%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO213+1 : 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 : 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 09:54:03 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 18 unt; 1 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 44 ~; 50 |; 11 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 75 ( 0 sgn 69 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f18,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f19,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(f23,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(f24,negated_conjecture,
~ ! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( distinct_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(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(f45,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,[],[f19]) ).
fof(f46,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,[],[f45]) ).
fof(f49,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f49]) ).
fof(f52,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f53,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f64,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f76,plain,
unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f50]) ).
fof(f77,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f78,plain,
~ distinct_lines(sK0,sK2),
inference(cnf_transformation,[],[f50]) ).
fof(f79,plain,
convergent_lines(sK1,sK2),
inference(resolution,[],[f68,f77]) ).
fof(f102,plain,
! [X0] :
( distinct_lines(X0,sK2)
| ~ distinct_lines(X0,sK0) ),
inference(resolution,[],[f55,f78]) ).
fof(f110,plain,
~ distinct_lines(sK2,sK0),
inference(resolution,[],[f102,f52]) ).
fof(f118,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X0) ),
inference(resolution,[],[f56,f53]) ).
fof(f141,plain,
! [X0] :
( convergent_lines(X0,sK2)
| ~ convergent_lines(X0,sK0) ),
inference(resolution,[],[f64,f78]) ).
fof(f145,plain,
! [X0] :
( ~ convergent_lines(X0,sK2)
| convergent_lines(X0,sK0) ),
inference(resolution,[],[f64,f110]) ).
fof(f146,plain,
~ convergent_lines(sK2,sK0),
inference(resolution,[],[f141,f53]) ).
fof(f166,definition,
( spl3_1
<=> convergent_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f167,plain,
( convergent_lines(sK0,sK1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f174,plain,
( ! [X0] :
( convergent_lines(X0,sK1)
| ~ convergent_lines(X0,sK0) )
| spl3_1 ),
inference(resolution,[],[f168,f56]) ).
fof(f215,plain,
! [X0] :
( ~ unorthogonal_lines(X0,sK1)
| ~ convergent_lines(X0,sK1)
| convergent_lines(X0,sK2) ),
inference(resolution,[],[f72,f77]) ).
fof(f238,plain,
( ~ convergent_lines(sK1,sK0)
| spl3_1 ),
inference(resolution,[],[f174,f53]) ).
fof(f305,plain,
( ~ convergent_lines(sK0,sK1)
| convergent_lines(sK0,sK2) ),
inference(resolution,[],[f215,f76]) ).
fof(f353,plain,
~ convergent_lines(sK0,sK2),
inference(resolution,[],[f118,f146]) ).
fof(f441,plain,
convergent_lines(sK1,sK0),
inference(resolution,[],[f145,f79]) ).
fof(f443,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f441,f238]) ).
fof(f444,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f443]) ).
fof(f445,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f305,f167]) ).
fof(f446,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f445,f353]) ).
fof(f447,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f446]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f444]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f447]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f448,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO213+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:41:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.46 % (1994888)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (1994897)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=59967289:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (1994894)% WARNING: option uhcvi not known.
% 0.16/0.46 % (1994897) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1994888-1994897"...
% 0.16/0.46 % (1994895)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=685513946:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (1994893)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1725914819_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (1994894)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1798553590:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (1994898)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=220724785:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (1994896)dis+10_1_sil=32000:sp=arity:random_seed=3156205914:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (1994897)...printing done.
% 0.16/0.46 % (1994899)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3755245301:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (1994897)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (1994897)------------------------------
% 0.16/0.46 % (1994897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (1994897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (1994897)CaDiCaL version: 2.1.3
% 0.16/0.46 % (1994897)Termination reason: Refutation
% 0.16/0.46 % (1994897)Time elapsed: 0.007 s
% 0.16/0.46 % (1994897)Peak memory usage: 12 MB
% 0.16/0.46 % (1994897)Instructions burned: 18 (million)
% 0.16/0.46 % (1994888)Success in time 0.043 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------