%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO210+1 : 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 : n019.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 09:52:01 AM UTC 2026
% Result : Theorem 2.58s 1.35s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 11 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 46 |; 8 &)
% ( 0 <=>; 5 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 69 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f14,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( distinct_lines(X1,X2)
| convergent_lines(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
fof(f17,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cup1) ).
fof(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f21,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
fof(f23,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) )
=> ~ distinct_lines(X1,orthogonal_through_point(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) )
=> ~ distinct_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,plain,
? [X0,X1,X2] :
( distinct_lines(X1,orthogonal_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f26,plain,
? [X0,X1,X2] :
( distinct_lines(X1,orthogonal_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ unorthogonal_lines(X1,X2) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f41,plain,
( distinct_lines(sK1,orthogonal_through_point(sK2,sK0))
& ~ apart_point_and_line(sK0,sK1)
& ~ unorthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f26]) ).
fof(f42,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f41]) ).
fof(f43,plain,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f44,plain,
distinct_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f41]) ).
fof(f45,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X2,X0,X1] :
( convergent_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( unorthogonal_lines(X2,X3)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f62,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X1,X0) ),
inference(resolution,[],[f46,f59]) ).
fof(f71,plain,
! [X2,X0,X1] :
( convergent_lines(X1,orthogonal_through_point(X2,X0))
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(resolution,[],[f45,f50]) ).
fof(f93,plain,
! [X0,X1] :
( unorthogonal_lines(X1,sK2)
| apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,sK1) ),
inference(resolution,[],[f52,f42]) ).
fof(f99,plain,
! [X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,X1))
| apart_point_and_line(X0,sK1)
| ~ distinct_lines(orthogonal_through_point(sK2,X1),sK1) ),
inference(resolution,[],[f93,f51]) ).
fof(f130,plain,
! [X0] :
( ~ distinct_lines(orthogonal_through_point(sK2,X0),sK1)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f99,f50]) ).
fof(f145,plain,
! [X0] :
( ~ convergent_lines(sK1,orthogonal_through_point(sK2,X0))
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f130,f62]) ).
fof(f159,plain,
! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK1)
| ~ distinct_lines(sK1,orthogonal_through_point(sK2,X0)) ),
inference(resolution,[],[f145,f71]) ).
fof(f162,plain,
! [X0] :
( ~ distinct_lines(sK1,orthogonal_through_point(sK2,X0))
| apart_point_and_line(X0,sK1) ),
inference(duplicate_literal_removal,[],[f159]) ).
fof(f165,plain,
apart_point_and_line(sK0,sK1),
inference(resolution,[],[f162,f44]) ).
fof(f169,plain,
$false,
inference(forward_subsumption_resolution,[],[f165,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n019.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 07:38:04 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 2.58/1.35 % (2768976)Detected formulas, will run a generic FOF schedule.
% 2.58/1.35 % (2768985)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1187745547:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.35 % (2768985)First to succeed.
% 2.58/1.35 % (2768985)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2768976"
% 2.58/1.35 % (2768987)dis-21_1_sil=8000:lcm=predicate:random_seed=2404457405: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)
% 2.58/1.35 % (2768981)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=2864637140:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.35 % (2768984)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2473870166:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.35 % (2768982)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=1027160126:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.35 % (2768983)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=782849931:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.35 % (2768987)Also succeeded, but the first one will report.
% 2.58/1.35 % (2768986)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4287075088:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.35 % (2768986)Also succeeded, but the first one will report.
% 2.58/1.35 % (2768984)Instruction limit reached!
% 2.58/1.35 % (2768984)------------------------------
% 2.58/1.35 % (2768984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.35 % (2768984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.35 % (2768984)CaDiCaL version: 2.1.3
% 2.58/1.35 % (2768984)Termination reason: Instruction limit
% 2.58/1.35 % (2768984)Termination phase: Saturation
% 2.58/1.35 % (2768984)Time elapsed: 0.062 s
% 2.58/1.35 % (2768984)Peak memory usage: 88 MB
% 2.58/1.35 % (2768984)Instructions burned: 110 (million)
% 2.58/1.35 % (2768985)Refutation found. Thanks to Tanya!
% 2.58/1.35 % SZS status Theorem for theBenchmark
% 2.58/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.35 % (2768985)------------------------------
% 2.58/1.35 % (2768985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.35 % (2768985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.35 % (2768985)CaDiCaL version: 2.1.3
% 2.58/1.35 % (2768985)Termination reason: Refutation
% 2.58/1.35 % (2768985)Time elapsed: 0.002 s
% 2.58/1.35 % (2768985)Peak memory usage: 88 MB
% 2.58/1.35 % (2768985)Instructions burned: 4 (million)
% 2.58/1.35 % (2768985)------------------------------
% 2.58/1.35 % (2768985)------------------------------
% 2.58/1.35 % (2768976)Success in time 0.284 s
% 2.58/1.35 % Vampire exiting
%------------------------------------------------------------------------------