%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO204+2 : 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 : n013.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 09:53:59 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 81 ( 18 unt; 7 def)
% Number of atoms : 209 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 212 ( 84 ~; 101 |; 14 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con1) ).
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/sandbox/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( distinct_points(X0,X2)
& ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ distinct_points(X1,X2) )
=> ( distinct_points(X0,X2)
& ~ distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f21]) ).
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(f32,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& ~ distinct_points(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ( ~ distinct_points(X0,X2)
| distinct_lines(line_connecting(X0,X1),line_connecting(X0,X2)) )
& distinct_points(X0,X1)
& ~ distinct_points(X1,X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ( ~ distinct_points(sK0,sK2)
| distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) )
& distinct_points(sK0,sK1)
& ~ distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X1)
| distinct_points(X1,X2)
| distinct_points(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
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(f49,plain,
~ distinct_points(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
( ~ distinct_points(sK0,sK2)
| distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,definition,
( spl3_1
<=> distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f55,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl3_2
<=> distinct_points(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f58,plain,
( distinct_points(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f51,f57,f53]) ).
fof(f61,plain,
! [X0] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(resolution,[],[f38,f50]) ).
fof(f62,plain,
distinct_points(sK0,sK2),
inference(resolution,[],[f61,f49]) ).
fof(f64,plain,
! [X0,X1] :
( distinct_points(sK0,X0)
| distinct_points(X0,X1)
| distinct_points(sK1,X1) ),
inference(resolution,[],[f61,f38]) ).
fof(f67,plain,
spl3_2,
inference(avatar_split_clause,[],[f62,f57]) ).
fof(f74,plain,
! [X0] :
( distinct_points(sK0,X0)
| distinct_points(X0,sK2) ),
inference(resolution,[],[f64,f49]) ).
fof(f75,plain,
! [X0] :
( distinct_points(sK0,X0)
| distinct_points(X0,sK1) ),
inference(resolution,[],[f64,f35]) ).
fof(f112,plain,
( ! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X1,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| ~ spl3_1 ),
inference(resolution,[],[f45,f55]) ).
fof(f137,plain,
( ! [X0] :
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(sK0,X0) )
| ~ spl3_1 ),
inference(resolution,[],[f112,f75]) ).
fof(f164,definition,
( spl3_5
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f165,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK0,sK2))
| spl3_5 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl3_6
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f170,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f173,definition,
( spl3_7
<=> ! [X0] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(sK0,X0)
| apart_point_and_line(X0,line_connecting(sK0,sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f174,plain,
( ! [X0] :
( apart_point_and_line(X0,line_connecting(sK0,sK2))
| distinct_points(sK0,X0)
| apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f181,definition,
( spl3_9
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f183,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f185,definition,
( spl3_10
<=> apart_point_and_line(sK1,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f187,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK2))
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f226,plain,
( spl3_7
| spl3_10
| spl3_9
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f137,f53,f181,f185,f173]) ).
fof(f246,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK2)
| ~ spl3_5 ),
inference(resolution,[],[f166,f42]) ).
fof(f250,plain,
( distinct_points(sK0,sK0)
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f246,f74]) ).
fof(f251,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f250,f35]) ).
fof(f252,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f253,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ spl3_6 ),
inference(resolution,[],[f170,f42]) ).
fof(f259,plain,
( distinct_points(sK0,sK0)
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f253,f75]) ).
fof(f260,plain,
( $false
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f259,f35]) ).
fof(f261,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f287,plain,
( distinct_points(sK0,sK0)
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| spl3_5
| ~ spl3_7 ),
inference(resolution,[],[f174,f165]) ).
fof(f289,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| spl3_5
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f287,f35]) ).
fof(f291,plain,
( spl3_6
| spl3_5
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f289,f173,f164,f168]) ).
fof(f367,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK0,sK1)
| ~ spl3_9 ),
inference(resolution,[],[f183,f41]) ).
fof(f373,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f367,f35]) ).
fof(f374,plain,
( $false
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f373,f50]) ).
fof(f375,plain,
~ spl3_9,
inference(avatar_contradiction_clause,[],[f374]) ).
fof(f383,plain,
( distinct_points(sK1,sK2)
| ~ distinct_points(sK0,sK2)
| ~ spl3_10 ),
inference(resolution,[],[f187,f41]) ).
fof(f390,plain,
( ~ distinct_points(sK0,sK2)
| ~ spl3_10 ),
inference(forward_subsumption_resolution,[],[f383,f49]) ).
fof(f391,plain,
( $false
| ~ spl3_2
| ~ spl3_10 ),
inference(forward_subsumption_resolution,[],[f390,f58]) ).
fof(f392,plain,
( ~ spl3_2
| ~ spl3_10 ),
inference(avatar_contradiction_clause,[],[f391]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f67]) ).
cnf(s21,plain,
( ~ spl3_1
| spl3_7
| spl3_9
| spl3_10 ),
inference(sat_conversion,[],[f226]) ).
cnf(s29,plain,
~ spl3_5,
inference(sat_conversion,[],[f252]) ).
cnf(s30,plain,
~ spl3_6,
inference(sat_conversion,[],[f261]) ).
cnf(s31,plain,
( spl3_5
| spl3_6
| ~ spl3_7 ),
inference(sat_conversion,[],[f291]) ).
cnf(s40,plain,
~ spl3_9,
inference(sat_conversion,[],[f375]) ).
cnf(s41,plain,
( ~ spl3_2
| ~ spl3_10 ),
inference(sat_conversion,[],[f392]) ).
cnf(s42,plain,
~ spl3_7,
inference(rat,[],[s31,s30,s29]) ).
cnf(s49,plain,
( ~ spl3_1
| spl3_10 ),
inference(rat,[],[s21,s40,s42]) ).
cnf(s64,plain,
~ spl3_10,
inference(rat,[],[s41,s3]) ).
cnf(s66,plain,
~ spl3_1,
inference(rat,[],[s49,s64]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s1,s3,s66]) ).
fof(f393,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.36 % Computer : n013.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 07:35:06 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.12/0.45 % (4086421)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (4086426)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=825088581_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.45 % TRYING [1]
% 0.12/0.45 % TRYING [2]
% 0.12/0.45 % TRYING [3]
% 0.12/0.45 % TRYING [4]
% 0.12/0.45 % TRYING [5]
% 0.12/0.45 % TRYING [6]
% 0.12/0.45 % TRYING [7]
% 0.12/0.45 % TRYING [8]
% 0.12/0.45 % TRYING [9]
% 0.12/0.45 % (4086427)% WARNING: option uhcvi not known.
% 0.12/0.45 % (4086432)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=697082435:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (4086428)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1740974513:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (4086429)dis+10_1_sil=32000:sp=arity:random_seed=553063908:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % TRYING [10]
% 0.12/0.45 % (4086430)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=471663911:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (4086431)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3522095390:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.45 % TRYING [11]
% 0.12/0.45 % TRYING [12]
% 0.12/0.45 % (4086429) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4086421-4086429"...
% 0.12/0.45 % (4086427)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=760820398:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % TRYING [13]
% 0.12/0.45 % (4086429)...printing done.
% 0.12/0.45 % (4086429)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (4086429)------------------------------
% 0.12/0.45 % (4086429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (4086429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (4086429)CaDiCaL version: 2.1.3
% 0.12/0.45 % (4086429)Termination reason: Refutation
% 0.12/0.45 % (4086429)Time elapsed: 0.008 s
% 0.12/0.45 % (4086429)Peak memory usage: 12 MB
% 0.12/0.45 % (4086429)Instructions burned: 11 (million)
% 0.12/0.45 % (4086421)Success in time 0.042 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------