%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO194+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 : n017.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 09:53:55 AM UTC 2026
% Result : Theorem 0.17s 0.54s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 19 unt; 4 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 151 ( 55 ~; 66 |; 17 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 65 !; 6 ?)
% 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(f12,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
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] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X0,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) )
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> apart_point_and_line(intersection_point(X0,X2),X1) ) ),
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(f29,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(f30,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
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] :
( ~ apart_point_and_line(intersection_point(X0,X2),X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(intersection_point(X0,X2),X1)
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1)
& convergent_lines(X2,X1)
& convergent_lines(X0,X2) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK1)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK1)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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(f49,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X2,X1)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
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,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
~ apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X0] :
( apart_point_and_line(X0,sK2)
| distinct_points(intersection_point(sK0,sK1),X0) ),
inference(resolution,[],[f49,f55]) ).
fof(f67,plain,
! [X0] :
( convergent_lines(sK0,X0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f51,f54]) ).
fof(f81,plain,
distinct_lines(sK1,sK0),
inference(resolution,[],[f67,f40]) ).
fof(f84,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK1)
| apart_point_and_line(X1,sK0)
| apart_point_and_line(X0,sK0)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f81,f48]) ).
fof(f92,plain,
! [X0] :
( ~ convergent_lines(X0,sK2)
| distinct_points(intersection_point(sK0,sK1),intersection_point(X0,sK2)) ),
inference(resolution,[],[f60,f47]) ).
fof(f238,plain,
distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)),
inference(resolution,[],[f92,f52]) ).
fof(f269,definition,
( spl3_2
<=> distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f271,plain,
( distinct_points(intersection_point(sK0,sK1),intersection_point(sK0,sK2))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f278,plain,
spl3_2,
inference(avatar_split_clause,[],[f238,f269]) ).
fof(f2127,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
| 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),sK1)
| ~ spl3_2 ),
inference(resolution,[],[f84,f271]) ).
fof(f2128,plain,
( 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),sK1)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f2127,f56]) ).
fof(f2130,definition,
( spl3_37
<=> apart_point_and_line(intersection_point(sK0,sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_37])],[avatar_definition]) ).
fof(f2132,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| ~ spl3_37 ),
inference(avatar_component_clause,[],[f2130]) ).
fof(f2134,definition,
( spl3_38
<=> apart_point_and_line(intersection_point(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_38])],[avatar_definition]) ).
fof(f2136,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ spl3_38 ),
inference(avatar_component_clause,[],[f2134]) ).
fof(f2165,definition,
( spl3_45
<=> apart_point_and_line(intersection_point(sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl3_45])],[avatar_definition]) ).
fof(f2167,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK0)
| ~ spl3_45 ),
inference(avatar_component_clause,[],[f2165]) ).
fof(f2168,plain,
( spl3_37
| spl3_38
| spl3_45
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f2128,f269,f2165,f2134,f2130]) ).
fof(f2169,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_37 ),
inference(resolution,[],[f2132,f47]) ).
fof(f2172,plain,
( $false
| ~ spl3_37 ),
inference(forward_subsumption_resolution,[],[f2169,f54]) ).
fof(f2173,plain,
~ spl3_37,
inference(avatar_contradiction_clause,[],[f2172]) ).
fof(f2188,plain,
( ~ convergent_lines(sK0,sK1)
| ~ spl3_38 ),
inference(resolution,[],[f2136,f46]) ).
fof(f2191,plain,
( $false
| ~ spl3_38 ),
inference(forward_subsumption_resolution,[],[f2188,f54]) ).
fof(f2192,plain,
~ spl3_38,
inference(avatar_contradiction_clause,[],[f2191]) ).
fof(f2203,plain,
( ~ convergent_lines(sK0,sK2)
| ~ spl3_45 ),
inference(resolution,[],[f2167,f46]) ).
fof(f2206,plain,
( $false
| ~ spl3_45 ),
inference(forward_subsumption_resolution,[],[f2203,f52]) ).
fof(f2207,plain,
~ spl3_45,
inference(avatar_contradiction_clause,[],[f2206]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f278]) ).
cnf(s93,plain,
( ~ spl3_2
| spl3_37
| spl3_38
| spl3_45 ),
inference(sat_conversion,[],[f2168]) ).
cnf(s94,plain,
~ spl3_37,
inference(sat_conversion,[],[f2173]) ).
cnf(s95,plain,
~ spl3_38,
inference(sat_conversion,[],[f2192]) ).
cnf(s96,plain,
~ spl3_45,
inference(sat_conversion,[],[f2207]) ).
cnf(s97,plain,
~ spl3_2,
inference(rat,[],[s93,s96,s95,s94]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s3,s97]) ).
fof(f2208,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO194+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:27:04 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.17/0.54 % (2213528)Will run a generic schedule for satisfiability detection.
% 0.17/0.54 % (2213533)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1966489976_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.54 % TRYING [1]
% 0.17/0.54 % TRYING [2]
% 0.17/0.54 % TRYING [3]
% 0.17/0.54 % TRYING [4]
% 0.17/0.54 % TRYING [5]
% 0.17/0.54 % (2213534)% WARNING: option uhcvi not known.
% 0.17/0.54 % TRYING [6]
% 0.17/0.54 % TRYING [7]
% 0.17/0.54 % (2213538)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=850823555:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.54 % (2213534)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=77830641:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.54 % (2213535)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4075655527:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.54 % (2213536)dis+10_1_sil=32000:sp=arity:random_seed=18403766:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.54 % (2213537)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2801070206:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.54 % (2213539)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=322329658:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.54 % TRYING [8]
% 0.17/0.54 % TRYING [9]
% 0.17/0.54 % TRYING [10]
% 0.17/0.54 % TRYING [11]
% 0.17/0.54 % (2213538) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2213528-2213538"...
% 0.17/0.54 % (2213539)Instruction limit reached!
% 0.17/0.54 % (2213539)------------------------------
% 0.17/0.54 % (2213539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.54 % (2213539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.54 % (2213539)CaDiCaL version: 2.1.3
% 0.17/0.54 % (2213539)Termination reason: Instruction limit
% 0.17/0.54 % (2213539)Termination phase: Saturation
% 0.17/0.54 % (2213539)Time elapsed: 0.052 s
% 0.17/0.54 % (2213539)Peak memory usage: 11 MB
% 0.17/0.54 % (2213539)Instructions burned: 160 (million)
% 0.17/0.54 % (2213538)...printing done.
% 0.17/0.54 % (2213538)Refutation found. Thanks to Tanya!
% 0.17/0.54 % SZS status Theorem for theBenchmark
% 0.17/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.54 % (2213538)------------------------------
% 0.17/0.54 % (2213538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.54 % (2213538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.54 % (2213538)CaDiCaL version: 2.1.3
% 0.17/0.54 % (2213538)Termination reason: Refutation
% 0.17/0.54 % (2213538)Time elapsed: 0.053 s
% 0.17/0.54 % (2213538)Peak memory usage: 13 MB
% 0.17/0.54 % (2213538)Instructions burned: 92 (million)
% 0.17/0.54 % (2213528)Success in time 0.102 s
% 0.17/0.54 % Vampire exiting
%------------------------------------------------------------------------------