%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO198+2 : 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 : n016.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 0.62s 1.34s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 21 unt; 5 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 186 ( 71 ~; 82 |; 21 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ceq1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/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(X0,X2),X1) ),
file('/export/starexec/sandbox/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(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& 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(f16,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2)
& ~ apart_point_and_line(intersection_point(X0,X1),X2) ),
inference(flattening,[],[f15]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f24,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(f25,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f24]) ).
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(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(flattening,[],[f26]) ).
fof(f32,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
& 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)],[f16]) ).
fof(f33,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f34,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f36,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f37,plain,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f38,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
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,[],[f27]) ).
fof(f47,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f56,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(resolution,[],[f38,f47]) ).
fof(f57,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(resolution,[],[f39,f47]) ).
fof(f58,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK2),
inference(resolution,[],[f56,f34]) ).
fof(f59,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolution,[],[f56,f36]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X3)
| ~ convergent_lines(X3,X1) ),
inference(resolution,[],[f45,f40]) ).
fof(f65,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK0),
inference(resolution,[],[f57,f34]) ).
fof(f66,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolution,[],[f57,f36]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( ~ convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X4)
| ~ apart_point_and_line(X3,X4) ),
inference(resolution,[],[f64,f44]) ).
fof(f94,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK2)
| ~ apart_point_and_line(X1,X2) ),
inference(resolution,[],[f70,f34]) ).
fof(f115,plain,
! [X0] :
( apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f94,f59]) ).
fof(f130,definition,
( spl3_3
<=> ! [X0] :
( apart_point_and_line(X0,sK2)
| ~ apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f131,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| ~ apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,definition,
( spl3_4
<=> apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f135,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK2)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,definition,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f138,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( spl3_4
| spl3_5
| spl3_3 ),
inference(avatar_split_clause,[],[f115,f130,f137,f134]) ).
fof(f152,definition,
( spl3_8
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f153,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl3_9
<=> apart_point_and_line(intersection_point(sK0,sK2),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f156,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK1)
| spl3_9 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f160,plain,
( $false
| spl3_9 ),
inference(resolution,[],[f156,f37]) ).
fof(f163,plain,
spl3_9,
inference(avatar_contradiction_clause,[],[f160]) ).
fof(f168,plain,
( $false
| ~ spl3_4 ),
inference(resolution,[],[f135,f33]) ).
fof(f169,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f170,plain,
( $false
| ~ spl3_5 ),
inference(resolution,[],[f138,f66]) ).
fof(f171,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f173,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK1)
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_3 ),
inference(resolution,[],[f131,f58]) ).
fof(f176,plain,
( spl3_8
| ~ spl3_9
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f173,f130,f155,f152]) ).
fof(f177,plain,
( $false
| ~ spl3_8 ),
inference(resolution,[],[f153,f65]) ).
fof(f178,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f177]) ).
cnf(s2,plain,
( spl3_3
| spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f139]) ).
cnf(s5,plain,
spl3_9,
inference(sat_conversion,[],[f163]) ).
cnf(s7,plain,
~ spl3_4,
inference(sat_conversion,[],[f169]) ).
cnf(s8,plain,
~ spl3_5,
inference(sat_conversion,[],[f171]) ).
cnf(s9,plain,
( ~ spl3_3
| spl3_8
| ~ spl3_9 ),
inference(sat_conversion,[],[f176]) ).
cnf(s10,plain,
~ spl3_8,
inference(sat_conversion,[],[f178]) ).
cnf(s11,plain,
( ~ spl3_3
| ~ spl3_9 ),
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
~ spl3_3,
inference(rat,[],[s11,s5]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s8,s7,s12]) ).
fof(f179,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.58 % Computer : n016.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Sun Sep 27 07:38:04 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.62/1.34 % (2299588)Detected formulas, will run a generic FOF schedule.
% 0.62/1.34 % (2299599)dis-21_1_sil=8000:lcm=predicate:random_seed=1058381633: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)
% 0.62/1.34 % (2299599)First to succeed.
% 0.62/1.34 % (2299599)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2299588"
% 0.62/1.34 % (2299594)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=2425722360:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.62/1.34 % (2299597)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4044426054:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.62/1.34 % (2299593)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=688798434:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.62/1.34 % (2299596)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3669311595:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.62/1.34 % (2299595)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=1625835430:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.62/1.34 % (2299598)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3886920337:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.62/1.34 % (2299596)Refutation not found, incomplete strategy
% 0.62/1.34 % (2299596)------------------------------
% 0.62/1.34 % (2299596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.62/1.34 % (2299596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/1.34 % (2299596)CaDiCaL version: 2.1.3
% 0.62/1.34 % (2299596)Termination reason: Refutation not found, incomplete strategy
% 0.62/1.34 % (2299596)Time elapsed: 0.001 s
% 0.62/1.34 % (2299596)Peak memory usage: 87 MB
% 0.62/1.34 % (2299598)Also succeeded, but the first one will report.
% 0.62/1.34 % (2299597)Also succeeded, but the first one will report.
% 0.62/1.34 % (2299599)Refutation found. Thanks to Tanya!
% 0.62/1.34 % SZS status Theorem for theBenchmark
% 0.62/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.52 % (2299599)------------------------------
% 2.65/1.52 % (2299599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.52 % (2299599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.52 % (2299599)CaDiCaL version: 2.1.3
% 2.65/1.52 % (2299599)Termination reason: Refutation
% 2.65/1.52 % (2299599)Time elapsed: 0.003 s
% 2.65/1.52 % (2299599)Peak memory usage: 89 MB
% 2.65/1.52 % (2299599)Instructions burned: 6 (million)
% 2.65/1.52 % (2299599)------------------------------
% 2.65/1.52 % (2299599)------------------------------
% 2.65/1.52 % (2299588)Success in time 0.287 s
% 2.65/1.52 % Vampire exiting
%------------------------------------------------------------------------------