%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO170+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:51:45 AM UTC 2026
% Result : Theorem 3.64s 1.49s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 18 unt; 4 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 54 ~; 49 |; 17 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
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/theBenchmark.p',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/theBenchmark.p',cu1) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) )
=> ~ distinct_lines(X2,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) )
=> ~ distinct_lines(X2,line_connecting(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ),
inference(flattening,[],[f15]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f21,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(f22,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,[],[f21]) ).
fof(f34,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1)
& ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f35,plain,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f36,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f37,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f38,plain,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f39,plain,
! [X2,X0,X1] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X2,X0,X1] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f42,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,[],[f22]) ).
fof(f44,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f59,plain,
! [X0,X1] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(resolution,[],[f39,f44]) ).
fof(f60,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolution,[],[f59,f37]) ).
fof(f64,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(resolution,[],[f40,f44]) ).
fof(f67,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolution,[],[f64,f37]) ).
fof(f73,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f42,f38]) ).
fof(f76,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2) ),
inference(resolution,[],[f73,f37]) ).
fof(f82,definition,
( spl3_1
<=> apart_point_and_line(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f83,plain,
( apart_point_and_line(sK0,sK2)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl3_2
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f86,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl3_3
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f89,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,definition,
( spl3_4
<=> apart_point_and_line(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f92,plain,
( apart_point_and_line(sK1,sK2)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f93,plain,
( spl3_1
| spl3_2
| spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f76,f91,f88,f85,f82]) ).
fof(f94,plain,
( $false
| ~ spl3_2 ),
inference(resolution,[],[f86,f67]) ).
fof(f95,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f96,plain,
( $false
| ~ spl3_3 ),
inference(resolution,[],[f89,f60]) ).
fof(f97,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f98,plain,
( $false
| ~ spl3_4 ),
inference(resolution,[],[f92,f35]) ).
fof(f99,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f100,plain,
( $false
| ~ spl3_1 ),
inference(resolution,[],[f83,f36]) ).
fof(f101,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f100]) ).
cnf(s1,plain,
( spl3_1
| spl3_2
| spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f93]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f95]) ).
cnf(s3,plain,
~ spl3_3,
inference(sat_conversion,[],[f97]) ).
cnf(s4,plain,
~ spl3_4,
inference(sat_conversion,[],[f99]) ).
cnf(s5,plain,
~ spl3_1,
inference(sat_conversion,[],[f101]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s3,s2,s5]) ).
fof(f102,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO170+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:25:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/1.49 % (1314286)Detected formulas, will run a generic FOF schedule.
% 3.64/1.49 % (1314291)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3770750572:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.64/1.49 % (1314297)dis-21_1_sil=8000:lcm=predicate:random_seed=1751445860:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.64/1.49 % (1314294)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=812160541:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.64/1.49 % (1314292)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1540201176:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.64/1.49 % (1314293)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=462519405:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.64/1.49 % (1314295)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2624981705:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.64/1.49 % (1314297)First to succeed.
% 3.64/1.49 % (1314297)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1314286"
% 3.64/1.49 % (1314294)Also succeeded, but the first one will report.
% 3.64/1.49 % (1314296)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1133193410:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.64/1.49 % (1314296)Also succeeded, but the first one will report.
% 3.64/1.49 % (1314295)Also succeeded, but the first one will report.
% 3.64/1.49 % (1314297)Refutation found. Thanks to Tanya!
% 3.64/1.49 % SZS status Theorem for theBenchmark
% 3.64/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.49 % (1314297)------------------------------
% 3.64/1.49 % (1314297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.49 % (1314297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.49 % (1314297)CaDiCaL version: 2.1.3
% 3.64/1.49 % (1314297)Termination reason: Refutation
% 3.64/1.49 % (1314297)Time elapsed: 0.003 s
% 3.64/1.49 % (1314297)Peak memory usage: 89 MB
% 3.64/1.49 % (1314297)Instructions burned: 2 (million)
% 3.64/1.49 % (1314297)------------------------------
% 3.64/1.49 % (1314297)------------------------------
% 3.64/1.49 % (1314286)Success in time 0.434 s
% 3.64/1.49 % Vampire exiting
%------------------------------------------------------------------------------