%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO212+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 : n016.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 09:52:02 AM UTC 2026
% Result : Theorem 2.67s 1.38s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 16 unt; 4 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 49 ~; 51 |; 13 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 50 ( 0 sgn 44 !; 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',apart6) ).
fof(f16,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f17,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',oac1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ~ convergent_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
? [X0,X1,X2] :
( ~ convergent_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( convergent_lines(X0,X2)
& unorthogonal_lines(X0,X2) )
| ( convergent_lines(X1,X2)
& unorthogonal_lines(X1,X2) )
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f30,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f30]) ).
fof(f44,plain,
( ~ convergent_lines(sK0,sK2)
& ~ unorthogonal_lines(sK1,sK2)
& unorthogonal_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f24]) ).
fof(f45,plain,
unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f44]) ).
fof(f46,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f47,plain,
~ convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f49,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| unorthogonal_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f50,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f56,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f69,plain,
convergent_lines(sK1,sK2),
inference(resolution,[],[f52,f46]) ).
fof(f72,plain,
! [X0] :
( convergent_lines(X0,sK2)
| ~ convergent_lines(X0,sK0) ),
inference(resolution,[],[f56,f47]) ).
fof(f76,plain,
~ convergent_lines(sK2,sK0),
inference(resolution,[],[f72,f57]) ).
fof(f79,plain,
! [X0] :
( ~ convergent_lines(X0,sK2)
| convergent_lines(X0,sK0) ),
inference(resolution,[],[f76,f56]) ).
fof(f83,plain,
convergent_lines(sK1,sK0),
inference(resolution,[],[f79,f69]) ).
fof(f95,plain,
! [X0] :
( unorthogonal_lines(X0,sK2)
| ~ convergent_lines(X0,sK0)
| ~ unorthogonal_lines(X0,sK0) ),
inference(resolution,[],[f49,f47]) ).
fof(f101,plain,
( ~ convergent_lines(sK1,sK0)
| ~ unorthogonal_lines(sK1,sK0) ),
inference(resolution,[],[f95,f46]) ).
fof(f104,definition,
( spl3_1
<=> unorthogonal_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f105,plain,
( ~ unorthogonal_lines(sK1,sK0)
| spl3_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,definition,
( spl3_2
<=> convergent_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f108,plain,
( ~ convergent_lines(sK1,sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f101,f107,f104]) ).
fof(f110,plain,
( ! [X0] :
( ~ unorthogonal_lines(X0,sK1)
| ~ convergent_lines(X0,sK1)
| convergent_lines(X0,sK0) )
| spl3_1 ),
inference(resolution,[],[f105,f50]) ).
fof(f113,plain,
( ~ convergent_lines(sK0,sK1)
| convergent_lines(sK0,sK0)
| spl3_1 ),
inference(resolution,[],[f110,f45]) ).
fof(f118,definition,
( spl3_3
<=> convergent_lines(sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f119,plain,
( convergent_lines(sK0,sK0)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl3_4
<=> convergent_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f122,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_4 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( spl3_3
| ~ spl3_4
| spl3_1 ),
inference(avatar_split_clause,[],[f113,f104,f121,f118]) ).
fof(f125,plain,
( ! [X0] :
( convergent_lines(X0,sK1)
| ~ convergent_lines(X0,sK0) )
| spl3_4 ),
inference(resolution,[],[f122,f56]) ).
fof(f130,plain,
( ~ convergent_lines(sK1,sK0)
| spl3_4 ),
inference(resolution,[],[f125,f57]) ).
fof(f133,plain,
( ~ spl3_2
| spl3_4 ),
inference(avatar_split_clause,[],[f130,f121,f107]) ).
fof(f134,plain,
( $false
| spl3_2 ),
inference(resolution,[],[f108,f83]) ).
fof(f137,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f142,plain,
( $false
| ~ spl3_3 ),
inference(resolution,[],[f119,f57]) ).
fof(f143,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f142]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f109]) ).
cnf(s2,plain,
( spl3_1
| spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f123]) ).
cnf(s3,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f133]) ).
cnf(s4,plain,
spl3_2,
inference(sat_conversion,[],[f137]) ).
cnf(s6,plain,
~ spl3_3,
inference(sat_conversion,[],[f143]) ).
cnf(s7,plain,
spl3_4,
inference(rat,[],[s3,s4]) ).
cnf(s8,plain,
spl3_1,
inference(rat,[],[s2,s7,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s4,s8]) ).
fof(f144,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 07:44:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.67/1.38 % (2302915)Detected formulas, will run a generic FOF schedule.
% 2.67/1.38 % (2303021)dis-21_1_sil=8000:lcm=predicate:random_seed=2013663021: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)
% 2.67/1.38 % (2303021)First to succeed.
% 2.67/1.38 % (2303021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2302915"
% 2.67/1.38 % (2303018)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3604393304:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.38 % (2303019)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3701630705:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.38 % (2303020)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3549301177:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.38 % (2303017)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=1970773351:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.38 % (2303016)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=1421960464:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.38 % (2303015)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=3278168752:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.38 % (2303019)Also succeeded, but the first one will report.
% 2.67/1.38 % (2303018)Also succeeded, but the first one will report.
% 2.67/1.38 % (2303020)Also succeeded, but the first one will report.
% 2.67/1.38 % (2303021)Refutation found. Thanks to Tanya!
% 2.67/1.38 % SZS status Theorem for theBenchmark
% 2.67/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.38 % (2303021)------------------------------
% 2.67/1.38 % (2303021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.38 % (2303021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.38 % (2303021)CaDiCaL version: 2.1.3
% 2.67/1.38 % (2303021)Termination reason: Refutation
% 2.67/1.38 % (2303021)Time elapsed: 0.002 s
% 2.67/1.38 % (2303021)Peak memory usage: 89 MB
% 2.67/1.38 % (2303021)Instructions burned: 3 (million)
% 2.67/1.38 % (2303021)------------------------------
% 2.67/1.38 % (2303021)------------------------------
% 2.67/1.38 % (2302915)Success in time 0.304 s
% 2.67/1.38 % Vampire exiting
%------------------------------------------------------------------------------