%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO221+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 : n008.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 09:54:06 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 13 unt; 2 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 25 ~; 30 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 39 ( 0 sgn 36 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f19,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
=> ~ distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0))
=> ~ distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
? [X0,X1,X2] :
( distinct_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1))
& ~ apart_point_and_line(X1,orthogonal_through_point(X2,X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
( distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1))
& ~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f46]) ).
fof(f70,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f71,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f72,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f47]) ).
fof(f74,plain,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f47]) ).
fof(f143,definition,
( spl3_2
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f144,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f151,plain,
( apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0))
| ~ spl3_2 ),
inference(resolution,[],[f144,f71]) ).
fof(f154,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f151,f73]) ).
fof(f155,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f154]) ).
fof(f169,plain,
! [X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK1),X1)
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) ),
inference(resolution,[],[f72,f74]) ).
fof(f187,definition,
( spl3_4
<=> ! [X1] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f188,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f169,f143,f187]) ).
fof(f191,plain,
( unorthogonal_lines(orthogonal_through_point(sK2,sK0),sK2)
| ~ spl3_4 ),
inference(resolution,[],[f188,f70]) ).
fof(f195,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f191,f70]) ).
fof(f196,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f195]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f155]) ).
cnf(s5,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f190]) ).
cnf(s6,plain,
~ spl3_4,
inference(sat_conversion,[],[f196]) ).
cnf(s7,plain,
spl3_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s3,s7]) ).
fof(f197,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO221+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:43:10 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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 % (895896)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (895904)dis+10_1_sil=32000:sp=arity:random_seed=813116730:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (895904) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-895896-895904"...
% 0.10/0.45 % (895904)...printing done.
% 0.10/0.45 % (895904)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 % (895904)------------------------------
% 0.10/0.45 % (895904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (895904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (895904)CaDiCaL version: 2.1.3
% 0.10/0.45 % (895904)Termination reason: Refutation
% 0.10/0.45 % (895904)Time elapsed: 0.002 s
% 0.10/0.45 % (895904)Peak memory usage: 12 MB
% 0.10/0.45 % (895904)Instructions burned: 5 (million)
% 0.10/0.45 % (895896)Success in time 0.027 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------