%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO219+2 : 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 : n011.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 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 10 unt; 2 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 94 ( 42 ~; 34 |; 12 &)
% ( 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 : 46 ( 0 sgn 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(f13,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(f14,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(f16,conjecture,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) )
=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) )
=> ~ unorthogonal_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f22,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f36,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,[],[f14]) ).
fof(f37,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,[],[f36]) ).
fof(f40,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f41,plain,
? [X0,X1,X2] :
( unorthogonal_lines(X1,X2)
& ~ unorthogonal_lines(X0,X1)
& ~ convergent_lines(X0,X2) ),
inference(flattening,[],[f40]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f57,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f62,plain,
~ convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f41]) ).
fof(f63,plain,
~ unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f64,plain,
unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f41]) ).
fof(f66,plain,
convergent_lines(sK0,sK1),
inference(resolution,[],[f56,f63]) ).
fof(f100,plain,
! [X0] :
( ~ convergent_lines(sK0,X0)
| convergent_lines(X0,sK2) ),
inference(resolution,[],[f47,f62]) ).
fof(f156,plain,
! [X0] :
( unorthogonal_lines(X0,sK1)
| convergent_lines(X0,sK2)
| ~ convergent_lines(sK1,sK2) ),
inference(resolution,[],[f57,f64]) ).
fof(f165,definition,
( spl3_1
<=> convergent_lines(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f167,plain,
( ~ convergent_lines(sK1,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f169,definition,
( spl3_2
<=> ! [X0] :
( unorthogonal_lines(X0,sK1)
| convergent_lines(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f170,plain,
( ! [X0] :
( unorthogonal_lines(X0,sK1)
| convergent_lines(X0,sK2) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f171,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f156,f169,f165]) ).
fof(f173,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_1 ),
inference(resolution,[],[f167,f100]) ).
fof(f177,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f173,f66]) ).
fof(f178,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f213,plain,
( convergent_lines(sK0,sK2)
| ~ spl3_2 ),
inference(resolution,[],[f170,f63]) ).
fof(f220,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f213,f62]) ).
fof(f221,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f220]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f178]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f221]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f222,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n011.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 07:42:15 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.13/0.45 % (2070796)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (2070805)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4275474611:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.45 % (2070805) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2070796-2070805"...
% 0.13/0.45 % (2070802)% WARNING: option uhcvi not known.
% 0.13/0.45 % (2070805)...printing done.
% 0.13/0.45 % (2070805)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (2070805)------------------------------
% 0.13/0.45 % (2070805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (2070805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (2070805)CaDiCaL version: 2.1.3
% 0.13/0.45 % (2070805)Termination reason: Refutation
% 0.13/0.45 % (2070805)Time elapsed: 0.003 s
% 0.13/0.45 % (2070805)Peak memory usage: 12 MB
% 0.13/0.45 % (2070805)Instructions burned: 9 (million)
% 0.13/0.45 % (2070796)Success in time 0.032 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------