%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO203+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 : n013.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 09:53:59 AM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 15 unt; 4 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 53 ~; 51 |; 14 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 50 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
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/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
=> equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) )
=> equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
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(f77,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1,X2] :
( ~ equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1,X2] :
( ~ equal_lines(line_connecting(intersection_point(X0,X1),intersection_point(X0,X2)),X0)
& convergent_lines(X0,X1)
& convergent_lines(X0,X2)
& distinct_points(intersection_point(X0,X1),intersection_point(X0,X2)) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
( ~ equal_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0)
& convergent_lines(sK0,sK1)
& convergent_lines(sK0,sK2)
& distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f79]) ).
fof(f87,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f88,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f89,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f91,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(f117,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f118,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(cnf_transformation,[],[f80]) ).
fof(f119,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
~ equal_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
distinct_lines(line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),sK0),
inference(resolution,[],[f117,f121]) ).
fof(f255,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
inference(resolution,[],[f91,f123]) ).
fof(f964,plain,
( apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| apart_point_and_line(intersection_point(sK0,sK2),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
inference(resolution,[],[f255,f118]) ).
fof(f977,definition,
( spl3_31
<=> apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_31])],[avatar_definition]) ).
fof(f979,plain,
( apart_point_and_line(intersection_point(sK0,sK1),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| ~ spl3_31 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f981,definition,
( spl3_32
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_32])],[avatar_definition]) ).
fof(f983,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_32 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f989,definition,
( spl3_34
<=> apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_34])],[avatar_definition]) ).
fof(f991,plain,
( apart_point_and_line(intersection_point(sK0,sK2),line_connecting(intersection_point(sK0,sK1),intersection_point(sK0,sK2)))
| ~ spl3_34 ),
inference(avatar_component_clause,[],[f989]) ).
fof(f993,definition,
( spl3_35
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_35])],[avatar_definition]) ).
fof(f995,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_35 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f1001,plain,
( spl3_31
| spl3_32
| spl3_35
| spl3_34 ),
inference(avatar_split_clause,[],[f964,f989,f993,f981,f977]) ).
fof(f1230,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_31 ),
inference(resolution,[],[f979,f87]) ).
fof(f1233,plain,
( $false
| ~ spl3_31 ),
inference(forward_subsumption_resolution,[],[f1230,f118]) ).
fof(f1234,plain,
~ spl3_31,
inference(avatar_contradiction_clause,[],[f1233]) ).
fof(f1235,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_32 ),
inference(resolution,[],[f983,f89]) ).
fof(f1238,plain,
( $false
| ~ spl3_32 ),
inference(forward_subsumption_resolution,[],[f1235,f120]) ).
fof(f1239,plain,
~ spl3_32,
inference(avatar_contradiction_clause,[],[f1238]) ).
fof(f1253,plain,
( ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_34 ),
inference(resolution,[],[f991,f88]) ).
fof(f1256,plain,
( $false
| ~ spl3_34 ),
inference(forward_subsumption_resolution,[],[f1253,f118]) ).
fof(f1257,plain,
~ spl3_34,
inference(avatar_contradiction_clause,[],[f1256]) ).
fof(f1258,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_35 ),
inference(resolution,[],[f995,f89]) ).
fof(f1261,plain,
( $false
| ~ spl3_35 ),
inference(forward_subsumption_resolution,[],[f1258,f119]) ).
fof(f1262,plain,
~ spl3_35,
inference(avatar_contradiction_clause,[],[f1261]) ).
cnf(s55,plain,
( spl3_31
| spl3_32
| spl3_34
| spl3_35 ),
inference(sat_conversion,[],[f1001]) ).
cnf(s59,plain,
~ spl3_31,
inference(sat_conversion,[],[f1234]) ).
cnf(s60,plain,
~ spl3_32,
inference(sat_conversion,[],[f1239]) ).
cnf(s61,plain,
~ spl3_34,
inference(sat_conversion,[],[f1257]) ).
cnf(s62,plain,
~ spl3_35,
inference(sat_conversion,[],[f1262]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s55,s62,s61,s60,s59]) ).
fof(f1263,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n013.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 07:35:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.48 % (4086861)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (4086870)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1373758782:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (4086867)% WARNING: option uhcvi not known.
% 0.15/0.48 % (4086866)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1056605451_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (4086867)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1468853805:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (4086868)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2108844176:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (4086869)dis+10_1_sil=32000:sp=arity:random_seed=1841574960:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (4086872)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=393526733:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % (4086871)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4181253692:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % TRYING [5]
% 0.15/0.48 % TRYING [6]
% 0.15/0.48 % (4086869) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4086861-4086869"...
% 0.15/0.48 % TRYING [7]
% 0.15/0.48 % (4086869)...printing done.
% 0.15/0.48 % (4086869)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (4086869)------------------------------
% 0.15/0.48 % (4086869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (4086869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (4086869)CaDiCaL version: 2.1.3
% 0.15/0.48 % (4086869)Termination reason: Refutation
% 0.15/0.48 % (4086869)Time elapsed: 0.023 s
% 0.15/0.48 % (4086869)Peak memory usage: 12 MB
% 0.15/0.48 % (4086869)Instructions burned: 37 (million)
% 0.15/0.48 % (4086861)Success in time 0.057 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------