%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 09:53:53 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 15 unt; 2 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 42 ~; 42 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 73 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(f36,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) )
=> ( incident_point_and_line(X2,line_connecting(X0,X1))
& incident_point_and_line(X3,line_connecting(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) )
=> ( incident_point_and_line(X2,line_connecting(X0,X1))
& incident_point_and_line(X3,line_connecting(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f52,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f55,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f76,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X2,line_connecting(X0,X1))
| ~ incident_point_and_line(X3,line_connecting(X0,X1)) )
& distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f77,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X2,line_connecting(X0,X1))
| ~ incident_point_and_line(X3,line_connecting(X0,X1)) )
& distinct_points(X0,X1)
& distinct_points(X2,X3)
& incident_point_and_line(X0,line_connecting(X2,X3))
& incident_point_and_line(X1,line_connecting(X2,X3)) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) )
& ( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f79,plain,
( ( ~ incident_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK3,line_connecting(sK0,sK1)) )
& distinct_points(sK0,sK1)
& distinct_points(sK2,sK3)
& incident_point_and_line(sK0,line_connecting(sK2,sK3))
& incident_point_and_line(sK1,line_connecting(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f92,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f94,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f117,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f122,plain,
( ~ incident_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ incident_point_and_line(sK3,line_connecting(sK0,sK1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f129,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f130,plain,
! [X0,X1] : apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f150,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(consistent_polarity_flipping,[],[f117]) ).
fof(f153,definition,
( spl4_1
<=> incident_point_and_line(sK3,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f155,plain,
( ~ incident_point_and_line(sK3,line_connecting(sK0,sK1))
| spl4_1 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f157,definition,
( spl4_2
<=> incident_point_and_line(sK2,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f159,plain,
( ~ incident_point_and_line(sK2,line_connecting(sK0,sK1))
| spl4_2 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f122,f157,f153]) ).
fof(f162,plain,
! [X0,X1] : ~ distinct_lines(parallel_through_point(X0,X1),X0),
inference(resolution,[],[f94,f95]) ).
fof(f164,plain,
( ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
| spl4_1 ),
inference(resolution,[],[f150,f155]) ).
fof(f165,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
| spl4_2 ),
inference(resolution,[],[f150,f159]) ).
fof(f179,plain,
! [X0,X1] :
( ~ convergent_lines(X1,X0)
| distinct_lines(X0,X1) ),
inference(resolution,[],[f93,f82]) ).
fof(f184,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ distinct_lines(X1,X0) ),
inference(resolution,[],[f179,f94]) ).
fof(f188,plain,
! [X0,X1] : ~ distinct_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[],[f184,f162]) ).
fof(f251,plain,
( ! [X0] :
( ~ apart_point_and_line(sK3,X0)
| distinct_lines(line_connecting(sK0,sK1),X0) )
| spl4_1 ),
inference(resolution,[],[f129,f164]) ).
fof(f252,plain,
( ! [X0] :
( ~ apart_point_and_line(sK2,X0)
| distinct_lines(line_connecting(sK0,sK1),X0) )
| spl4_2 ),
inference(resolution,[],[f129,f165]) ).
fof(f274,plain,
( ! [X0] : distinct_lines(line_connecting(sK0,sK1),parallel_through_point(X0,sK3))
| spl4_1 ),
inference(resolution,[],[f251,f130]) ).
fof(f277,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f274,f188]) ).
fof(f280,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f287,plain,
( ! [X0] : distinct_lines(line_connecting(sK0,sK1),parallel_through_point(X0,sK2))
| spl4_2 ),
inference(resolution,[],[f252,f130]) ).
fof(f290,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f287,f188]) ).
fof(f293,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f290]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f160]) ).
cnf(s8,plain,
spl4_1,
inference(sat_conversion,[],[f280]) ).
cnf(s10,plain,
spl4_2,
inference(sat_conversion,[],[f293]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s8]) ).
fof(f294,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 07:30:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.12/0.45 % (166030)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (166049)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2564263368:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (166049) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-166030-166049"...
% 0.12/0.45 % (166044)% WARNING: option uhcvi not known.
% 0.12/0.45 % (166049)...printing done.
% 0.12/0.45 % (166049)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (166049)------------------------------
% 0.12/0.46 % (166049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (166049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (166049)CaDiCaL version: 2.1.3
% 0.12/0.46 % (166049)Termination reason: Refutation
% 0.12/0.46 % (166049)Time elapsed: 0.003 s
% 0.12/0.46 % (166049)Peak memory usage: 12 MB
% 0.12/0.46 % (166049)Instructions burned: 6 (million)
% 0.12/0.46 % (166030)Success in time 0.036 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------