%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO222+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 : n018.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 09:54:07 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 23 unt; 4 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 63 ~; 80 |; 9 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 98 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/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/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(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f16,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
=> ( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f20,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(f21,conjecture,
! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f27,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f31,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(f32,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,[],[f31]) ).
fof(f39,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f42]) ).
fof(f44,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,[],[f20]) ).
fof(f45,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,[],[f44]) ).
fof(f46,plain,
? [X0,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f46]) ).
fof(f48,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f50,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f65,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f70,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f72,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,[],[f45]) ).
fof(f73,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
distinct_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(resolution,[],[f61,f73]) ).
fof(f75,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f65,f70]) ).
fof(f81,plain,
! [X2,X0,X1] :
( convergent_lines(orthogonal_through_point(X0,X2),X1)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f53,f75]) ).
fof(f103,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f56,f48]) ).
fof(f106,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f57,f48]) ).
fof(f142,plain,
! [X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| unorthogonal_lines(sK1,X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f72,f74]) ).
fof(f152,definition,
( spl2_1
<=> ! [X1] :
( unorthogonal_lines(sK1,X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f153,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| unorthogonal_lines(sK1,X1) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl2_2
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f156,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X0,sK1) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f142,f155,f152]) ).
fof(f172,plain,
( ! [X0] :
( apart_point_and_line(intersection_point(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),sK1)
| ~ convergent_lines(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) )
| ~ spl2_2 ),
inference(resolution,[],[f103,f156]) ).
fof(f205,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[],[f81,f50]) ).
fof(f422,plain,
( ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ spl2_2 ),
inference(resolution,[],[f172,f106]) ).
fof(f427,plain,
( ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| ~ spl2_2 ),
inference(duplicate_literal_removal,[],[f422]) ).
fof(f428,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f427,f73]) ).
fof(f429,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f428]) ).
fof(f431,plain,
( unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
| ~ spl2_1 ),
inference(resolution,[],[f153,f70]) ).
fof(f437,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| ~ convergent_lines(sK1,orthogonal_through_point(sK1,sK0))
| convergent_lines(sK1,X0) )
| ~ spl2_1 ),
inference(resolution,[],[f431,f68]) ).
fof(f441,definition,
( spl2_7
<=> convergent_lines(sK1,orthogonal_through_point(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f443,plain,
( ~ convergent_lines(sK1,orthogonal_through_point(sK1,sK0))
| spl2_7 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f453,definition,
( spl2_10
<=> ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(sK1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f454,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(sK1,X0) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f455,plain,
( ~ spl2_7
| spl2_10
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f437,f152,f453,f441]) ).
fof(f710,plain,
( $false
| spl2_7 ),
inference(resolution,[],[f205,f443]) ).
fof(f716,plain,
spl2_7,
inference(avatar_contradiction_clause,[],[f710]) ).
fof(f734,plain,
( convergent_lines(sK1,sK1)
| ~ spl2_10 ),
inference(resolution,[],[f454,f70]) ).
fof(f741,plain,
( $false
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f734,f50]) ).
fof(f742,plain,
~ spl2_10,
inference(avatar_contradiction_clause,[],[f741]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f157]) ).
cnf(s4,plain,
~ spl2_2,
inference(sat_conversion,[],[f429]) ).
cnf(s8,plain,
( ~ spl2_1
| ~ spl2_7
| spl2_10 ),
inference(sat_conversion,[],[f455]) ).
cnf(s14,plain,
spl2_7,
inference(sat_conversion,[],[f716]) ).
cnf(s15,plain,
~ spl2_10,
inference(sat_conversion,[],[f742]) ).
cnf(s16,plain,
~ spl2_1,
inference(rat,[],[s8,s15,s14]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s1,s4,s16]) ).
fof(f743,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:46:08 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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 % (1997906)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1997915)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=938382007:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (1997912)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1997912)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=397843998:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1997911)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2985501513_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1997913)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=255024658:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1997914)dis+10_1_sil=32000:sp=arity:random_seed=3173171558:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1997916)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1217111322:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1997917)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4054673632:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % TRYING [5]
% 0.17/0.47 % TRYING [6]
% 0.17/0.47 % (1997914) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1997906-1997914"...
% 0.17/0.47 % (1997914)...printing done.
% 0.17/0.47 % (1997914)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
% 0.17/0.48 % (1997914)------------------------------
% 0.17/0.48 % (1997914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1997914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1997914)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1997914)Termination reason: Refutation
% 0.17/0.48 % (1997914)Time elapsed: 0.018 s
% 0.17/0.48 % (1997914)Peak memory usage: 12 MB
% 0.17/0.48 % (1997914)Instructions burned: 27 (million)
% 0.17/0.48 % (1997906)Success in time 0.053 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------