)------------------------------
% 0.14/0.39 % (30829)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39 % (30829)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (30829)Memory used [KB]: 1158
% 0.14/0.39 % (30829)Time elapsed: 0.017 s
% 0.14/0.39 % (30829)Instructions burned: 30 (million)
% 0.14/0.39 % (30829)------------------------------
% 0.14/0.39 % (30829)------------------------------
% 0.14/0.39 % (30824)Success in time 0.032 s
%------------------------------------------------------------------------------