%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO186+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 0.11s 0.46s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 15 unt; 2 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 50 ~; 62 |; 15 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 70 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/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/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(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(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,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) )
=> ~ distinct_points(X0,intersection_point(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) )
=> ~ distinct_points(X0,intersection_point(X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
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,X2,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( distinct_points(X0,intersection_point(X2,X3))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f45,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,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(f50,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0] : convergent_lines(X0,X0),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f62,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f63,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| convergent_lines(X0,X1) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f64,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(consistent_polarity_flipping,[],[f47]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X2)
| convergent_lines(X0,X1)
| distinct_lines(X1,X2) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f67,plain,
~ distinct_points(sK0,intersection_point(sK2,sK3)),
inference(consistent_polarity_flipping,[],[f55]) ).
fof(f69,plain,
~ convergent_lines(sK2,sK3),
inference(consistent_polarity_flipping,[],[f53]) ).
fof(f72,plain,
! [X0,X1] :
( distinct_lines(X1,X0)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f66,f57]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( convergent_lines(X0,X1)
| distinct_points(X2,X3)
| apart_point_and_line(X3,X0)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) ),
inference(resolution,[],[f72,f64]) ).
fof(f88,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,sK3)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK3) ),
inference(resolution,[],[f76,f69]) ).
fof(f132,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| apart_point_and_line(intersection_point(sK2,sK3),sK3)
| apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,sK3) ),
inference(resolution,[],[f88,f67]) ).
fof(f135,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| apart_point_and_line(intersection_point(sK2,sK3),sK3)
| apart_point_and_line(sK0,sK3) ),
inference(forward_subsumption_resolution,[],[f132,f52]) ).
fof(f137,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| apart_point_and_line(intersection_point(sK2,sK3),sK3) ),
inference(forward_subsumption_resolution,[],[f135,f51]) ).
fof(f140,definition,
( spl4_1
<=> apart_point_and_line(intersection_point(sK2,sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f142,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f144,definition,
( spl4_2
<=> apart_point_and_line(intersection_point(sK2,sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f146,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f147,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f137,f144,f140]) ).
fof(f202,plain,
( convergent_lines(sK2,sK3)
| ~ spl4_2 ),
inference(resolution,[],[f146,f62]) ).
fof(f205,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f202,f69]) ).
fof(f206,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f205]) ).
fof(f212,plain,
( convergent_lines(sK2,sK3)
| ~ spl4_1 ),
inference(resolution,[],[f142,f63]) ).
fof(f215,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f212,f69]) ).
fof(f216,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f215]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f147]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f206]) ).
cnf(s4,plain,
~ spl4_1,
inference(sat_conversion,[],[f216]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f217,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:30:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.46 % (1991470)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (1991479)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3350520861:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (1991476)% WARNING: option uhcvi not known.
% 0.11/0.46 % (1991475)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2509288448_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (1991477)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3669685932:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (1991476)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=112545490:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (1991478)dis+10_1_sil=32000:sp=arity:random_seed=3475378530:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (1991480)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1323885772:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (1991481)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3729061771:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % TRYING [4]
% 0.11/0.46 % TRYING [5]
% 0.11/0.46 % (1991476) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1991470-1991476"...
% 0.11/0.46 % (1991476)...printing done.
% 0.11/0.46 % TRYING [6]
% 0.11/0.46 % (1991476)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.46 % (1991476)------------------------------
% 0.36/0.46 % (1991476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.46 % (1991476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.46 % (1991476)CaDiCaL version: 2.1.3
% 0.36/0.46 % (1991476)Termination reason: Refutation
% 0.36/0.46 % (1991476)Time elapsed: 0.006 s
% 0.36/0.46 % (1991476)Peak memory usage: 12 MB
% 0.36/0.46 % (1991476)Instructions burned: 7 (million)
% 0.36/0.46 % (1991470)Success in time 0.041 s
% 0.36/0.46 % Vampire exiting
%------------------------------------------------------------------------------