%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:52:04 AM UTC 2026
% Result : Theorem 2.50s 1.36s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 13 unt; 1 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 48 ~; 44 |; 14 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 69 ( 0 sgn 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f19,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( ( ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) )
& ( ~ convergent_lines(X0,X2)
| ~ unorthogonal_lines(X0,X2) ) )
=> ( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cotno1) ).
fof(f33,axiom,
! [X0,X1] :
( parallel_lines(X0,X1)
<=> ~ convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
fof(f35,axiom,
! [X0,X1] :
( orthogonal_lines(X0,X1)
<=> ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( parallel_lines(X0,X1)
& orthogonal_lines(X0,X2) )
=> orthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( parallel_lines(X0,X1)
& orthogonal_lines(X0,X2) )
=> orthogonal_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( parallel_lines(X0,X1)
=> ~ convergent_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f33]) ).
fof(f43,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| ( convergent_lines(X0,X1)
& unorthogonal_lines(X0,X1) )
| ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) ) ),
inference(flattening,[],[f65]) ).
fof(f77,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1,X2] :
( ~ orthogonal_lines(X1,X2)
& parallel_lines(X0,X1)
& orthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
? [X0,X1,X2] :
( ~ orthogonal_lines(X1,X2)
& parallel_lines(X0,X1)
& orthogonal_lines(X0,X2) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ( orthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X1) )
& ( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f81,plain,
( ~ orthogonal_lines(sK1,sK2)
& parallel_lines(sK0,sK1)
& orthogonal_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f79]) ).
fof(f84,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f100,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f111,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X2)
| ~ unorthogonal_lines(X1,X2)
| convergent_lines(X0,X1)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f118,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| ~ parallel_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f119,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X0,X1] :
( orthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f121,plain,
orthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f122,plain,
parallel_lines(sK0,sK1),
inference(cnf_transformation,[],[f81]) ).
fof(f123,plain,
~ orthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f81]) ).
fof(f124,plain,
unorthogonal_lines(sK1,sK2),
inference(resolution,[],[f120,f123]) ).
fof(f126,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f100,f119]) ).
fof(f129,plain,
convergent_lines(sK0,sK2),
inference(resolution,[],[f126,f121]) ).
fof(f133,plain,
! [X0] :
( convergent_lines(sK2,X0)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f87,f129]) ).
fof(f137,plain,
! [X0,X1] :
( convergent_lines(sK2,X1)
| convergent_lines(X0,X1)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f133,f87]) ).
fof(f151,plain,
! [X0] :
( convergent_lines(sK0,X0)
| convergent_lines(X0,sK2) ),
inference(resolution,[],[f137,f84]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ orthogonal_lines(X2,X1)
| convergent_lines(X2,X0)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(resolution,[],[f111,f119]) ).
fof(f261,plain,
! [X0] :
( convergent_lines(sK0,X0)
| ~ convergent_lines(X0,sK2)
| ~ unorthogonal_lines(X0,sK2) ),
inference(resolution,[],[f168,f121]) ).
fof(f263,plain,
! [X0] :
( convergent_lines(sK0,X0)
| ~ unorthogonal_lines(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f261,f151]) ).
fof(f420,definition,
( spl3_4
<=> convergent_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f421,plain,
( convergent_lines(sK0,sK1)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f422,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_4 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f473,plain,
( ~ unorthogonal_lines(sK1,sK2)
| spl3_4 ),
inference(resolution,[],[f422,f263]) ).
fof(f481,plain,
( $false
| spl3_4 ),
inference(forward_subsumption_resolution,[],[f473,f124]) ).
fof(f482,plain,
spl3_4,
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f497,plain,
( ~ parallel_lines(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f421,f118]) ).
fof(f498,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f497,f122]) ).
fof(f499,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f498]) ).
cnf(s6,plain,
spl3_4,
inference(sat_conversion,[],[f482]) ).
cnf(s9,plain,
~ spl3_4,
inference(sat_conversion,[],[f499]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s9]) ).
fof(f500,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n026.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Sun Sep 27 07:44:41 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 2.50/1.36 % (2503395)Detected formulas, will run a generic FOF schedule.
% 2.50/1.36 % (2503424)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=572078549:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.36 % (2503424)First to succeed.
% 2.50/1.36 % (2503424)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2503395"
% 2.50/1.36 % (2503421)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=2191809817:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.36 % (2503419)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=2173564894:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.36 % (2503422)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3910269992:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.36 % (2503425)dis-21_1_sil=8000:lcm=predicate:random_seed=2405420284: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)
% 2.50/1.36 % (2503423)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1380202224:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.36 % (2503422)Refutation not found, incomplete strategy
% 2.50/1.36 % (2503422)------------------------------
% 2.50/1.36 % (2503422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.36 % (2503422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.36 % (2503422)CaDiCaL version: 2.1.3
% 2.50/1.36 % (2503422)Termination reason: Refutation not found, incomplete strategy
% 2.50/1.36 % (2503422)Time elapsed: 0.001 s
% 2.50/1.36 % (2503422)Peak memory usage: 87 MB
% 2.50/1.36 % (2503423)Also succeeded, but the first one will report.
% 2.50/1.36 % (2503425)Also succeeded, but the first one will report.
% 2.50/1.36 % (2503420)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=1588398908:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.36 % (2503424)Refutation found. Thanks to Tanya!
% 2.50/1.36 % SZS status Theorem for theBenchmark
% 2.50/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.36 % (2503424)------------------------------
% 2.50/1.36 % (2503424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.36 % (2503424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.36 % (2503424)CaDiCaL version: 2.1.3
% 2.50/1.36 % (2503424)Termination reason: Refutation
% 2.50/1.36 % (2503424)Time elapsed: 0.006 s
% 2.50/1.36 % (2503424)Peak memory usage: 89 MB
% 2.50/1.36 % (2503424)Instructions burned: 15 (million)
% 2.50/1.36 % (2503424)------------------------------
% 2.50/1.36 % (2503424)------------------------------
% 2.50/1.36 % (2503395)Success in time 0.276 s
% 2.50/1.36 % Vampire exiting
%------------------------------------------------------------------------------