%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO210+2 : 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 : n007.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 09:54:02 AM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 13 unt; 2 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 75 ( 32 ~; 30 |; 8 &)
% ( 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 : 42 ( 0 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f19,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) )
=> ~ distinct_lines(X1,orthogonal_through_point(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) )
=> ~ distinct_lines(X1,orthogonal_through_point(X2,X0)) ),
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(X1,orthogonal_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f47,plain,
? [X0,X1,X2] :
( distinct_lines(X1,orthogonal_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( distinct_lines(sK1,orthogonal_through_point(sK2,sK0))
& ~ apart_point_and_line(sK0,sK1)
& ~ unorthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f47]) ).
fof(f71,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f72,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f73,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(f74,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
distinct_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f48]) ).
fof(f128,definition,
( spl3_4
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| apart_point_and_line(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f129,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| apart_point_and_line(X0,sK1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f150,plain,
! [X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| unorthogonal_lines(sK1,X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f73,f76]) ).
fof(f157,definition,
( spl3_5
<=> ! [X1] :
( unorthogonal_lines(sK1,X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f158,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1)
| unorthogonal_lines(sK1,X1) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( spl3_5
| spl3_4 ),
inference(avatar_split_clause,[],[f150,f128,f157]) ).
fof(f175,plain,
( apart_point_and_line(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f129,f72]) ).
fof(f180,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f175,f75]) ).
fof(f181,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f180]) ).
fof(f182,plain,
( unorthogonal_lines(sK1,sK2)
| ~ spl3_5 ),
inference(resolution,[],[f158,f71]) ).
fof(f187,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f182,f74]) ).
fof(f188,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f187]) ).
cnf(s3,plain,
( spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f159]) ).
cnf(s4,plain,
~ spl3_4,
inference(sat_conversion,[],[f181]) ).
cnf(s5,plain,
~ spl3_5,
inference(sat_conversion,[],[f188]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f189,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n007.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 07:36:40 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.19/0.47 % (1075562)Will run a generic schedule for satisfiability detection.
% 0.19/0.47 % (1075572)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=521648739:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.47 % (1075572) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1075562-1075572"...
% 0.19/0.47 % (1075568)% WARNING: option uhcvi not known.
% 0.19/0.47 % (1075572)...printing done.
% 0.19/0.47 % (1075572)Refutation found. Thanks to Tanya!
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47 % (1075572)------------------------------
% 0.19/0.47 % (1075572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.47 % (1075572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.47 % (1075572)CaDiCaL version: 2.1.3
% 0.19/0.47 % (1075572)Termination reason: Refutation
% 0.19/0.47 % (1075572)Time elapsed: 0.002 s
% 0.19/0.47 % (1075572)Peak memory usage: 12 MB
% 0.19/0.47 % (1075572)Instructions burned: 5 (million)
% 0.19/0.47 % (1075562)Success in time 0.035 s
% 0.19/0.47 % Vampire exiting
%------------------------------------------------------------------------------