%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO213+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 : n005.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 09:54:03 AM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 16 unt; 3 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 42 ~; 54 |; 13 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 71 ( 0 sgn 65 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).
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(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f16,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f25]) ).
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(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(f46,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( ~ distinct_lines(sK0,sK2)
& ~ unorthogonal_lines(sK1,sK2)
& unorthogonal_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f47]) ).
fof(f50,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f51,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f66,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f69,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(f74,plain,
unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
~ distinct_lines(sK0,sK2),
inference(cnf_transformation,[],[f48]) ).
fof(f77,plain,
convergent_lines(sK1,sK2),
inference(resolution,[],[f66,f75]) ).
fof(f83,plain,
! [X0] :
( convergent_lines(sK2,X0)
| convergent_lines(sK1,X0) ),
inference(resolution,[],[f54,f77]) ).
fof(f86,plain,
! [X0] :
( convergent_lines(sK1,X0)
| distinct_lines(sK2,X0) ),
inference(resolution,[],[f83,f62]) ).
fof(f88,plain,
! [X0,X1] :
( convergent_lines(sK1,X1)
| convergent_lines(X0,X1)
| distinct_lines(sK2,X0) ),
inference(resolution,[],[f86,f54]) ).
fof(f133,definition,
( spl3_3
<=> convergent_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f135,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_3 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f145,plain,
! [X0] :
( unorthogonal_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f69,f74]) ).
fof(f232,plain,
! [X0] :
( convergent_lines(X0,sK1)
| distinct_lines(sK2,X0) ),
inference(resolution,[],[f88,f51]) ).
fof(f245,plain,
( distinct_lines(sK2,sK0)
| spl3_3 ),
inference(resolution,[],[f232,f135]) ).
fof(f258,plain,
( ! [X0] :
( distinct_lines(sK2,X0)
| distinct_lines(sK0,X0) )
| spl3_3 ),
inference(resolution,[],[f245,f53]) ).
fof(f309,plain,
( distinct_lines(sK0,sK2)
| spl3_3 ),
inference(resolution,[],[f258,f50]) ).
fof(f314,plain,
( $false
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f309,f76]) ).
fof(f315,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f321,definition,
( spl3_10
<=> ! [X0] :
( unorthogonal_lines(sK1,X0)
| convergent_lines(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f322,plain,
( ! [X0] :
( unorthogonal_lines(sK1,X0)
| convergent_lines(sK0,X0) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f323,plain,
( ~ spl3_3
| spl3_10 ),
inference(avatar_split_clause,[],[f145,f321,f133]) ).
fof(f342,definition,
( spl3_12
<=> convergent_lines(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f343,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f358,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_10 ),
inference(resolution,[],[f322,f75]) ).
fof(f364,plain,
( spl3_12
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f358,f321,f342]) ).
fof(f366,plain,
( distinct_lines(sK0,sK2)
| ~ spl3_12 ),
inference(resolution,[],[f343,f62]) ).
fof(f367,plain,
( $false
| ~ spl3_12 ),
inference(forward_subsumption_resolution,[],[f366,f76]) ).
fof(f368,plain,
~ spl3_12,
inference(avatar_contradiction_clause,[],[f367]) ).
cnf(s8,plain,
spl3_3,
inference(sat_conversion,[],[f315]) ).
cnf(s10,plain,
( ~ spl3_3
| spl3_10 ),
inference(sat_conversion,[],[f323]) ).
cnf(s16,plain,
( ~ spl3_10
| spl3_12 ),
inference(sat_conversion,[],[f364]) ).
cnf(s17,plain,
~ spl3_12,
inference(sat_conversion,[],[f368]) ).
cnf(s18,plain,
~ spl3_10,
inference(rat,[],[s16,s17]) ).
cnf(s19,plain,
~ spl3_3,
inference(rat,[],[s10,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s8,s19]) ).
fof(f369,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 07:40:02 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.47 % (3655961)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (3655966)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3869524206_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % TRYING [4]
% 0.15/0.47 % (3655967)% WARNING: option uhcvi not known.
% 0.15/0.47 % TRYING [5]
% 0.15/0.47 % TRYING [6]
% 0.15/0.47 % (3655967)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=291851990:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (3655969)dis+10_1_sil=32000:sp=arity:random_seed=3734211539:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (3655968)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1369445750:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (3655970)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=844866866:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (3655971)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=282173556:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (3655972)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3117618868:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % TRYING [7]
% 0.15/0.47 % (3655969) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3655961-3655969"...
% 0.15/0.47 % (3655969)...printing done.
% 0.15/0.47 % (3655969)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (3655969)------------------------------
% 0.15/0.47 % (3655969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (3655969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (3655969)CaDiCaL version: 2.1.3
% 0.15/0.47 % (3655969)Termination reason: Refutation
% 0.15/0.47 % (3655969)Time elapsed: 0.008 s
% 0.15/0.47 % (3655969)Peak memory usage: 12 MB
% 0.15/0.47 % (3655969)Instructions burned: 10 (million)
% 0.15/0.47 % (3655961)Success in time 0.044 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------