%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO185+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 : n001.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 09:53:52 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 11 unt; 2 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 108 ( 48 ~; 37 |; 12 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(f31,axiom,
! [X0,X1] :
( equal_points(X0,X1)
<=> ~ distinct_points(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax1) ).
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)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) )
=> ( incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) )
=> ( incident_point_and_line(X0,X2)
& incident_point_and_line(X0,X3) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
=> incident_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( equal_points(X0,X1)
=> ~ distinct_points(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f48,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] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f52,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f53,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f52]) ).
fof(f78,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ equal_points(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f79,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
| apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X0,X2)
| ~ incident_point_and_line(X0,X3) )
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f81,plain,
? [X0,X1,X2,X3] :
( ( ~ incident_point_and_line(X0,X2)
| ~ incident_point_and_line(X0,X3) )
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& equal_points(X0,intersection_point(X2,X3)) ),
inference(flattening,[],[f80]) ).
fof(f90,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f91,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f118,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f119,plain,
! [X0,X1] :
( apart_point_and_line(X0,X1)
| incident_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
( ~ incident_point_and_line(sK0,sK3)
| ~ incident_point_and_line(sK0,sK2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f121,plain,
equal_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f81]) ).
fof(f122,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X0)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f133,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(X0,X1),X1)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X2)
| ~ apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1) ),
inference(consistent_polarity_flipping,[],[f93]) ).
fof(f158,plain,
! [X0,X1] :
( ~ equal_points(X0,X1)
| distinct_points(X0,X1) ),
inference(consistent_polarity_flipping,[],[f118]) ).
fof(f159,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(consistent_polarity_flipping,[],[f119]) ).
fof(f161,plain,
~ convergent_lines(sK2,sK3),
inference(consistent_polarity_flipping,[],[f122]) ).
fof(f162,plain,
( incident_point_and_line(sK0,sK3)
| incident_point_and_line(sK0,sK2) ),
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f164,definition,
( spl4_1
<=> incident_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f166,plain,
( incident_point_and_line(sK0,sK2)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl4_2
<=> incident_point_and_line(sK0,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f170,plain,
( incident_point_and_line(sK0,sK3)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f162,f168,f164]) ).
fof(f175,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(resolution,[],[f158,f121]) ).
fof(f176,plain,
( ~ apart_point_and_line(sK0,sK3)
| ~ spl4_2 ),
inference(resolution,[],[f159,f170]) ).
fof(f196,plain,
! [X0] :
( ~ apart_point_and_line(intersection_point(sK2,sK3),X0)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f135,f175]) ).
fof(f201,plain,
( apart_point_and_line(sK0,sK2)
| convergent_lines(sK2,sK3) ),
inference(resolution,[],[f196,f132]) ).
fof(f202,plain,
( apart_point_and_line(sK0,sK3)
| convergent_lines(sK2,sK3) ),
inference(resolution,[],[f196,f133]) ).
fof(f207,plain,
( convergent_lines(sK2,sK3)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f202,f176]) ).
fof(f208,plain,
apart_point_and_line(sK0,sK2),
inference(forward_subsumption_resolution,[],[f201,f161]) ).
fof(f209,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f207,f161]) ).
fof(f210,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f209]) ).
fof(f212,plain,
( ~ apart_point_and_line(sK0,sK2)
| ~ spl4_1 ),
inference(resolution,[],[f166,f159]) ).
fof(f213,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f208,f212]) ).
fof(f214,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f213]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f210]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f214]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f215,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO185+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 07:34:00 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.19/0.48 % (3223606)Will run a generic schedule for satisfiability detection.
% 0.19/0.48 % (3223616)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4267247380_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.48 % TRYING [1]
% 0.19/0.48 % TRYING [2]
% 0.19/0.48 % TRYING [3]
% 0.19/0.48 % TRYING [4]
% 0.19/0.48 % (3223617)% WARNING: option uhcvi not known.
% 0.19/0.48 % TRYING [5]
% 0.19/0.48 % TRYING [6]
% 0.19/0.48 % (3223620)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=162052189:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.48 % (3223617)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=485238282:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.48 % (3223619)dis+10_1_sil=32000:sp=arity:random_seed=142376735:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.48 % (3223622)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2005589690:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.48 % (3223621)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=104668947:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.48 % (3223618)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=116124325:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.48 % (3223617) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3223606-3223617"...
% 0.19/0.48 % (3223622) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3223606-3223622"...
% 0.19/0.48 % (3223620) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3223606-3223620"...
% 0.19/0.48 % (3223617)...printing done.
% 0.19/0.48 % TRYING [7]
% 0.19/0.48 % (3223622)...printing done.
% 0.19/0.48 % (3223617)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (3223617)------------------------------
% 0.19/0.49 % (3223617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.49 % (3223617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.49 % (3223617)CaDiCaL version: 2.1.3
% 0.19/0.49 % (3223617)Termination reason: Refutation
% 0.19/0.49 % (3223617)Time elapsed: 0.004 s
% 0.19/0.49 % (3223617)Peak memory usage: 12 MB
% 0.19/0.49 % (3223617)Instructions burned: 3 (million)
% 0.19/0.49 % (3223606)Success in time 0.047 s
% 0.19/0.49 % Vampire exiting
%------------------------------------------------------------------------------