%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO200+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 : 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 09:51:57 AM UTC 2026
% Result : Theorem 1.87s 1.13s
% Output : Refutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 14 unt; 6 def)
% Number of atoms : 210 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 225 ( 82 ~; 125 |; 6 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 81 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/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] :
( distinct_points(X0,X1)
=> ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( distinct_points(X0,X1)
=> ~ distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1] :
( distinct_lines(line_connecting(X0,X1),line_connecting(X1,X0))
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,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(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(flattening,[],[f16]) ).
fof(f20,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(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(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f33,plain,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0))
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f34,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f35,plain,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0)),
inference(cnf_transformation,[],[f33]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f39,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,[],[f21]) ).
fof(f40,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f61,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X1,line_connecting(sK1,sK0))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(sK1,sK0)) ),
inference(resolution,[],[f39,f35]) ).
fof(f67,plain,
! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| apart_point_and_line(X0,line_connecting(sK1,sK0))
| ~ distinct_points(X1,X0)
| apart_point_and_line(X1,line_connecting(sK1,sK0))
| distinct_points(X1,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f61,f36]) ).
fof(f69,definition,
( spl2_1
<=> distinct_points(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f70,plain,
( ~ distinct_points(sK0,sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl2_2
<=> ! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(X1,sK1)
| apart_point_and_line(X1,line_connecting(sK1,sK0))
| ~ distinct_points(X1,X0)
| apart_point_and_line(X0,line_connecting(sK1,sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK1,sK0))
| distinct_points(X1,sK1)
| apart_point_and_line(X1,line_connecting(sK1,sK0))
| ~ distinct_points(X1,X0)
| apart_point_and_line(X0,line_connecting(sK0,sK1)) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f67,f72,f69]) ).
fof(f83,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f70,f34]) ).
fof(f85,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f83]) ).
fof(f88,plain,
( ! [X0,X1] :
( distinct_points(X0,sK1)
| apart_point_and_line(X0,line_connecting(sK1,sK0))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| distinct_points(X1,sK0)
| ~ distinct_points(sK1,sK0) )
| ~ spl2_2 ),
inference(resolution,[],[f73,f36]) ).
fof(f90,definition,
( spl2_5
<=> distinct_points(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f91,plain,
( ~ distinct_points(sK1,sK0)
| spl2_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl2_6
<=> ! [X0,X1] :
( distinct_points(X0,sK1)
| distinct_points(X1,sK0)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,line_connecting(sK1,sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f94,plain,
( ! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK1,sK0))
| distinct_points(X1,sK0)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| ~ distinct_points(X0,X1)
| distinct_points(X0,sK1) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( ~ spl2_5
| spl2_6
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f88,f72,f93,f90]) ).
fof(f100,plain,
( ! [X0] :
( ~ distinct_points(X0,sK1)
| distinct_points(X0,sK0) )
| spl2_5 ),
inference(resolution,[],[f91,f40]) ).
fof(f104,plain,
( distinct_points(sK0,sK0)
| spl2_5 ),
inference(resolution,[],[f100,f34]) ).
fof(f109,plain,
( $false
| spl2_5 ),
inference(resolution,[],[f104,f41]) ).
fof(f110,plain,
spl2_5,
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f132,plain,
( ! [X0,X1] :
( distinct_points(X0,sK0)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X1,X0)
| distinct_points(X1,sK1)
| distinct_points(X1,sK1)
| ~ distinct_points(sK1,sK0) )
| ~ spl2_6 ),
inference(resolution,[],[f94,f37]) ).
fof(f134,plain,
( ! [X0,X1] :
( distinct_points(X0,sK0)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X1,X0)
| distinct_points(X1,sK1)
| ~ distinct_points(sK1,sK0) )
| ~ spl2_6 ),
inference(duplicate_literal_removal,[],[f132]) ).
fof(f136,definition,
( spl2_13
<=> ! [X0,X1] :
( distinct_points(X0,sK0)
| distinct_points(X1,sK1)
| ~ distinct_points(X1,X0)
| apart_point_and_line(X0,line_connecting(sK0,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f137,plain,
( ! [X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK1))
| distinct_points(X1,sK1)
| ~ distinct_points(X1,X0)
| distinct_points(X0,sK0) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f138,plain,
( ~ spl2_5
| spl2_13
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f134,f93,f136,f90]) ).
fof(f144,plain,
( ! [X0,X1] :
( distinct_points(X0,sK1)
| ~ distinct_points(X0,X1)
| distinct_points(X1,sK0)
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK1) )
| ~ spl2_13 ),
inference(resolution,[],[f137,f37]) ).
fof(f146,plain,
( ! [X0,X1] :
( distinct_points(X0,sK1)
| ~ distinct_points(X0,X1)
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK1) )
| ~ spl2_13 ),
inference(duplicate_literal_removal,[],[f144]) ).
fof(f148,definition,
( spl2_15
<=> ! [X0,X1] :
( distinct_points(X0,sK1)
| distinct_points(X1,sK0)
| ~ distinct_points(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f149,plain,
( ! [X0,X1] :
( distinct_points(X1,sK0)
| distinct_points(X0,sK1)
| ~ distinct_points(X0,X1) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f150,plain,
( ~ spl2_1
| spl2_15
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f146,f136,f148,f69]) ).
fof(f167,plain,
( ! [X0] :
( distinct_points(X0,sK1)
| ~ distinct_points(X0,sK0) )
| ~ spl2_15 ),
inference(resolution,[],[f149,f41]) ).
fof(f184,plain,
( ~ distinct_points(sK1,sK0)
| ~ spl2_15 ),
inference(resolution,[],[f167,f41]) ).
fof(f185,plain,
( ~ spl2_5
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f184,f148,f90]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f74]) ).
cnf(s4,plain,
spl2_1,
inference(sat_conversion,[],[f85]) ).
cnf(s5,plain,
( ~ spl2_2
| ~ spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f95]) ).
cnf(s7,plain,
spl2_5,
inference(sat_conversion,[],[f110]) ).
cnf(s13,plain,
( ~ spl2_5
| ~ spl2_6
| spl2_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s15,plain,
( ~ spl2_1
| ~ spl2_13
| spl2_15 ),
inference(sat_conversion,[],[f150]) ).
cnf(s22,plain,
( ~ spl2_5
| ~ spl2_15 ),
inference(sat_conversion,[],[f185]) ).
cnf(s23,plain,
~ spl2_15,
inference(rat,[],[s22,s7]) ).
cnf(s25,plain,
( ~ spl2_2
| spl2_6 ),
inference(rat,[],[s5,s7]) ).
cnf(s26,plain,
~ spl2_13,
inference(rat,[],[s15,s23,s4]) ).
cnf(s27,plain,
~ spl2_6,
inference(rat,[],[s13,s7,s26]) ).
cnf(s28,plain,
~ spl2_2,
inference(rat,[],[s25,s27]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s1,s28,s4]) ).
fof(f186,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.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 07:34:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 1.87/1.13 % (2655910)Detected formulas, will run a generic FOF schedule.
% 1.87/1.13 % (2655921)dis-21_1_sil=8000:lcm=predicate:random_seed=4202822257: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)
% 1.87/1.13 % (2655921)First to succeed.
% 1.87/1.13 % (2655921)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2655910"
% 1.87/1.13 % (2655919)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3289850495:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.87/1.13 % (2655916)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=1516650401:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.87/1.13 % (2655918)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1333509777:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.87/1.13 % (2655915)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=55472849:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.87/1.13 % (2655917)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=602326930:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.87/1.13 % (2655918)Refutation not found, incomplete strategy
% 1.87/1.13 % (2655918)------------------------------
% 1.87/1.13 % (2655918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.87/1.13 % (2655918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.87/1.13 % (2655918)CaDiCaL version: 2.1.3
% 1.87/1.13 % (2655920)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=564023257:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.87/1.13 % (2655918)Termination reason: Refutation not found, incomplete strategy
% 1.87/1.13 % (2655918)Time elapsed: 0.001 s
% 1.87/1.13 % (2655918)Peak memory usage: 88 MB
% 1.87/1.13 % (2655919)Also succeeded, but the first one will report.
% 1.87/1.13 % (2655920)Also succeeded, but the first one will report.
% 1.87/1.13 % (2655921)Refutation found. Thanks to Tanya!
% 1.87/1.13 % SZS status Theorem for theBenchmark
% 1.87/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.46/1.23 % (2655921)------------------------------
% 2.46/1.23 % (2655921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.46/1.23 % (2655921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/1.23 % (2655921)CaDiCaL version: 2.1.3
% 2.46/1.23 % (2655921)Termination reason: Refutation
% 2.46/1.23 % (2655921)Time elapsed: 0.003 s
% 2.46/1.23 % (2655921)Peak memory usage: 89 MB
% 2.46/1.23 % (2655921)Instructions burned: 5 (million)
% 2.46/1.23 % (2655921)------------------------------
% 2.46/1.23 % (2655921)------------------------------
% 2.46/1.23 % (2655910)Success in time 0.278 s
% 2.46/1.23 % Vampire exiting
%------------------------------------------------------------------------------