%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO212+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 : n016.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 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 13 unt; 3 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 34 ~; 43 |; 13 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 50 ( 0 sgn 44 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f21,conjecture,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
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(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] :
( ~ convergent_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ~ convergent_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( ~ convergent_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(f51,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
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,
~ convergent_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(f85,plain,
! [X0,X1] :
( convergent_lines(sK1,X0)
| convergent_lines(X0,X1)
| convergent_lines(sK2,X1) ),
inference(resolution,[],[f83,f54]) ).
fof(f97,plain,
! [X0] :
( convergent_lines(sK1,X0)
| convergent_lines(X0,sK2) ),
inference(resolution,[],[f85,f51]) ).
fof(f134,definition,
( spl3_3
<=> convergent_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f146,definition,
( spl3_5
<=> convergent_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f147,plain,
( ~ convergent_lines(sK1,sK0)
| spl3_5 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f148,plain,
( convergent_lines(sK1,sK0)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f153,plain,
! [X0] :
( unorthogonal_lines(sK1,X0)
| ~ convergent_lines(sK0,sK1)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f69,f74]) ).
fof(f155,plain,
( ! [X0] :
( convergent_lines(sK1,X0)
| convergent_lines(sK0,X0) )
| ~ spl3_5 ),
inference(resolution,[],[f148,f54]) ).
fof(f239,plain,
( convergent_lines(sK0,sK1)
| ~ spl3_5 ),
inference(resolution,[],[f155,f51]) ).
fof(f246,definition,
( spl3_10
<=> ! [X0] :
( unorthogonal_lines(sK1,X0)
| convergent_lines(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f247,plain,
( ! [X0] :
( unorthogonal_lines(sK1,X0)
| convergent_lines(sK0,X0) )
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( ~ spl3_3
| spl3_10 ),
inference(avatar_split_clause,[],[f153,f246,f134]) ).
fof(f249,plain,
( spl3_3
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f239,f146,f134]) ).
fof(f258,plain,
( convergent_lines(sK0,sK2)
| spl3_5 ),
inference(resolution,[],[f147,f97]) ).
fof(f260,plain,
( $false
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f258,f76]) ).
fof(f261,plain,
spl3_5,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f266,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_10 ),
inference(resolution,[],[f247,f75]) ).
fof(f270,plain,
( $false
| ~ spl3_10 ),
inference(forward_subsumption_resolution,[],[f266,f76]) ).
fof(f271,plain,
~ spl3_10,
inference(avatar_contradiction_clause,[],[f270]) ).
cnf(s12,plain,
( ~ spl3_3
| spl3_10 ),
inference(sat_conversion,[],[f248]) ).
cnf(s13,plain,
( spl3_3
| ~ spl3_5 ),
inference(sat_conversion,[],[f249]) ).
cnf(s14,plain,
spl3_5,
inference(sat_conversion,[],[f261]) ).
cnf(s16,plain,
~ spl3_10,
inference(sat_conversion,[],[f271]) ).
cnf(s17,plain,
spl3_3,
inference(rat,[],[s13,s14]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s12,s16,s17]) ).
fof(f272,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 07:43:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 Running first-order model finding
% 0.14/0.41 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
% 0.14/0.45 % (2302178)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (2302186)dis+10_1_sil=32000:sp=arity:random_seed=2762999682:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.45 % (2302186) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2302178-2302186"...
% 0.14/0.45 % (2302186)...printing done.
% 0.14/0.45 % (2302186)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (2302186)------------------------------
% 0.14/0.45 % (2302186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (2302186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (2302186)CaDiCaL version: 2.1.3
% 0.14/0.45 % (2302186)Termination reason: Refutation
% 0.14/0.45 % (2302186)Time elapsed: 0.005 s
% 0.14/0.45 % (2302186)Peak memory usage: 12 MB
% 0.14/0.45 % (2302186)Instructions burned: 6 (million)
% 0.14/0.45 % (2302178)Success in time 0.027 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------