%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO189+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 : 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 09:53:53 AM UTC 2026
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 15 unt; 5 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 154 ( 58 ~; 66 |; 19 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 53 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
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(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X1,line_connecting(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X1,line_connecting(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f23,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
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(f31,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f35,plain,
? [X0,X1,X2] :
( apart_point_and_line(X1,line_connecting(X0,X2))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f36,plain,
? [X0,X1,X2] :
( apart_point_and_line(X1,line_connecting(X0,X2))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK2))
& distinct_points(sK0,sK1)
& distinct_points(sK0,sK2)
& distinct_points(sK1,sK2)
& ~ apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
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(f50,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f37]) ).
fof(f67,plain,
! [X0] :
( distinct_lines(line_connecting(sK0,sK2),X0)
| apart_point_and_line(sK1,X0) ),
inference(resolution,[],[f50,f56]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ distinct_points(X1,X2)
| apart_point_and_line(X1,X0)
| apart_point_and_line(X2,line_connecting(sK0,sK2))
| apart_point_and_line(X2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X1,line_connecting(sK0,sK2)) ),
inference(resolution,[],[f67,f48]) ).
fof(f185,plain,
! [X0] :
( apart_point_and_line(sK0,X0)
| apart_point_and_line(sK2,line_connecting(sK0,sK2))
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
inference(resolution,[],[f77,f54]) ).
fof(f206,definition,
( spl3_1
<=> apart_point_and_line(sK2,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f208,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f219,definition,
( spl3_4
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f221,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f223,definition,
( spl3_5
<=> ! [X0] :
( apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f224,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f225,plain,
( spl3_4
| spl3_1
| spl3_5 ),
inference(avatar_split_clause,[],[f185,f223,f206,f219]) ).
fof(f257,plain,
( ~ distinct_points(sK0,sK2)
| ~ spl3_4 ),
inference(resolution,[],[f221,f44]) ).
fof(f260,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f257,f54]) ).
fof(f261,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f264,plain,
( ~ distinct_points(sK0,sK2)
| ~ spl3_1 ),
inference(resolution,[],[f208,f45]) ).
fof(f267,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f264,f54]) ).
fof(f268,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f269,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_5 ),
inference(resolution,[],[f224,f52]) ).
fof(f275,definition,
( spl3_13
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f277,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f279,definition,
( spl3_14
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f281,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f282,plain,
( spl3_13
| spl3_14
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f269,f223,f279,f275]) ).
fof(f305,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_13 ),
inference(resolution,[],[f277,f44]) ).
fof(f308,plain,
( $false
| ~ spl3_13 ),
inference(forward_subsumption_resolution,[],[f305,f55]) ).
fof(f309,plain,
~ spl3_13,
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f343,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_14 ),
inference(resolution,[],[f281,f45]) ).
fof(f346,plain,
( $false
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f343,f55]) ).
fof(f347,plain,
~ spl3_14,
inference(avatar_contradiction_clause,[],[f346]) ).
cnf(s3,plain,
( spl3_1
| spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f225]) ).
cnf(s11,plain,
~ spl3_4,
inference(sat_conversion,[],[f261]) ).
cnf(s12,plain,
~ spl3_1,
inference(sat_conversion,[],[f268]) ).
cnf(s13,plain,
( ~ spl3_5
| spl3_13
| spl3_14 ),
inference(sat_conversion,[],[f282]) ).
cnf(s14,plain,
~ spl3_13,
inference(sat_conversion,[],[f309]) ).
cnf(s15,plain,
~ spl3_14,
inference(sat_conversion,[],[f347]) ).
cnf(s16,plain,
~ spl3_5,
inference(rat,[],[s13,s15,s14]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s3,s16,s11,s12]) ).
fof(f348,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO189+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 07:31:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.18/0.46 % (2496621)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (2496630)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4231318982:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.46 % (2496627)% WARNING: option uhcvi not known.
% 0.18/0.46 % (2496627)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1381618942:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.46 % (2496626)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4021654508_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.46 % (2496631)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3787290274:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.46 % (2496628)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4194379732:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.46 % (2496629)dis+10_1_sil=32000:sp=arity:random_seed=703069811:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.46 % (2496632)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3998928609:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.46 % TRYING [1]
% 0.18/0.46 % TRYING [2]
% 0.18/0.46 % TRYING [3]
% 0.18/0.46 % TRYING [4]
% 0.18/0.46 % TRYING [5]
% 0.18/0.46 % (2496629) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2496621-2496629"...
% 0.18/0.46 % TRYING [6]
% 0.18/0.46 % (2496629)...printing done.
% 0.18/0.46 % (2496629)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (2496629)------------------------------
% 0.18/0.46 % (2496629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (2496629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (2496629)CaDiCaL version: 2.1.3
% 0.18/0.46 % (2496629)Termination reason: Refutation
% 0.18/0.46 % (2496629)Time elapsed: 0.007 s
% 0.18/0.46 % (2496629)Peak memory usage: 12 MB
% 0.18/0.46 % (2496629)Instructions burned: 10 (million)
% 0.18/0.46 % (2496621)Success in time 0.042 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------