%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO186+2 : 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 09:53:52 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 13 unt; 2 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 52 ~; 49 |; 21 &)
% ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 53 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X0)
| apart_point_and_line(X2,X1) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(f9,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/GEO008+0.ax',cu1) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,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)],[f13]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X0)
& ~ apart_point_and_line(X2,X1) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f25,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,[],[f9]) ).
fof(f26,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,[],[f25]) ).
fof(f31,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f32,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,[],[f14]) ).
fof(f33,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,[],[f32]) ).
fof(f34,plain,
( distinct_points(sK0,intersection_point(sK2,sK3))
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f43,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,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,[],[f26]) ).
fof(f48,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
distinct_lines(sK2,sK3),
inference(resolution,[],[f48,f51]) ).
fof(f72,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f43,f35]) ).
fof(f80,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f44,f35]) ).
fof(f85,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,sK3)
| apart_point_and_line(X0,sK3)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f45,f54]) ).
fof(f127,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)
| apart_point_and_line(sK0,sK2) ),
inference(resolution,[],[f85,f53]) ).
fof(f152,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) ),
inference(forward_subsumption_resolution,[],[f127,f49]) ).
fof(f155,definition,
( spl4_5
<=> apart_point_and_line(intersection_point(sK2,sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f157,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f159,definition,
( spl4_6
<=> apart_point_and_line(intersection_point(sK2,sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f161,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK3)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f176,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| apart_point_and_line(intersection_point(sK2,sK3),sK3) ),
inference(forward_subsumption_resolution,[],[f152,f50]) ).
fof(f178,plain,
( spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f176,f155,f159]) ).
fof(f184,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_5 ),
inference(resolution,[],[f157,f80]) ).
fof(f189,plain,
( $false
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f184,f51]) ).
fof(f190,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f191,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_6 ),
inference(resolution,[],[f161,f72]) ).
fof(f196,plain,
( $false
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f191,f51]) ).
fof(f197,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f196]) ).
cnf(s8,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f178]) ).
cnf(s10,plain,
~ spl4_5,
inference(sat_conversion,[],[f190]) ).
cnf(s11,plain,
~ spl4_6,
inference(sat_conversion,[],[f197]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s8,s11,s10]) ).
fof(f198,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.04/0.38 % CPULimit : 300
% 0.04/0.38 % WCLimit : 300
% 0.04/0.38 % DateTime : Sun Sep 27 07:31:26 UTC 2026
% 0.04/0.38 % CPUTime :
% 0.04/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.41 Running first-order model finding
% 0.04/0.41 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
% 0.17/0.47 % (2495782)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2495792)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3309484038:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2495788)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2495787)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=757412362_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2495790)dis+10_1_sil=32000:sp=arity:random_seed=2857813319:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2495789)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4143685800:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2495788)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4075594373:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2495791)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4047597971:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2495793)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2066591352:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (2495790) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2495782-2495790"...
% 0.17/0.47 % TRYING [5]
% 0.17/0.47 % (2495790)...printing done.
% 0.17/0.47 % (2495790)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2495790)------------------------------
% 0.17/0.47 % (2495790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2495790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2495790)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2495790)Termination reason: Refutation
% 0.17/0.47 % (2495790)Time elapsed: 0.004 s
% 0.17/0.47 % (2495790)Peak memory usage: 12 MB
% 0.17/0.47 % (2495790)Instructions burned: 5 (million)
% 0.17/0.47 % (2495782)Success in time 0.043 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------