%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO182+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 : n006.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 09:53:50 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 16 unt; 5 def)
% Number of atoms : 188 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 180 ( 65 ~; 91 |; 10 &)
% ( 5 <=>; 9 =>; 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 : 80 ( 0 sgn 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(f11,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/GEO008+0.ax',ceq2) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X2,line_connecting(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X2,line_connecting(X1,X0)) ) ),
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(f29,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X1,X0))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X1,X0))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK1,sK0))
& apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1) ),
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(f47,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
~ apart_point_and_line(sK2,line_connecting(sK1,sK0)),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
! [X0] :
( distinct_points(sK1,X0)
| distinct_points(sK0,X0) ),
inference(resolution,[],[f38,f49]) ).
fof(f54,plain,
! [X0,X1] :
( distinct_points(sK0,X0)
| distinct_points(X0,X1)
| distinct_points(sK1,X1) ),
inference(resolution,[],[f52,f38]) ).
fof(f58,plain,
! [X0] :
( distinct_points(sK0,X0)
| distinct_points(X0,sK1) ),
inference(resolution,[],[f54,f35]) ).
fof(f66,plain,
! [X0] :
( distinct_lines(line_connecting(sK0,sK1),X0)
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f47,f50]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ distinct_points(X0,X2)
| apart_point_and_line(X2,line_connecting(sK0,sK1))
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,X1) ),
inference(resolution,[],[f45,f66]) ).
fof(f221,plain,
! [X0] :
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f89,f49]) ).
fof(f270,definition,
( spl3_1
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f272,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f287,definition,
( spl3_5
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f289,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f303,definition,
( spl3_9
<=> ! [X0] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X0)
| apart_point_and_line(sK0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f304,plain,
( ! [X0] :
( apart_point_and_line(sK2,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f305,plain,
( spl3_5
| spl3_9
| spl3_1 ),
inference(avatar_split_clause,[],[f221,f270,f303,f287]) ).
fof(f316,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ spl3_5 ),
inference(resolution,[],[f289,f42]) ).
fof(f322,plain,
( distinct_points(sK0,sK0)
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f316,f58]) ).
fof(f323,plain,
( $false
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f322,f35]) ).
fof(f324,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f390,definition,
( spl3_13
<=> apart_point_and_line(sK0,line_connecting(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f392,plain,
( apart_point_and_line(sK0,line_connecting(sK1,sK0))
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f394,definition,
( spl3_14
<=> apart_point_and_line(sK1,line_connecting(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f396,plain,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f399,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK0,sK1)
| ~ spl3_1 ),
inference(resolution,[],[f272,f41]) ).
fof(f404,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f399,f35]) ).
fof(f406,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f404,f49]) ).
fof(f407,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f406]) ).
fof(f411,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK1,sK0)
| ~ spl3_13 ),
inference(resolution,[],[f392,f41]) ).
fof(f416,plain,
( distinct_points(sK0,sK0)
| ~ spl3_13 ),
inference(forward_subsumption_resolution,[],[f411,f52]) ).
fof(f417,plain,
( $false
| ~ spl3_13 ),
inference(forward_subsumption_resolution,[],[f416,f35]) ).
fof(f418,plain,
~ spl3_13,
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f419,plain,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,line_connecting(sK1,sK0))
| ~ spl3_9 ),
inference(resolution,[],[f304,f51]) ).
fof(f426,plain,
( spl3_13
| spl3_14
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f419,f303,f394,f390]) ).
fof(f430,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK1,sK0)
| ~ spl3_14 ),
inference(resolution,[],[f396,f42]) ).
fof(f436,plain,
( ~ distinct_points(sK1,sK0)
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f430,f35]) ).
fof(f458,plain,
( distinct_points(sK0,sK0)
| ~ spl3_14 ),
inference(resolution,[],[f436,f52]) ).
fof(f462,plain,
( $false
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f458,f35]) ).
fof(f463,plain,
~ spl3_14,
inference(avatar_contradiction_clause,[],[f462]) ).
cnf(s7,plain,
( spl3_1
| spl3_5
| spl3_9 ),
inference(sat_conversion,[],[f305]) ).
cnf(s12,plain,
~ spl3_5,
inference(sat_conversion,[],[f324]) ).
cnf(s16,plain,
~ spl3_1,
inference(sat_conversion,[],[f407]) ).
cnf(s17,plain,
~ spl3_13,
inference(sat_conversion,[],[f418]) ).
cnf(s18,plain,
( ~ spl3_9
| spl3_13
| spl3_14 ),
inference(sat_conversion,[],[f426]) ).
cnf(s19,plain,
~ spl3_14,
inference(sat_conversion,[],[f463]) ).
cnf(s20,plain,
( ~ spl3_9
| spl3_13 ),
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
~ spl3_9,
inference(rat,[],[s20,s17]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s7,s21,s12,s16]) ).
fof(f465,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO182+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 07:25:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.45 % (2654221)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2654226)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=896813869_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % TRYING [1]
% 0.11/0.45 % TRYING [2]
% 0.11/0.45 % TRYING [3]
% 0.11/0.45 % TRYING [4]
% 0.11/0.45 % TRYING [5]
% 0.11/0.45 % TRYING [6]
% 0.11/0.45 % TRYING [7]
% 0.11/0.45 % TRYING [8]
% 0.11/0.45 % (2654227)% WARNING: option uhcvi not known.
% 0.11/0.45 % TRYING [9]
% 0.11/0.45 % TRYING [10]
% 0.11/0.45 % (2654232)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3273391014:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (2654231)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4223240881:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (2654228)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4043269545:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (2654229)dis+10_1_sil=32000:sp=arity:random_seed=1924596620:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (2654230)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1858982074:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (2654227)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4282911932:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % TRYING [11]
% 0.11/0.45 % TRYING [12]
% 0.11/0.45 % TRYING [13]
% 0.11/0.45 % (2654229) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2654221-2654229"...
% 0.11/0.45 % (2654229)...printing done.
% 0.11/0.45 % TRYING [14]
% 0.11/0.45 % (2654229)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2654229)------------------------------
% 0.11/0.45 % (2654229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2654229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2654229)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2654229)Termination reason: Refutation
% 0.11/0.45 % (2654229)Time elapsed: 0.010 s
% 0.11/0.45 % (2654229)Peak memory usage: 12 MB
% 0.11/0.45 % (2654229)Instructions burned: 14 (million)
% 0.11/0.45 % (2654221)Success in time 0.045 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------