%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO199+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:51:57 AM UTC 2026
% Result : Theorem 0.27s 0.78s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 15 unt; 3 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 201 ( 77 ~; 92 |; 21 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 92 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart6) ).
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/theBenchmark.p',con2) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X1,X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) )
=> ~ apart_point_and_line(intersection_point(X1,X0),X2) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f23,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(f24,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,[],[f23]) ).
fof(f25,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,[],[f9]) ).
fof(f26,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,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X1,X0),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X1,X0),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK2)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK2)
& ~ apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X0,X1] :
( apart_point_and_line(X2,X1)
| distinct_points(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
apart_point_and_line(intersection_point(sK1,sK0),sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f40,f37]) ).
fof(f57,plain,
! [X0] :
( distinct_points(X0,intersection_point(sK0,sK1))
| ~ apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f46,f49]) ).
fof(f67,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f43,f35]) ).
fof(f70,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f44,f35]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ convergent_lines(X3,X1)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| ~ distinct_points(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X1) ),
inference(resolution,[],[f45,f48]) ).
fof(f84,plain,
! [X0,X1] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0)
| ~ distinct_points(X1,X0)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X1,sK1) ),
inference(resolution,[],[f73,f52]) ).
fof(f100,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,sK1),sK0)
| ~ distinct_points(X1,intersection_point(X0,sK1))
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X1,sK1)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f84,f67]) ).
fof(f108,definition,
( spl3_4
<=> ! [X0] :
( ~ distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0] :
( apart_point_and_line(X0,sK1)
| ~ distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f120,plain,
( ! [X0] :
( apart_point_and_line(intersection_point(sK1,X0),sK0)
| ~ distinct_points(intersection_point(sK1,X0),intersection_point(sK0,sK1))
| ~ convergent_lines(sK1,X0) )
| ~ spl3_4 ),
inference(resolution,[],[f109,f70]) ).
fof(f146,plain,
( ~ distinct_points(intersection_point(sK1,sK0),intersection_point(sK0,sK1))
| ~ convergent_lines(sK1,sK0)
| ~ convergent_lines(sK1,sK0)
| ~ spl3_4 ),
inference(resolution,[],[f120,f67]) ).
fof(f147,plain,
( ~ distinct_points(intersection_point(sK1,sK0),intersection_point(sK0,sK1))
| ~ convergent_lines(sK1,sK0)
| ~ spl3_4 ),
inference(duplicate_literal_removal,[],[f146]) ).
fof(f149,definition,
( spl3_8
<=> convergent_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f151,plain,
( ~ convergent_lines(sK1,sK0)
| spl3_8 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f153,definition,
( spl3_9
<=> distinct_points(intersection_point(sK1,sK0),intersection_point(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f155,plain,
( ~ distinct_points(intersection_point(sK1,sK0),intersection_point(sK0,sK1))
| spl3_9 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,plain,
( ~ spl3_8
| ~ spl3_9
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f147,f108,f153,f149]) ).
fof(f160,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_8 ),
inference(resolution,[],[f151,f55]) ).
fof(f162,plain,
( $false
| spl3_8 ),
inference(forward_subsumption_resolution,[],[f160,f52]) ).
fof(f163,plain,
spl3_8,
inference(avatar_contradiction_clause,[],[f162]) ).
fof(f187,plain,
! [X0] :
( ~ distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1)
| ~ convergent_lines(sK0,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f100,f70]) ).
fof(f190,plain,
! [X0] :
( ~ distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1)
| ~ convergent_lines(sK0,sK1) ),
inference(duplicate_literal_removal,[],[f187]) ).
fof(f196,plain,
( ~ apart_point_and_line(intersection_point(sK1,sK0),sK2)
| spl3_9 ),
inference(resolution,[],[f155,f57]) ).
fof(f205,plain,
( $false
| spl3_9 ),
inference(forward_subsumption_resolution,[],[f196,f53]) ).
fof(f206,plain,
spl3_9,
inference(avatar_contradiction_clause,[],[f205]) ).
fof(f208,plain,
! [X0] :
( ~ distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f190,f52]) ).
fof(f210,plain,
spl3_4,
inference(avatar_split_clause,[],[f208,f108]) ).
cnf(s6,plain,
( ~ spl3_4
| ~ spl3_8
| ~ spl3_9 ),
inference(sat_conversion,[],[f156]) ).
cnf(s7,plain,
spl3_8,
inference(sat_conversion,[],[f163]) ).
cnf(s10,plain,
spl3_9,
inference(sat_conversion,[],[f206]) ).
cnf(s12,plain,
spl3_4,
inference(sat_conversion,[],[f210]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s10,s7,s12]) ).
fof(f211,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO199+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 07:33:35 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.78 % (2038060)Detected formulas, will run a generic FOF schedule.
% 0.27/0.78 % (2038067)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=723446553:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.27/0.78 % (2038069)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2432166789:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.27/0.78 % (2038068)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2838009945:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.27/0.78 % (2038071)dis-21_1_sil=8000:lcm=predicate:random_seed=3655379647: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)
% 0.27/0.78 % (2038066)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=3392713489:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.27/0.78 % (2038065)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=1840917863:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.27/0.78 % (2038070)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1994936968:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.27/0.78 % (2038068)Refutation not found, incomplete strategy
% 0.27/0.78 % (2038068)------------------------------
% 0.27/0.78 % (2038068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/0.78 % (2038068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.78 % (2038068)CaDiCaL version: 2.1.3
% 0.27/0.78 % (2038068)Termination reason: Refutation not found, incomplete strategy
% 0.27/0.78 % (2038068)Time elapsed: 0.0000 s
% 0.27/0.78 % (2038068)Peak memory usage: 87 MB
% 0.27/0.78 % (2038070)First to succeed.
% 0.27/0.78 % (2038070)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2038060"
% 0.27/0.78 % (2038071)Also succeeded, but the first one will report.
% 0.27/0.78 % (2038069)Also succeeded, but the first one will report.
% 0.27/0.78 % (2038068)------------------------------
% 0.27/0.78 % (2038068)------------------------------
% 0.27/0.78 % (2038070)Refutation found. Thanks to Tanya!
% 0.27/0.78 % SZS status Theorem for theBenchmark
% 0.27/0.78 % SZS output start Proof for theBenchmark
% See solution above
% 2.03/0.87 % (2038070)------------------------------
% 2.03/0.87 % (2038070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/0.87 % (2038070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.87 % (2038070)CaDiCaL version: 2.1.3
% 2.03/0.87 % (2038070)Termination reason: Refutation
% 2.03/0.87 % (2038070)Time elapsed: 0.005 s
% 2.03/0.87 % (2038070)Peak memory usage: 89 MB
% 2.03/0.87 % (2038070)Instructions burned: 10 (million)
% 2.03/0.87 % (2038070)------------------------------
% 2.03/0.87 % (2038070)------------------------------
% 2.03/0.87 % (2038060)Success in time 0.264 s
% 2.03/0.87 % Vampire exiting
%------------------------------------------------------------------------------