%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO175+1 : 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 : n019.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 09:53:47 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 13 unt; 2 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 43 ~; 50 |; 17 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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(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,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,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] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X0,X3)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_points(X0,intersection_point(X2,X3)) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK0,sK3)
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& distinct_points(sK0,intersection_point(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f36]) ).
fof(f40,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,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,[],[f28]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(sK0,intersection_point(sK2,sK3)),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
convergent_lines(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
~ apart_point_and_line(sK0,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f71,plain,
! [X0] :
( convergent_lines(sK2,X0)
| distinct_lines(sK3,X0) ),
inference(resolution,[],[f51,f53]) ).
fof(f73,plain,
distinct_lines(sK3,sK2),
inference(resolution,[],[f71,f40]) ).
fof(f76,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK3)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK3) ),
inference(resolution,[],[f73,f48]) ).
fof(f373,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK3)
| apart_point_and_line(intersection_point(sK2,sK3),sK2)
| apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,sK3) ),
inference(resolution,[],[f76,f52]) ).
fof(f410,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK3)
| apart_point_and_line(intersection_point(sK2,sK3),sK2)
| apart_point_and_line(sK0,sK3) ),
inference(forward_subsumption_resolution,[],[f373,f56]) ).
fof(f413,definition,
( spl4_7
<=> apart_point_and_line(intersection_point(sK2,sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f415,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK3)
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f417,definition,
( spl4_8
<=> apart_point_and_line(intersection_point(sK2,sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f419,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK2)
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f470,plain,
( apart_point_and_line(intersection_point(sK2,sK3),sK3)
| apart_point_and_line(intersection_point(sK2,sK3),sK2) ),
inference(forward_subsumption_resolution,[],[f410,f55]) ).
fof(f474,plain,
( spl4_8
| spl4_7 ),
inference(avatar_split_clause,[],[f470,f413,f417]) ).
fof(f478,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_7 ),
inference(resolution,[],[f415,f47]) ).
fof(f481,plain,
( $false
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f478,f53]) ).
fof(f482,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f483,plain,
( ~ convergent_lines(sK2,sK3)
| ~ spl4_8 ),
inference(resolution,[],[f419,f46]) ).
fof(f486,plain,
( $false
| ~ spl4_8 ),
inference(forward_subsumption_resolution,[],[f483,f53]) ).
fof(f487,plain,
~ spl4_8,
inference(avatar_contradiction_clause,[],[f486]) ).
cnf(s26,plain,
( spl4_7
| spl4_8 ),
inference(sat_conversion,[],[f474]) ).
cnf(s28,plain,
~ spl4_7,
inference(sat_conversion,[],[f482]) ).
cnf(s29,plain,
~ spl4_8,
inference(sat_conversion,[],[f487]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s26,s29,s28]) ).
fof(f488,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO175+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n019.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 07:23:49 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.44 Running first-order model finding
% 0.12/0.44 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
% 0.17/0.48 % (2760957)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (2760967)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1341571536:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (2760963)% WARNING: option uhcvi not known.
% 0.17/0.48 % (2760967) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2760957-2760967"...
% 0.17/0.48 % (2760964)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2312327307:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (2760962)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3933034534_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (2760963)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2948598656:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (2760967)...printing done.
% 0.17/0.48 % (2760965)dis+10_1_sil=32000:sp=arity:random_seed=152921279:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (2760966)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2805938945:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (2760968)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1857600317:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (2760967)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2760967)------------------------------
% 0.17/0.48 % (2760967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2760967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2760967)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2760967)Termination reason: Refutation
% 0.17/0.48 % (2760967)Time elapsed: 0.006 s
% 0.17/0.48 % (2760967)Peak memory usage: 12 MB
% 0.17/0.48 % (2760967)Instructions burned: 18 (million)
% 0.17/0.48 % (2760957)Success in time 0.032 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------