%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO221+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 : n026.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 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 13 unt; 2 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 60 ( 24 ~; 30 |; 1 &)
% ( 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(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f21,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f22,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/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f23,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/sandbox/benchmark/theBenchmark.p',con) ).
fof(f24,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)],[f23]) ).
fof(f47,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,[],[f22]) ).
fof(f48,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,[],[f47]) ).
fof(f49,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,[],[f24]) ).
fof(f72,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f73,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f49]) ).
fof(f76,plain,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f49]) ).
fof(f164,definition,
( spl3_1
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f165,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f187,plain,
( apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0))
| ~ spl3_1 ),
inference(resolution,[],[f165,f73]) ).
fof(f190,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f187,f75]) ).
fof(f191,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f190]) ).
fof(f235,plain,
! [X0,X1] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0)
| apart_point_and_line(X1,orthogonal_through_point(sK2,sK1))
| apart_point_and_line(X1,orthogonal_through_point(sK2,sK0)) ),
inference(resolution,[],[f74,f76]) ).
fof(f252,definition,
( spl3_4
<=> ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0)
| unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f253,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X0)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X0) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f255,plain,
( spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f235,f252,f164]) ).
fof(f256,plain,
( unorthogonal_lines(orthogonal_through_point(sK2,sK0),sK2)
| ~ spl3_4 ),
inference(resolution,[],[f253,f72]) ).
fof(f261,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f256,f72]) ).
fof(f262,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f261]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f191]) ).
cnf(s5,plain,
( spl3_1
| spl3_4 ),
inference(sat_conversion,[],[f255]) ).
cnf(s6,plain,
~ spl3_4,
inference(sat_conversion,[],[f262]) ).
cnf(s7,plain,
spl3_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s3,s7]) ).
fof(f263,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO221+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:45:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.45 % (2504680)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2504689)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2021277282:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (2504686)% WARNING: option uhcvi not known.
% 0.11/0.45 % (2504689) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2504680-2504689"...
% 0.11/0.45 % (2504689)...printing done.
% 0.11/0.45 % (2504689)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2504689)------------------------------
% 0.11/0.45 % (2504689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2504689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2504689)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2504689)Termination reason: Refutation
% 0.11/0.45 % (2504689)Time elapsed: 0.004 s
% 0.11/0.45 % (2504689)Peak memory usage: 12 MB
% 0.11/0.45 % (2504689)Instructions burned: 10 (million)
% 0.11/0.45 % (2504680)Success in time 0.032 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------