%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO209+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 09:54:01 AM UTC 2026
% Result : Theorem 0.12s 0.48s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 11 unt; 2 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 44 ~; 32 |; 23 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 36 !; 8 ?)
% 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(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,X3] :
( ( apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& ~ convergent_lines(X2,X1)
& ~ convergent_lines(X3,X1) )
=> ~ distinct_lines(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& ~ convergent_lines(X2,X1)
& ~ convergent_lines(X3,X1) )
=> ~ distinct_lines(X2,X3) ),
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,X3] :
( distinct_lines(X2,X3)
& apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& ~ convergent_lines(X2,X1)
& ~ convergent_lines(X3,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f38,plain,
? [X0,X1,X2,X3] :
( distinct_lines(X2,X3)
& apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& ~ convergent_lines(X2,X1)
& ~ convergent_lines(X3,X1) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
( distinct_lines(sK2,sK3)
& apart_point_and_line(sK0,sK1)
& ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK0,sK3)
& ~ convergent_lines(sK2,sK1)
& ~ convergent_lines(sK3,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f38]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
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(sK3,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
~ convergent_lines(sK2,sK1),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f62,plain,
distinct_lines(sK2,sK3),
inference(cnf_transformation,[],[f39]) ).
fof(f98,plain,
! [X0] :
( apart_point_and_line(X0,sK3)
| convergent_lines(sK2,sK3)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f56,f62]) ).
fof(f104,definition,
( spl4_1
<=> convergent_lines(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f106,plain,
( convergent_lines(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl4_2
<=> ! [X0] :
( apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0] :
( apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f98,f108,f104]) ).
fof(f141,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_2 ),
inference(resolution,[],[f109,f59]) ).
fof(f144,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f141,f60]) ).
fof(f145,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f144]) ).
fof(f146,plain,
( ! [X0] :
( convergent_lines(sK3,X0)
| convergent_lines(sK2,X0) )
| ~ spl4_1 ),
inference(resolution,[],[f106,f45]) ).
fof(f150,plain,
( convergent_lines(sK2,sK1)
| ~ spl4_1 ),
inference(resolution,[],[f146,f57]) ).
fof(f154,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f150,f58]) ).
fof(f155,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f154]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f110]) ).
cnf(s4,plain,
~ spl4_2,
inference(sat_conversion,[],[f145]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f155]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s5]) ).
fof(f156,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:43:17 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.12/0.48 % (2300903)Will run a generic schedule for satisfiability detection.
% 0.12/0.48 % (2300911)dis+10_1_sil=32000:sp=arity:random_seed=3570607136:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.48 % (2300911) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2300903-2300911"...
% 0.12/0.48 % (2300911)...printing done.
% 0.12/0.48 % (2300909)% WARNING: option uhcvi not known.
% 0.12/0.48 % (2300911)Refutation found. Thanks to Tanya!
% 0.12/0.48 % SZS status Theorem for theBenchmark
% 0.12/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.48 % (2300911)------------------------------
% 0.12/0.48 % (2300911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.48 % (2300911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.48 % (2300911)CaDiCaL version: 2.1.3
% 0.12/0.48 % (2300911)Termination reason: Refutation
% 0.12/0.48 % (2300911)Time elapsed: 0.002 s
% 0.12/0.48 % (2300911)Peak memory usage: 12 MB
% 0.12/0.48 % (2300911)Instructions burned: 4 (million)
% 0.12/0.48 % (2300903)Success in time 0.038 s
% 0.12/0.48 % Vampire exiting
%------------------------------------------------------------------------------