%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:53:58 AM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 17 unt; 4 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 54 ~; 59 |; 3 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 63 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
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,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(f36,conjecture,
! [X0,X1] :
( convergent_lines(X0,X1)
=> equal_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( convergent_lines(X0,X1)
=> equal_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
=> equal_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f55,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f56,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f77,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] :
( ~ equal_points(intersection_point(X0,X1),intersection_point(X1,X0))
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
( ~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0))
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f78]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f88,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f89,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f116,plain,
! [X0,X1] :
( equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
~ equal_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(resolution,[],[f116,f118]) ).
fof(f149,plain,
! [X0] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f93,f117]) ).
fof(f165,plain,
distinct_lines(sK1,sK0),
inference(resolution,[],[f149,f82]) ).
fof(f170,plain,
convergent_lines(sK1,sK0),
inference(resolution,[],[f165,f94]) ).
fof(f224,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f90,f165]) ).
fof(f2096,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK1)
| apart_point_and_line(intersection_point(sK1,sK0),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
inference(resolution,[],[f224,f120]) ).
fof(f2109,definition,
( spl2_49
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_49])],[avatar_definition]) ).
fof(f2111,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl2_49 ),
inference(avatar_component_clause,[],[f2109]) ).
fof(f2113,definition,
( spl2_50
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_50])],[avatar_definition]) ).
fof(f2115,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl2_50 ),
inference(avatar_component_clause,[],[f2113]) ).
fof(f2121,definition,
( spl2_52
<=> apart_point_and_line(intersection_point(sK1,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_52])],[avatar_definition]) ).
fof(f2123,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK1)
| ~ spl2_52 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f2125,definition,
( spl2_53
<=> apart_point_and_line(intersection_point(sK1,sK0),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_53])],[avatar_definition]) ).
fof(f2127,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f2125]) ).
fof(f2133,plain,
( spl2_49
| spl2_50
| spl2_53
| spl2_52 ),
inference(avatar_split_clause,[],[f2096,f2121,f2125,f2113,f2109]) ).
fof(f2134,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_49 ),
inference(resolution,[],[f2111,f89]) ).
fof(f2137,plain,
( $false
| ~ spl2_49 ),
inference(forward_subsumption_resolution,[],[f2134,f117]) ).
fof(f2138,plain,
~ spl2_49,
inference(avatar_contradiction_clause,[],[f2137]) ).
fof(f2336,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl2_50 ),
inference(resolution,[],[f2115,f88]) ).
fof(f2339,plain,
( $false
| ~ spl2_50 ),
inference(forward_subsumption_resolution,[],[f2336,f117]) ).
fof(f2340,plain,
~ spl2_50,
inference(avatar_contradiction_clause,[],[f2339]) ).
fof(f2507,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl2_52 ),
inference(resolution,[],[f2123,f88]) ).
fof(f2510,plain,
( $false
| ~ spl2_52 ),
inference(forward_subsumption_resolution,[],[f2507,f170]) ).
fof(f2511,plain,
~ spl2_52,
inference(avatar_contradiction_clause,[],[f2510]) ).
fof(f2623,plain,
( ~ convergent_lines(sK1,sK0)
| ~ spl2_53 ),
inference(resolution,[],[f2127,f89]) ).
fof(f2626,plain,
( $false
| ~ spl2_53 ),
inference(forward_subsumption_resolution,[],[f2623,f170]) ).
fof(f2627,plain,
~ spl2_53,
inference(avatar_contradiction_clause,[],[f2626]) ).
cnf(s155,plain,
( spl2_49
| spl2_50
| spl2_52
| spl2_53 ),
inference(sat_conversion,[],[f2133]) ).
cnf(s156,plain,
~ spl2_49,
inference(sat_conversion,[],[f2138]) ).
cnf(s182,plain,
~ spl2_50,
inference(sat_conversion,[],[f2340]) ).
cnf(s199,plain,
~ spl2_52,
inference(sat_conversion,[],[f2511]) ).
cnf(s218,plain,
~ spl2_53,
inference(sat_conversion,[],[f2627]) ).
cnf(s219,plain,
$false,
inference(rat,[],[s155,s218,s199,s182,s156]) ).
fof(f2628,plain,
$false,
inference(avatar_sat_refutation,[],[s219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 07:36:41 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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 % (168684)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (168692)dis+10_1_sil=32000:sp=arity:random_seed=960949313:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (168690)% WARNING: option uhcvi not known.
% 0.18/0.48 % (168689)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3056531772_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (168690)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=231342291:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (168691)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1803803737:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (168694)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1420086060:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (168693)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=43315685:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (168695)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=621380701:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % TRYING [1]
% 0.18/0.48 % TRYING [2]
% 0.18/0.48 % TRYING [3]
% 0.18/0.48 % TRYING [4]
% 0.18/0.48 % TRYING [5]
% 0.18/0.48 % TRYING [6]
% 0.18/0.48 % TRYING [7]
% 0.18/0.48 % (168692) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-168684-168692"...
% 0.18/0.48 % (168692)...printing done.
% 0.18/0.48 % (168692)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 % (168692)------------------------------
% 0.18/0.48 % (168692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (168692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (168692)CaDiCaL version: 2.1.3
% 0.18/0.48 % (168692)Termination reason: Refutation
% 0.18/0.48 % (168692)Time elapsed: 0.032 s
% 0.18/0.48 % (168692)Peak memory usage: 13 MB
% 0.18/0.48 % (168692)Instructions burned: 103 (million)
% 0.18/0.48 % (168684)Success in time 0.048 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------