%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO201+1 : 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 : 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 09:53:58 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 15 unt; 3 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 154 ( 61 ~; 81 |; 2 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 90 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(f15,conjecture,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f27]) ).
fof(f33,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0,X1] :
( distinct_points(intersection_point(X0,X1),intersection_point(X1,X0))
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f38,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f51,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0] : convergent_lines(X0,X0),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X2)
| ~ convergent_lines(X1,X2)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f60,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X0)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f61,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X1)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( ~ apart_point_and_line(X1,X3)
| distinct_points(X0,X1)
| distinct_lines(X2,X3)
| ~ apart_point_and_line(X1,X2)
| ~ apart_point_and_line(X0,X3)
| ~ apart_point_and_line(X0,X2) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X2)
| convergent_lines(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f66,plain,
~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f67,plain,
~ convergent_lines(sK0,sK1),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f71,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X0) ),
inference(resolution,[],[f57,f54]) ).
fof(f75,plain,
! [X0,X1] :
( ~ distinct_lines(X1,X0)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f65,f54]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ apart_point_and_line(intersection_point(X1,X2),X3)
| distinct_lines(X3,X1)
| distinct_points(X0,intersection_point(X1,X2))
| ~ apart_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X3)
| convergent_lines(X1,X2) ),
inference(resolution,[],[f62,f60]) ).
fof(f103,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| distinct_points(X2,intersection_point(X1,X0))
| ~ apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X2,X0)
| convergent_lines(X1,X0)
| convergent_lines(X1,X0) ),
inference(resolution,[],[f78,f61]) ).
fof(f104,plain,
! [X2,X0,X1] :
( distinct_lines(X0,X1)
| distinct_points(X2,intersection_point(X1,X0))
| ~ apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X2,X0)
| convergent_lines(X1,X0) ),
inference(duplicate_literal_removal,[],[f103]) ).
fof(f106,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X1,X0))
| ~ apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X2,X0)
| convergent_lines(X1,X0) ),
inference(forward_subsumption_resolution,[],[f104,f75]) ).
fof(f107,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ apart_point_and_line(intersection_point(sK0,sK1),sK0)
| convergent_lines(sK1,sK0) ),
inference(resolution,[],[f106,f66]) ).
fof(f111,definition,
( spl2_1
<=> convergent_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f113,plain,
( convergent_lines(sK1,sK0)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f115,definition,
( spl2_2
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f117,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK0)
| spl2_2 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f119,definition,
( spl2_3
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f121,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK1),sK1)
| spl2_3 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f107,f119,f115,f111]) ).
fof(f123,plain,
( convergent_lines(sK0,sK1)
| spl2_2 ),
inference(resolution,[],[f117,f60]) ).
fof(f124,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f123,f67]) ).
fof(f125,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f124]) ).
fof(f166,plain,
( convergent_lines(sK0,sK1)
| spl2_3 ),
inference(resolution,[],[f121,f61]) ).
fof(f167,plain,
( $false
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f166,f67]) ).
fof(f168,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f170,plain,
( convergent_lines(sK0,sK1)
| ~ spl2_1 ),
inference(resolution,[],[f113,f71]) ).
fof(f172,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f170,f67]) ).
fof(f173,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f172]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f122]) ).
cnf(s2,plain,
spl2_2,
inference(sat_conversion,[],[f125]) ).
cnf(s3,plain,
spl2_3,
inference(sat_conversion,[],[f168]) ).
cnf(s4,plain,
~ spl2_1,
inference(sat_conversion,[],[f173]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s2,s4]) ).
fof(f174,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO201+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 07:37:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.46 % (2498332)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (2498337)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3283945378_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % TRYING [4]
% 0.16/0.46 % TRYING [5]
% 0.16/0.46 % (2498338)% WARNING: option uhcvi not known.
% 0.16/0.46 % TRYING [6]
% 0.16/0.46 % TRYING [7]
% 0.16/0.46 % (2498338)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4035826487:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (2498342)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=222550109:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (2498339)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3440489686:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (2498340)dis+10_1_sil=32000:sp=arity:random_seed=801732758:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (2498341)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4083921800:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (2498343)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2239855492:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % TRYING [8]
% 0.16/0.46 % (2498338) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2498332-2498338"...
% 0.16/0.46 % (2498338)...printing done.
% 0.16/0.46 % (2498338)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2498338)------------------------------
% 0.16/0.47 % (2498338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2498338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2498338)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2498338)Termination reason: Refutation
% 0.16/0.47 % (2498338)Time elapsed: 0.006 s
% 0.16/0.47 % (2498338)Peak memory usage: 12 MB
% 0.16/0.47 % (2498338)Instructions burned: 6 (million)
% 0.16/0.47 % (2498332)Success in time 0.046 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------