%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO201+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 09:53:58 AM UTC 2026
% Result : Theorem 0.04s 0.45s
% Output : Refutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 19 unt; 4 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 152 ( 63 ~; 73 |; 5 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 69 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',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/sandbox/benchmark/Axioms/GEO008+0.ax',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/Axioms/GEO008+0.ax',cu1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,conjecture,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
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(f31,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1] :
( distinct_points(intersection_point(X0,X1),intersection_point(X1,X0))
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
fof(f34,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f42,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(f43,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(f44,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(f47,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
distinct_lines(sK0,sK1),
inference(resolution,[],[f47,f48]) ).
fof(f57,plain,
! [X0] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f39,f48]) ).
fof(f60,plain,
! [X0] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f57,f47]) ).
fof(f62,plain,
! [X0,X1] :
( convergent_lines(sK0,X1)
| convergent_lines(X0,X1)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f60,f39]) ).
fof(f79,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f42,f34]) ).
fof(f84,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f43,f34]) ).
fof(f89,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f44,f50]) ).
fof(f128,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| apart_point_and_line(intersection_point(sK1,sK0),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
inference(resolution,[],[f89,f49]) ).
fof(f143,definition,
( spl2_3
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f145,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f147,definition,
( spl2_4
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f149,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f155,definition,
( spl2_6
<=> apart_point_and_line(intersection_point(sK1,sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f157,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f159,definition,
( spl2_7
<=> apart_point_and_line(intersection_point(sK1,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f161,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK1)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f167,plain,
( spl2_3
| spl2_4
| spl2_7
| spl2_6 ),
inference(avatar_split_clause,[],[f128,f155,f159,f147,f143]) ).
fof(f168,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_3 ),
inference(resolution,[],[f145,f84]) ).
fof(f173,plain,
( $false
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f168,f48]) ).
fof(f174,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f175,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_4 ),
inference(resolution,[],[f149,f79]) ).
fof(f180,plain,
( $false
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f175,f48]) ).
fof(f181,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f180]) ).
fof(f182,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl2_6 ),
inference(resolution,[],[f157,f79]) ).
fof(f198,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK1)
| ~ spl2_6 ),
inference(resolution,[],[f182,f62]) ).
fof(f199,plain,
( distinct_lines(sK1,sK1)
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f198,f36]) ).
fof(f204,plain,
( $false
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f199,f35]) ).
fof(f205,plain,
~ spl2_6,
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f206,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl2_7 ),
inference(resolution,[],[f161,f84]) ).
fof(f224,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK1)
| ~ spl2_7 ),
inference(resolution,[],[f206,f62]) ).
fof(f225,plain,
( distinct_lines(sK1,sK1)
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f224,f36]) ).
fof(f230,plain,
( $false
| ~ spl2_7 ),
inference(forward_subsumption_resolution,[],[f225,f35]) ).
fof(f231,plain,
~ spl2_7,
inference(avatar_contradiction_clause,[],[f230]) ).
cnf(s5,plain,
( spl2_3
| spl2_4
| spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f167]) ).
cnf(s6,plain,
~ spl2_3,
inference(sat_conversion,[],[f174]) ).
cnf(s7,plain,
~ spl2_4,
inference(sat_conversion,[],[f181]) ).
cnf(s10,plain,
~ spl2_6,
inference(sat_conversion,[],[f205]) ).
cnf(s13,plain,
~ spl2_7,
inference(sat_conversion,[],[f231]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s5,s13,s10,s7,s6]) ).
fof(f232,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 07:36:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.39 Running first-order model finding
% 0.04/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.45 % (168403)Will run a generic schedule for satisfiability detection.
% 0.04/0.45 % (168414)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1056682145:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.04/0.45 % (168409)% WARNING: option uhcvi not known.
% 0.04/0.45 % (168410)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2587735628:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.04/0.45 % (168409)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=319803535:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.04/0.45 % (168411)dis+10_1_sil=32000:sp=arity:random_seed=3734935334:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.04/0.45 % (168412)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4136962969:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.04/0.45 % (168413)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3629222959:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.04/0.45 % (168411) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-168403-168411"...
% 0.04/0.45 % (168411)...printing done.
% 0.04/0.45 % (168408)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2130298756_2999 on theBenchmark for (2999ds/0Mi)
% 0.04/0.45 % (168411)Refutation found. Thanks to Tanya!
% 0.04/0.45 % SZS status Theorem for theBenchmark
% 0.04/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.04/0.45 % (168411)------------------------------
% 0.04/0.45 % (168411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.04/0.45 % (168411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.04/0.45 % (168411)CaDiCaL version: 2.1.3
% 0.04/0.45 % (168411)Termination reason: Refutation
% 0.04/0.45 % (168411)Time elapsed: 0.006 s
% 0.04/0.45 % (168411)Peak memory usage: 12 MB
% 0.04/0.45 % (168411)Instructions burned: 6 (million)
% 0.04/0.45 % (168403)Success in time 0.048 s
% 0.04/0.45 % Vampire exiting
%------------------------------------------------------------------------------