%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO174+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 : n015.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 09:53:47 AM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 10 unt; 2 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 102 ( 36 ~; 43 |; 16 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 43 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq2) ).
fof(f13,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) )
=> distinct_lines(X2,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) )
=> distinct_lines(X2,line_connecting(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
? [X0,X1,X2,X3] :
( ~ distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( ~ distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ distinct_lines(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& ( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
( apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK1,sK2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f54,definition,
( spl4_1
<=> apart_point_and_line(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f56,plain,
( apart_point_and_line(sK1,sK2)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f58,definition,
( spl4_2
<=> apart_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f60,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f49,f58,f54]) ).
fof(f75,plain,
( ! [X0] :
( apart_point_and_line(sK0,X0)
| distinct_lines(sK2,X0) )
| ~ spl4_2 ),
inference(resolution,[],[f47,f60]) ).
fof(f83,plain,
( ! [X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(sK0,X0)
| distinct_lines(sK2,line_connecting(X0,X1)) )
| ~ spl4_2 ),
inference(resolution,[],[f42,f75]) ).
fof(f182,plain,
( distinct_points(sK0,sK0)
| distinct_lines(sK2,line_connecting(sK0,sK1))
| ~ spl4_2 ),
inference(resolution,[],[f83,f51]) ).
fof(f193,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f182,f35]) ).
fof(f194,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f193,f52]) ).
fof(f195,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f198,plain,
( ! [X0] :
( apart_point_and_line(sK1,X0)
| distinct_lines(sK2,X0) )
| ~ spl4_1 ),
inference(resolution,[],[f56,f47]) ).
fof(f205,plain,
( ! [X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(sK1,X1)
| distinct_lines(sK2,line_connecting(X0,X1)) )
| ~ spl4_1 ),
inference(resolution,[],[f198,f41]) ).
fof(f324,plain,
( distinct_points(sK1,sK1)
| distinct_lines(sK2,line_connecting(sK0,sK1))
| ~ spl4_1 ),
inference(resolution,[],[f205,f51]) ).
fof(f343,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f324,f35]) ).
fof(f345,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f343,f52]) ).
fof(f346,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f345]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f195]) ).
cnf(s8,plain,
~ spl4_1,
inference(sat_conversion,[],[f346]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s3,s8]) ).
fof(f347,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n015.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 07:27:00 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 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
% 0.18/0.48 % (1316303)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (1316313)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3137732884:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (1316309)% WARNING: option uhcvi not known.
% 0.18/0.48 % (1316313) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1316303-1316313"...
% 0.18/0.48 % (1316313)...printing done.
% 0.18/0.48 % (1316313)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (1316313)------------------------------
% 0.18/0.48 % (1316313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (1316313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (1316313)CaDiCaL version: 2.1.3
% 0.18/0.48 % (1316313)Termination reason: Refutation
% 0.18/0.48 % (1316313)Time elapsed: 0.004 s
% 0.18/0.48 % (1316313)Peak memory usage: 12 MB
% 0.18/0.48 % (1316313)Instructions burned: 10 (million)
% 0.18/0.48 % (1316303)Success in time 0.037 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------