%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO205+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 : n026.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 09:54:00 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 16 unt; 6 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 214 ( 89 ~; 98 |; 13 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq2) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& ~ distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) )
=> ( convergent_lines(X0,X2)
& ~ distinct_points(intersection_point(X0,X1),intersection_point(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(f29,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ( ~ convergent_lines(X0,X2)
| distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ( ~ convergent_lines(X0,X2)
| distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
& convergent_lines(X0,X1)
& ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ( ~ convergent_lines(sK0,sK2)
| distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) )
& convergent_lines(sK0,sK1)
& ~ distinct_lines(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(f40,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
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(f47,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
~ distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
( ~ convergent_lines(sK0,sK2)
| distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,definition,
( spl3_1
<=> distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f55,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl3_2
<=> convergent_lines(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f58,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( ~ convergent_lines(sK0,sK2)
| spl3_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f51,f57,f53]) ).
fof(f61,plain,
distinct_lines(sK0,sK1),
inference(resolution,[],[f48,f50]) ).
fof(f66,plain,
! [X0] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f40,f50]) ).
fof(f70,plain,
! [X0] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f66,f48]) ).
fof(f71,plain,
( distinct_lines(sK1,sK2)
| spl3_2 ),
inference(resolution,[],[f70,f59]) ).
fof(f75,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f71,f49]) ).
fof(f76,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f75]) ).
fof(f88,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f43,f35]) ).
fof(f92,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f44,f35]) ).
fof(f94,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,[],[f45,f61]) ).
fof(f151,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK2),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_1 ),
inference(resolution,[],[f94,f55]) ).
fof(f166,definition,
( spl3_5
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f168,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f170,definition,
( spl3_6
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f172,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f178,definition,
( spl3_8
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f180,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f182,definition,
( spl3_9
<=> apart_point_and_line(intersection_point(sK0,sK2),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f184,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f190,plain,
( spl3_5
| spl3_6
| spl3_9
| spl3_8
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f151,f53,f178,f182,f170,f166]) ).
fof(f191,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_5 ),
inference(resolution,[],[f168,f92]) ).
fof(f196,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f191,f50]) ).
fof(f197,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f196]) ).
fof(f198,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_6 ),
inference(resolution,[],[f172,f88]) ).
fof(f203,plain,
( $false
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f198,f50]) ).
fof(f204,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f203]) ).
fof(f205,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_8 ),
inference(resolution,[],[f180,f92]) ).
fof(f210,plain,
( $false
| ~ spl3_2
| ~ spl3_8 ),
inference(forward_subsumption_resolution,[],[f205,f58]) ).
fof(f211,plain,
( ~ spl3_2
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[],[f210]) ).
fof(f214,plain,
( ! [X0] :
( apart_point_and_line(intersection_point(sK0,sK2),X0)
| distinct_lines(sK1,X0) )
| ~ spl3_9 ),
inference(resolution,[],[f184,f47]) ).
fof(f344,plain,
( distinct_lines(sK1,sK2)
| ~ convergent_lines(sK0,sK2)
| ~ spl3_9 ),
inference(resolution,[],[f214,f88]) ).
fof(f352,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f344,f49]) ).
fof(f353,plain,
( $false
| ~ spl3_2
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f352,f58]) ).
fof(f354,plain,
( ~ spl3_2
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[],[f353]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f76]) ).
cnf(s7,plain,
( ~ spl3_1
| spl3_5
| spl3_6
| spl3_8
| spl3_9 ),
inference(sat_conversion,[],[f190]) ).
cnf(s8,plain,
~ spl3_5,
inference(sat_conversion,[],[f197]) ).
cnf(s9,plain,
~ spl3_6,
inference(sat_conversion,[],[f204]) ).
cnf(s10,plain,
( ~ spl3_2
| ~ spl3_8 ),
inference(sat_conversion,[],[f211]) ).
cnf(s12,plain,
( ~ spl3_2
| ~ spl3_9 ),
inference(sat_conversion,[],[f354]) ).
cnf(s13,plain,
( ~ spl3_1
| spl3_8
| spl3_9 ),
inference(rat,[],[s7,s9,s8]) ).
cnf(s15,plain,
~ spl3_9,
inference(rat,[],[s12,s2]) ).
cnf(s16,plain,
~ spl3_8,
inference(rat,[],[s10,s2]) ).
cnf(s17,plain,
~ spl3_1,
inference(rat,[],[s13,s15,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s2,s17]) ).
fof(f355,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO205+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:38:41 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.47 % (2500417)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2500426)dis+10_1_sil=32000:sp=arity:random_seed=1974509444:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2500425)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2801078469:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2500423)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3747136583_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2500424)% WARNING: option uhcvi not known.
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2500427)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2504958565:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (2500429)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2846688159:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2500424)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3317690940:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % TRYING [5]
% 0.17/0.47 % (2500426) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2500417-2500426"...
% 0.17/0.47 % (2500428)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1749796492:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % TRYING [6]
% 0.17/0.47 % (2500426)...printing done.
% 0.17/0.47 % (2500426)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2500426)------------------------------
% 0.17/0.47 % (2500426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2500426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2500426)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2500426)Termination reason: Refutation
% 0.17/0.47 % (2500426)Time elapsed: 0.008 s
% 0.17/0.47 % (2500426)Peak memory usage: 12 MB
% 0.17/0.47 % (2500426)Instructions burned: 10 (million)
% 0.17/0.47 % (2500417)Success in time 0.045 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------