%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO253+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 09:54:15 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 53 ( 24 ~; 13 |; 13 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( apart_point_and_line(X0,X1)
<=> ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',apt_def) ).
fof(f15,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag10) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( ( apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,parallel_through_point(X2,X0)) )
=> apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,parallel_through_point(X2,X0)) )
=> apart_point_and_line(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f46,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f68,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,X2)
& apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,parallel_through_point(X2,X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f69,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,X2)
& apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,parallel_through_point(X2,X0)) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ) )
& ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f71,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ) )
& ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
( ~ apart_point_and_line(sK1,sK2)
& apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK1,parallel_through_point(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1))
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f89,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f46]) ).
fof(f110,plain,
apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f114,plain,
! [X0,X1] :
( ~ left_apart_point(X0,reverse_line(X1))
| ~ left_apart_point(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(consistent_polarity_flipping,[],[f73]) ).
fof(f119,plain,
! [X0,X1] : left_apart_point(X0,X1),
inference(consistent_polarity_flipping,[],[f89]) ).
fof(f138,plain,
~ apart_point_and_line(sK0,sK2),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f166,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(resolution,[],[f114,f119]) ).
fof(f167,plain,
! [X0,X1] : apart_point_and_line(X0,X1),
inference(resolution,[],[f166,f119]) ).
fof(f168,plain,
$false,
inference(resolution,[],[f167,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO253+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:53:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.44 % (480621)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (480632)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2470883762:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.44 % (480632) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-480621-480632"...
% 0.10/0.44 % (480632)...printing done.
% 0.10/0.44 % (480632)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (480632)------------------------------
% 0.10/0.44 % (480632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (480632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (480632)CaDiCaL version: 2.1.3
% 0.10/0.44 % (480632)Termination reason: Refutation
% 0.10/0.44 % (480632)Time elapsed: 0.002 s
% 0.10/0.44 % (480632)Peak memory usage: 12 MB
% 0.10/0.44 % (480632)Instructions burned: 3 (million)
% 0.10/0.44 % (480621)Success in time 0.037 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------