%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO189+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:51:53 AM UTC 2026
% Result : Theorem 2.50s 1.40s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 13 unt; 1 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 163 ( 53 ~; 80 |; 22 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 85 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',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/theBenchmark.p',ceq2) ).
fof(f13,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(f14,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)],[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(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,[],[f14]) ).
fof(f33,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,[],[f32]) ).
fof(f34,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)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X2,X0,X1] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X2,X0,X1] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ 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] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0,X1] :
( distinct_points(X0,X1)
| ~ distinct_points(X1,X0) ),
inference(resolution,[],[f38,f35]) ).
fof(f59,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X1,X0))
| ~ distinct_points(X1,X0) ),
inference(resolution,[],[f41,f35]) ).
fof(f61,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(resolution,[],[f42,f35]) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( ~ apart_point_and_line(X4,X3)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| ~ distinct_points(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X4,X1)
| apart_point_and_line(X0,X1) ),
inference(resolution,[],[f45,f47]) ).
fof(f77,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,line_connecting(sK0,sK2))
| apart_point_and_line(X0,X1)
| ~ distinct_points(X2,X0)
| apart_point_and_line(X2,line_connecting(sK0,sK2))
| apart_point_and_line(sK1,X1)
| apart_point_and_line(X2,X1) ),
inference(resolution,[],[f65,f53]) ).
fof(f80,plain,
! [X0,X1] :
( apart_point_and_line(sK0,X0)
| ~ distinct_points(X1,sK0)
| apart_point_and_line(X1,line_connecting(sK0,sK2))
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X1,X0)
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[],[f77,f61]) ).
fof(f82,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0,sK2))
| ~ distinct_points(X1,sK0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(X1,X0) ),
inference(forward_subsumption_resolution,[],[f80,f51]) ).
fof(f94,plain,
! [X0] :
( ~ distinct_points(sK2,sK0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X0)
| ~ distinct_points(sK0,sK2) ),
inference(resolution,[],[f82,f59]) ).
fof(f99,plain,
! [X0] :
( apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK2,X0)
| ~ distinct_points(sK0,sK2) ),
inference(forward_subsumption_resolution,[],[f94,f54]) ).
fof(f100,plain,
! [X0] :
( apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f99,f51]) ).
fof(f114,plain,
! [X0] :
( ~ distinct_points(X0,sK1)
| apart_point_and_line(sK2,line_connecting(X0,sK1))
| apart_point_and_line(sK0,line_connecting(X0,sK1)) ),
inference(resolution,[],[f100,f59]) ).
fof(f134,definition,
( spl3_2
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f135,plain,
( ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
| spl3_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f201,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f136,f61]) ).
fof(f204,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f201,f52]) ).
fof(f205,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f236,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(resolution,[],[f114,f52]) ).
fof(f246,plain,
apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f236,f49]) ).
fof(f247,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f246,f135]) ).
fof(f248,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f247]) ).
cnf(s13,plain,
~ spl3_2,
inference(sat_conversion,[],[f205]) ).
cnf(s14,plain,
spl3_2,
inference(sat_conversion,[],[f248]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s13,s14]) ).
fof(f249,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO189+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 07:30:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.50/1.40 % (2064034)Detected formulas, will run a generic FOF schedule.
% 2.50/1.40 % (2064046)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4250024142:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.40 % (2064046)Instruction limit reached!
% 2.50/1.40 % (2064046)------------------------------
% 2.50/1.40 % (2064046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.40 % (2064046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.40 % (2064046)CaDiCaL version: 2.1.3
% 2.50/1.40 % (2064046)Termination reason: Instruction limit
% 2.50/1.40 % (2064046)Termination phase: Saturation
% 2.50/1.40 % (2064046)Time elapsed: 0.026 s
% 2.50/1.40 % (2064046)Peak memory usage: 87 MB
% 2.50/1.40 % (2064046)Instructions burned: 122 (million)
% 2.50/1.40 % (2064048)dis-21_1_sil=8000:lcm=predicate:random_seed=2218014188: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)
% 2.50/1.40 % (2064047)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1583990811:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.40 % (2064042)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=1044077843:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.40 % (2064045)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=267389670:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.40 % (2064044)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=3938809751:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.40 % (2064043)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=3811090740:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.40 % (2064047)First to succeed.
% 2.50/1.40 % (2064047)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2064034"
% 2.50/1.40 % (2064045)Instruction limit reached!
% 2.50/1.40 % (2064045)------------------------------
% 2.50/1.40 % (2064045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.40 % (2064045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.40 % (2064045)CaDiCaL version: 2.1.3
% 2.50/1.40 % (2064045)Termination reason: Instruction limit
% 2.50/1.40 % (2064045)Termination phase: Saturation
% 2.50/1.40 % (2064045)Time elapsed: 0.054 s
% 2.50/1.40 % (2064045)Peak memory usage: 88 MB
% 2.50/1.40 % (2064045)Instructions burned: 110 (million)
% 2.50/1.40 % (2064048)Instruction limit reached!
% 2.50/1.40 % (2064048)------------------------------
% 2.50/1.40 % (2064048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.40 % (2064048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.40 % (2064048)CaDiCaL version: 2.1.3
% 2.50/1.40 % (2064048)Termination reason: Instruction limit
% 2.50/1.40 % (2064048)Termination phase: Saturation
% 2.50/1.40 % (2064048)Time elapsed: 0.054 s
% 2.50/1.40 % (2064048)Peak memory usage: 88 MB
% 2.50/1.40 % (2064048)Instructions burned: 129 (million)
% 2.50/1.40 % (2064069)lrs+10_1_sil=8000:sp=occurrence:random_seed=560840578:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.50/1.40 % (2064069)Also succeeded, but the first one will report.
% 2.50/1.40 % (2064103)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3370409806:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 2.50/1.40 % (2064102)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2311510925:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.50/1.40 % (2064102)Also succeeded, but the first one will report.
% 2.50/1.40 % (2064103)Also succeeded, but the first one will report.
% 2.50/1.40 % (2064047)Refutation found. Thanks to Tanya!
% 2.50/1.40 % SZS status Theorem for theBenchmark
% 2.50/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.49 % (2064047)------------------------------
% 2.50/1.49 % (2064047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.49 % (2064047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.49 % (2064047)CaDiCaL version: 2.1.3
% 2.50/1.49 % (2064047)Termination reason: Refutation
% 2.50/1.49 % (2064047)Time elapsed: 0.018 s
% 2.50/1.49 % (2064047)Peak memory usage: 89 MB
% 2.50/1.49 % (2064047)Instructions burned: 35 (million)
% 2.50/1.49 % (2064047)------------------------------
% 2.50/1.49 % (2064047)------------------------------
% 2.50/1.49 % (2064034)Success in time 0.418 s
% 2.50/1.49 % Vampire exiting
%------------------------------------------------------------------------------