%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO215+1 : 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 : n010.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 09:54:04 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 16 unt; 3 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 149 ( 56 ~; 76 |; 6 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 92 ( 0 sgn 86 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f23,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( unorthogonal_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f27,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f41]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
? [X0,X1,X2] :
( ~ unorthogonal_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( ~ unorthogonal_lines(sK0,sK2)
& ~ unorthogonal_lines(sK1,sK2)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f50]) ).
fof(f53,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f54,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f60,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f77,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f51]) ).
fof(f79,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f51]) ).
fof(f92,plain,
! [X0] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f65,f77]) ).
fof(f97,plain,
distinct_lines(sK1,sK0),
inference(resolution,[],[f92,f54]) ).
fof(f99,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| convergent_lines(sK0,X1)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f92,f57]) ).
fof(f101,plain,
! [X0] :
( distinct_lines(sK1,X0)
| distinct_lines(sK0,X0) ),
inference(resolution,[],[f97,f56]) ).
fof(f103,definition,
( spl3_1
<=> convergent_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f104,plain,
( ~ convergent_lines(sK1,sK0)
| spl3_1 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f105,plain,
( convergent_lines(sK1,sK0)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f107,definition,
( spl3_2
<=> ! [X0] :
( apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f108,plain,
( ! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f167,plain,
distinct_lines(sK0,sK1),
inference(resolution,[],[f101,f53]) ).
fof(f176,plain,
! [X0,X1] :
( apart_point_and_line(X0,sK1)
| unorthogonal_lines(sK0,X1)
| unorthogonal_lines(sK1,X1)
| apart_point_and_line(X0,sK0) ),
inference(resolution,[],[f167,f76]) ).
fof(f184,plain,
( ! [X0] :
( ~ convergent_lines(sK1,X0)
| apart_point_and_line(intersection_point(sK1,X0),sK0) )
| ~ spl3_2 ),
inference(resolution,[],[f108,f60]) ).
fof(f190,plain,
! [X0] :
( convergent_lines(X0,sK0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f99,f54]) ).
fof(f489,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| distinct_lines(sK1,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f184,f190]) ).
fof(f495,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f489,f53]) ).
fof(f510,definition,
( spl3_11
<=> ! [X1] :
( unorthogonal_lines(sK1,X1)
| unorthogonal_lines(sK0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f511,plain,
( ! [X1] :
( unorthogonal_lines(sK1,X1)
| unorthogonal_lines(sK0,X1) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f513,plain,
( spl3_11
| spl3_2 ),
inference(avatar_split_clause,[],[f176,f107,f510]) ).
fof(f522,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl3_2 ),
inference(resolution,[],[f495,f61]) ).
fof(f525,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f522,f105]) ).
fof(f526,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f544,plain,
( convergent_lines(sK0,sK0)
| distinct_lines(sK1,sK1)
| spl3_1 ),
inference(resolution,[],[f104,f99]) ).
fof(f559,plain,
( distinct_lines(sK1,sK1)
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f544,f54]) ).
fof(f566,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f559,f53]) ).
fof(f567,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f566]) ).
fof(f570,plain,
( unorthogonal_lines(sK0,sK2)
| ~ spl3_11 ),
inference(resolution,[],[f511,f78]) ).
fof(f575,plain,
( $false
| ~ spl3_11 ),
inference(forward_subsumption_resolution,[],[f570,f79]) ).
fof(f576,plain,
~ spl3_11,
inference(avatar_contradiction_clause,[],[f575]) ).
cnf(s10,plain,
( spl3_2
| spl3_11 ),
inference(sat_conversion,[],[f513]) ).
cnf(s11,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f526]) ).
cnf(s15,plain,
spl3_1,
inference(sat_conversion,[],[f567]) ).
cnf(s16,plain,
~ spl3_11,
inference(sat_conversion,[],[f576]) ).
cnf(s17,plain,
~ spl3_2,
inference(rat,[],[s11,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s10,s16,s17]) ).
fof(f577,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:41:16 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.48 % (614259)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (614266)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3334657599:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (614265)% WARNING: option uhcvi not known.
% 0.17/0.48 % (614264)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=401430004_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (614265)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1392338869:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (614269)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1688897522:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (614267)dis+10_1_sil=32000:sp=arity:random_seed=1343238678:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (614268)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3574598346:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (614270)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3538204250:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % TRYING [6]
% 0.17/0.48 % (614269) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-614259-614269"...
% 0.17/0.48 % (614267) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-614259-614267"...
% 0.17/0.48 % (614269)...printing done.
% 0.17/0.48 % (614267)...printing done.
% 0.17/0.48 % (614269)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (614269)------------------------------
% 0.17/0.48 % (614269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (614269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (614269)CaDiCaL version: 2.1.3
% 0.17/0.48 % (614269)Termination reason: Refutation
% 0.17/0.48 % (614269)Time elapsed: 0.015 s
% 0.17/0.48 % (614269)Peak memory usage: 12 MB
% 0.17/0.48 % (614269)Instructions burned: 22 (million)
% 0.17/0.48 % (614259)Success in time 0.048 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------