%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:51:58 AM UTC 2026
% Result : Theorem 3.51s 1.47s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 14 unt; 4 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 122 ( 49 ~; 49 |; 14 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
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(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
=> ~ distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
=> ~ distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f25,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f27]) ).
fof(f35,plain,
? [X0,X1,X2] :
( distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( distinct_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0)
& convergent_lines(sK0,sK1)
& convergent_lines(sK0,sK2)
& distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f64,plain,
! [X0,X1] :
( ~ distinct_lines(X1,X0)
| apart_point_and_line(intersection_point(sK0,sK2),X1)
| apart_point_and_line(intersection_point(sK0,sK2),X0)
| apart_point_and_line(intersection_point(sK0,sK1),X1)
| apart_point_and_line(intersection_point(sK0,sK1),X0) ),
inference(resolution,[],[f48,f52]) ).
fof(f67,plain,
( apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(resolution,[],[f64,f55]) ).
fof(f72,definition,
( spl3_1
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f74,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl3_2
<=> apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f78,plain,
( apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl3_3
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f82,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl3_4
<=> apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f86,plain,
( apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl3_1
| spl3_2
| spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f67,f84,f80,f76,f72]) ).
fof(f90,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_2 ),
inference(resolution,[],[f78,f44]) ).
fof(f93,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f90,f52]) ).
fof(f94,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f95,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_3 ),
inference(resolution,[],[f82,f46]) ).
fof(f98,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f95,f53]) ).
fof(f99,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f100,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_4 ),
inference(resolution,[],[f86,f45]) ).
fof(f103,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f100,f52]) ).
fof(f104,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f105,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_1 ),
inference(resolution,[],[f74,f46]) ).
fof(f108,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f105,f54]) ).
fof(f109,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f108]) ).
cnf(s1,plain,
( spl3_1
| spl3_2
| spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f87]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f94]) ).
cnf(s3,plain,
~ spl3_3,
inference(sat_conversion,[],[f99]) ).
cnf(s4,plain,
~ spl3_4,
inference(sat_conversion,[],[f104]) ).
cnf(s5,plain,
~ spl3_1,
inference(sat_conversion,[],[f109]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s3,s2,s5]) ).
fof(f110,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 07:35:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/1.47 % (1696415)Detected formulas, will run a generic FOF schedule.
% 3.51/1.47 % (1696420)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1313306645:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.47 % (1696423)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2892235519:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.47 % (1696424)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3040792837:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.47 % (1696421)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2723423084:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.47 % (1696425)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3972602264:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.47 % (1696422)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1064878079:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.47 % (1696426)dis-21_1_sil=8000:lcm=predicate:random_seed=2637879542:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.51/1.47 % (1696425)First to succeed.
% 3.51/1.47 % (1696426)Also succeeded, but the first one will report.
% 3.51/1.47 % (1696425)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1696415"
% 3.51/1.47 % (1696423)Also succeeded, but the first one will report.
% 3.51/1.47 % (1696424)Also succeeded, but the first one will report.
% 3.51/1.47 % (1696425)Refutation found. Thanks to Tanya!
% 3.51/1.47 % SZS status Theorem for theBenchmark
% 3.51/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.47 % (1696425)------------------------------
% 3.51/1.47 % (1696425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.47 % (1696425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.47 % (1696425)CaDiCaL version: 2.1.3
% 3.51/1.47 % (1696425)Termination reason: Refutation
% 3.51/1.47 % (1696425)Time elapsed: 0.004 s
% 3.51/1.47 % (1696425)Peak memory usage: 89 MB
% 3.51/1.47 % (1696425)Instructions burned: 3 (million)
% 3.51/1.47 % (1696425)------------------------------
% 3.51/1.47 % (1696425)------------------------------
% 3.51/1.47 % (1696415)Success in time 0.418 s
% 3.51/1.47 % Vampire exiting
%------------------------------------------------------------------------------