%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO206+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 : n011.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 09:54:00 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 13 unt; 2 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 32 |; 8 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(f13,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f14,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,parallel_through_point(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,parallel_through_point(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f22,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f35,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
? [X0,X1,X2] :
( distinct_lines(X1,parallel_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f38,plain,
? [X0,X1,X2] :
( distinct_lines(X1,parallel_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
( distinct_lines(sK1,parallel_through_point(sK2,sK0))
& ~ apart_point_and_line(sK0,sK1)
& ~ convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f13]) ).
fof(f55,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
~ convergent_lines(sK1,sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
distinct_lines(sK1,parallel_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f39]) ).
fof(f112,plain,
! [X0] :
( apart_point_and_line(X0,parallel_through_point(sK2,sK0))
| convergent_lines(sK1,parallel_through_point(sK2,sK0))
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f56,f59]) ).
fof(f134,definition,
( spl3_4
<=> ! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,parallel_through_point(sK2,sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f135,plain,
( ! [X0] :
( apart_point_and_line(X0,parallel_through_point(sK2,sK0))
| apart_point_and_line(X0,sK1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f138,definition,
( spl3_5
<=> convergent_lines(sK1,parallel_through_point(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f140,plain,
( convergent_lines(sK1,parallel_through_point(sK2,sK0))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( spl3_5
| spl3_4 ),
inference(avatar_split_clause,[],[f112,f134,f138]) ).
fof(f142,plain,
( apart_point_and_line(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f135,f55]) ).
fof(f145,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f142,f58]) ).
fof(f146,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f145]) ).
fof(f164,plain,
( ! [X0] :
( convergent_lines(parallel_through_point(sK2,sK0),X0)
| convergent_lines(sK1,X0) )
| ~ spl3_5 ),
inference(resolution,[],[f140,f45]) ).
fof(f170,plain,
( convergent_lines(sK1,sK2)
| ~ spl3_5 ),
inference(resolution,[],[f164,f54]) ).
fof(f174,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f170,f57]) ).
fof(f175,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f174]) ).
cnf(s3,plain,
( spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f141]) ).
cnf(s4,plain,
~ spl3_4,
inference(sat_conversion,[],[f146]) ).
cnf(s5,plain,
~ spl3_5,
inference(sat_conversion,[],[f175]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f176,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n011.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 07:36:45 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 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
% 0.10/0.45 % (2069104)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2069112)dis+10_1_sil=32000:sp=arity:random_seed=3265173428:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2069112) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2069104-2069112"...
% 0.10/0.45 % (2069112)...printing done.
% 0.10/0.45 % (2069112)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2069112)------------------------------
% 0.10/0.45 % (2069112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2069112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2069112)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2069112)Termination reason: Refutation
% 0.10/0.45 % (2069112)Time elapsed: 0.002 s
% 0.10/0.45 % (2069112)Peak memory usage: 12 MB
% 0.10/0.45 % (2069112)Instructions burned: 5 (million)
% 0.10/0.45 % (2069104)Success in time 0.029 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------