%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO215+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:54:04 AM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 16 unt; 2 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 122 ( 55 ~; 53 |; 6 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f31,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f32,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f39,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ 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(cnf_transformation,[],[f45]) ).
fof(f73,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f47]) ).
fof(f75,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f47]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X0)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X2,intersection_point(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( ~ 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(consistent_polarity_flipping,[],[f72]) ).
fof(f93,plain,
unorthogonal_lines(sK0,sK2),
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f94,plain,
unorthogonal_lines(sK1,sK2),
inference(consistent_polarity_flipping,[],[f74]) ).
fof(f95,plain,
distinct_lines(sK0,sK1),
inference(resolution,[],[f61,f73]) ).
fof(f105,plain,
! [X0] :
( distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f78,f73]) ).
fof(f109,plain,
! [X0] :
( distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f79,f73]) ).
fof(f125,definition,
( spl3_3
<=> ! [X0] :
( ~ unorthogonal_lines(sK1,X0)
| ~ unorthogonal_lines(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f126,plain,
( ! [X0] :
( ~ unorthogonal_lines(sK1,X0)
| ~ unorthogonal_lines(sK0,X0) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f137,plain,
! [X0,X1] :
( ~ unorthogonal_lines(sK1,X0)
| ~ unorthogonal_lines(sK0,X0)
| ~ apart_point_and_line(X1,sK1)
| ~ apart_point_and_line(X1,sK0) ),
inference(resolution,[],[f92,f95]) ).
fof(f139,definition,
( spl3_4
<=> ! [X1] :
( ~ apart_point_and_line(X1,sK1)
| ~ apart_point_and_line(X1,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f140,plain,
( ! [X1] :
( ~ apart_point_and_line(X1,sK1)
| ~ apart_point_and_line(X1,sK0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f141,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f137,f125,f139]) ).
fof(f151,plain,
( ~ unorthogonal_lines(sK0,sK2)
| ~ spl3_3 ),
inference(resolution,[],[f126,f94]) ).
fof(f152,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f151,f93]) ).
fof(f153,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f152]) ).
fof(f178,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolution,[],[f105,f48]) ).
fof(f183,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolution,[],[f109,f48]) ).
fof(f231,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_4 ),
inference(resolution,[],[f140,f183]) ).
fof(f232,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f231,f178]) ).
fof(f233,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f232]) ).
cnf(s3,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f141]) ).
cnf(s4,plain,
~ spl3_3,
inference(sat_conversion,[],[f153]) ).
cnf(s7,plain,
~ spl3_4,
inference(sat_conversion,[],[f233]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s3,s7,s4]) ).
fof(f234,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO215+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 % Computer : n019.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 07:41:04 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.42 Running first-order model finding
% 0.09/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.48 % (2770261)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (2770270)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2687399212:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (2770267)% WARNING: option uhcvi not known.
% 0.16/0.48 % (2770266)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2668361419_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (2770267)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4092200159:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (2770271)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=495740999:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (2770268)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2284031141:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (2770269)dis+10_1_sil=32000:sp=arity:random_seed=774707905:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (2770272)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3126867919:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (2770267) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2770261-2770267"...
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (2770267)...printing done.
% 0.16/0.48 % (2770267)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 % (2770267)------------------------------
% 0.16/0.48 % (2770267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (2770267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (2770267)CaDiCaL version: 2.1.3
% 0.16/0.48 % (2770267)Termination reason: Refutation
% 0.16/0.48 % (2770267)Time elapsed: 0.005 s
% 0.16/0.48 % (2770267)Peak memory usage: 12 MB
% 0.16/0.48 % (2770267)Instructions burned: 5 (million)
% 0.16/0.48 % (2770261)Success in time 0.053 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------