%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO218+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 09:54:05 AM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 13 unt; 2 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 45 ~; 37 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 51 ( 0 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f15,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f16,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/sandbox2/benchmark/Axioms/GEO006+4.ax',cotno1) ).
fof(f18,conjecture,
! [X0,X1,X2] :
( ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ unorthogonal_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f24,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f38,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f39,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,[],[f16]) ).
fof(f40,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,[],[f39]) ).
fof(f43,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
& ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
& ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
( unorthogonal_lines(sK1,sK2)
& ~ convergent_lines(sK0,sK1)
& ~ unorthogonal_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f44]) ).
fof(f48,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f60,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X1,X2)
| ~ convergent_lines(X1,X2)
| convergent_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f66,plain,
~ unorthogonal_lines(sK0,sK2),
inference(cnf_transformation,[],[f45]) ).
fof(f67,plain,
~ convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f45]) ).
fof(f68,plain,
unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f45]) ).
fof(f69,plain,
convergent_lines(sK0,sK2),
inference(resolution,[],[f60,f66]) ).
fof(f70,plain,
! [X0] :
( convergent_lines(sK2,X0)
| convergent_lines(sK0,X0) ),
inference(resolution,[],[f51,f69]) ).
fof(f72,plain,
! [X0,X1] :
( convergent_lines(sK0,X0)
| convergent_lines(X0,X1)
| convergent_lines(sK2,X1) ),
inference(resolution,[],[f70,f51]) ).
fof(f76,plain,
! [X0] :
( convergent_lines(sK0,X0)
| convergent_lines(X0,sK2) ),
inference(resolution,[],[f72,f48]) ).
fof(f102,definition,
( spl3_2
<=> convergent_lines(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f104,plain,
( ~ convergent_lines(sK1,sK2)
| spl3_2 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,plain,
! [X0] :
( ~ convergent_lines(sK1,sK2)
| convergent_lines(X0,sK1)
| unorthogonal_lines(X0,sK2) ),
inference(resolution,[],[f63,f68]) ).
fof(f127,plain,
( convergent_lines(sK0,sK1)
| spl3_2 ),
inference(resolution,[],[f76,f104]) ).
fof(f128,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f127,f67]) ).
fof(f129,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f131,definition,
( spl3_3
<=> ! [X0] :
( convergent_lines(X0,sK1)
| unorthogonal_lines(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f132,plain,
( ! [X0] :
( unorthogonal_lines(X0,sK2)
| convergent_lines(X0,sK1) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f106,f102,f131]) ).
fof(f144,plain,
( convergent_lines(sK0,sK1)
| ~ spl3_3 ),
inference(resolution,[],[f132,f66]) ).
fof(f148,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f144,f67]) ).
fof(f149,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f148]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f129]) ).
cnf(s3,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f133]) ).
cnf(s5,plain,
~ spl3_3,
inference(sat_conversion,[],[f149]) ).
cnf(s6,plain,
~ spl3_2,
inference(rat,[],[s3,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6]) ).
fof(f150,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO218+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 07:42:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.45 % (895463)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (895470)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1382619819:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (895469)% WARNING: option uhcvi not known.
% 0.09/0.45 % (895468)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1282008323_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (895474)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2076582844:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % (895471)dis+10_1_sil=32000:sp=arity:random_seed=301156932:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (895472)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1627950130:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (895473)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3220826553:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (895469)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=805989680:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % TRYING [4]
% 0.09/0.45 % (895471) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-895463-895471"...
% 0.09/0.45 % (895473) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-895463-895473"...
% 0.09/0.45 % TRYING [5]
% 0.09/0.45 % (895471)...printing done.
% 0.09/0.45 % (895473)...printing done.
% 0.09/0.45 % (895472) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-895463-895472"...
% 0.09/0.45 % (895474) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-895463-895474"...
% 0.09/0.45 % (895471)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (895471)------------------------------
% 0.09/0.45 % (895471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (895471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (895471)CaDiCaL version: 2.1.3
% 0.09/0.45 % (895471)Termination reason: Refutation
% 0.09/0.45 % (895471)Time elapsed: 0.004 s
% 0.09/0.45 % (895471)Peak memory usage: 12 MB
% 0.09/0.45 % (895471)Instructions burned: 3 (million)
% 0.09/0.45 % (895463)Success in time 0.037 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------