%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO209+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 : n019.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 0.09s 0.45s
% Output : Refutation 0.09s
% 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/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f17,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/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(f18,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/sandbox/benchmark/theBenchmark.p',con) ).
fof(f19,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)],[f18]) ).
fof(f24,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f38,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,[],[f17]) ).
fof(f39,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,[],[f38]) ).
fof(f40,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,[],[f19]) ).
fof(f41,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,[],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f59,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,[],[f39]) ).
fof(f60,plain,
~ convergent_lines(sK3,sK1),
inference(cnf_transformation,[],[f42]) ).
fof(f61,plain,
~ convergent_lines(sK2,sK1),
inference(cnf_transformation,[],[f42]) ).
fof(f62,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
distinct_lines(sK2,sK3),
inference(cnf_transformation,[],[f42]) ).
fof(f83,plain,
! [X0] :
( apart_point_and_line(X0,sK3)
| convergent_lines(sK2,sK3)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f59,f65]) ).
fof(f95,definition,
( spl4_3
<=> convergent_lines(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f97,plain,
( convergent_lines(sK2,sK3)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f99,definition,
( spl4_4
<=> ! [X0] :
( apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f100,plain,
( ! [X0] :
( apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f101,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f83,f99,f95]) ).
fof(f103,plain,
( ! [X0] :
( convergent_lines(sK3,X0)
| convergent_lines(sK2,X0) )
| ~ spl4_3 ),
inference(resolution,[],[f97,f48]) ).
fof(f127,plain,
( convergent_lines(sK2,sK1)
| ~ spl4_3 ),
inference(resolution,[],[f103,f60]) ).
fof(f131,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f127,f61]) ).
fof(f132,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f131]) ).
fof(f133,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_4 ),
inference(resolution,[],[f100,f62]) ).
fof(f138,plain,
( $false
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f133,f63]) ).
fof(f139,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f138]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f101]) ).
cnf(s4,plain,
~ spl4_3,
inference(sat_conversion,[],[f132]) ).
cnf(s5,plain,
~ spl4_4,
inference(sat_conversion,[],[f139]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s5,s4]) ).
fof(f140,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 07:37:49 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 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
% 0.09/0.45 % (2768566)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (2768576)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1399136602:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (2768576) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2768566-2768576"...
% 0.09/0.45 % (2768576)...printing done.
% 0.09/0.45 % (2768576)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (2768576)------------------------------
% 0.09/0.45 % (2768576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (2768576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (2768576)CaDiCaL version: 2.1.3
% 0.09/0.45 % (2768576)Termination reason: Refutation
% 0.09/0.45 % (2768576)Time elapsed: 0.002 s
% 0.09/0.45 % (2768576)Peak memory usage: 12 MB
% 0.09/0.45 % (2768576)Instructions burned: 3 (million)
% 0.09/0.45 % (2768566)Success in time 0.028 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------