%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO225+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 : n010.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 09:52:07 AM UTC 2026
% Result : Theorem 3.51s 1.46s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 66 ( 23 ~; 16 |; 21 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 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(f17,conjecture,
! [X0,X1] :
( ( point(X0)
& point(X1)
& distinct_points(X0,X1) )
=> ? [X2] :
( line(X2)
=> ( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( point(X0)
& point(X1)
& distinct_points(X0,X1) )
=> ? [X2] :
( line(X2)
=> ( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f25,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(f26,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,[],[f25]) ).
fof(f44,plain,
? [X0,X1] :
( ! [X2] :
( ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) )
& line(X2) )
& point(X0)
& point(X1)
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f45,plain,
? [X0,X1] :
( ! [X2] :
( ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) )
& line(X2) )
& point(X0)
& point(X1)
& distinct_points(X0,X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X2] :
( ( apart_point_and_line(sK0,X2)
| apart_point_and_line(sK1,X2) )
& line(X2) )
& point(sK0)
& point(sK1)
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f45]) ).
fof(f47,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f53,plain,
! [X2,X0,X1] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f54,plain,
! [X2,X0,X1] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f65,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
! [X2] :
( apart_point_and_line(sK1,X2)
| apart_point_and_line(sK0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f72,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X1,X0))
| ~ distinct_points(X1,X0) ),
inference(resolution,[],[f53,f47]) ).
fof(f73,plain,
! [X0] :
( apart_point_and_line(sK0,line_connecting(X0,sK1))
| ~ distinct_points(X0,sK1) ),
inference(resolution,[],[f72,f69]) ).
fof(f76,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(resolution,[],[f54,f47]) ).
fof(f80,plain,
( ~ distinct_points(sK0,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f76,f73]) ).
fof(f81,plain,
~ distinct_points(sK0,sK1),
inference(duplicate_literal_removal,[],[f80]) ).
fof(f82,plain,
$false,
inference(forward_subsumption_resolution,[],[f81,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 07:46:07 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.51/1.46 % (615131)Detected formulas, will run a generic FOF schedule.
% 3.51/1.46 % (615137)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=1859490906:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.46 % (615140)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3468672928:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.46 % (615140)Refutation not found, incomplete strategy
% 3.51/1.46 % (615140)------------------------------
% 3.51/1.46 % (615140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.46 % (615140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.46 % (615140)CaDiCaL version: 2.1.3
% 3.51/1.46 % (615140)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.46 % (615140)Time elapsed: 0.001 s
% 3.51/1.46 % (615140)Peak memory usage: 88 MB
% 3.51/1.46 % (615136)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=1289549145:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.46 % (615138)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=3829748284:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.46 % (615139)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=718994735:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.46 % (615139)Refutation not found, incomplete strategy
% 3.51/1.46 % (615139)------------------------------
% 3.51/1.46 % (615139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.46 % (615139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.46 % (615139)CaDiCaL version: 2.1.3
% 3.51/1.46 % (615139)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.46 % (615139)Time elapsed: 0.001 s
% 3.51/1.46 % (615139)Peak memory usage: 88 MB
% 3.51/1.46 % (615141)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3462628803:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.46 % (615142)dis-21_1_sil=8000:lcm=predicate:random_seed=1624156756: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)
% 3.51/1.46 % (615141)First to succeed.
% 3.51/1.46 % (615142)Also succeeded, but the first one will report.
% 3.51/1.46 % (615141)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-615131"
% 3.51/1.46 % (615140)------------------------------
% 3.51/1.46 % (615140)------------------------------
% 3.51/1.46 % (615139)------------------------------
% 3.51/1.46 % (615139)------------------------------
% 3.51/1.46 % (615141)Refutation found. Thanks to Tanya!
% 3.51/1.46 % SZS status Theorem for theBenchmark
% 3.51/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.46 % (615141)------------------------------
% 3.51/1.46 % (615141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.46 % (615141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.46 % (615141)CaDiCaL version: 2.1.3
% 3.51/1.46 % (615141)Termination reason: Refutation
% 3.51/1.46 % (615141)Time elapsed: 0.002 s
% 3.51/1.46 % (615141)Peak memory usage: 89 MB
% 3.51/1.46 % (615141)Instructions burned: 2 (million)
% 3.51/1.46 % (615141)------------------------------
% 3.51/1.46 % (615141)------------------------------
% 3.51/1.46 % (615131)Success in time 0.411 s
% 3.51/1.46 % Vampire exiting
%------------------------------------------------------------------------------