%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 09:54:02 AM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 16 unt; 2 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 93 ( 38 ~; 36 |; 8 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f22,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f23,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/Axioms/GEO006+3.ax',ouo1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(f34,axiom,
! [X0,X1] :
( incident_point_and_line(X0,X1)
<=> ~ apart_point_and_line(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(f35,axiom,
! [X0,X1] :
( orthogonal_lines(X0,X1)
<=> ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( ( incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) )
=> equal_lines(X1,orthogonal_through_point(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( ( incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) )
=> equal_lines(X1,orthogonal_through_point(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( orthogonal_lines(X0,X1)
=> ~ unorthogonal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f39,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
=> ~ apart_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f40,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f64,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,[],[f23]) ).
fof(f65,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,[],[f64]) ).
fof(f79,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f80,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f81,plain,
! [X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| ~ orthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f82,plain,
? [X0,X1,X2] :
( ~ equal_lines(X1,orthogonal_through_point(X2,X0))
& incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f83,plain,
? [X0,X1,X2] :
( ~ equal_lines(X1,orthogonal_through_point(X2,X0))
& incident_point_and_line(X0,X1)
& orthogonal_lines(X1,X2) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
( ~ equal_lines(sK1,orthogonal_through_point(sK2,sK0))
& incident_point_and_line(sK0,sK1)
& orthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f83]) ).
fof(f108,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f109,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| unorthogonal_lines(X1,X3)
| unorthogonal_lines(X2,X3)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f122,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X0,X1] :
( ~ orthogonal_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f124,plain,
orthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f84]) ).
fof(f125,plain,
incident_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f84]) ).
fof(f126,plain,
~ equal_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f84]) ).
fof(f128,plain,
distinct_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(resolution,[],[f121,f126]) ).
fof(f129,plain,
~ apart_point_and_line(sK0,sK1),
inference(resolution,[],[f122,f125]) ).
fof(f130,plain,
~ unorthogonal_lines(sK1,sK2),
inference(resolution,[],[f123,f124]) ).
fof(f214,plain,
! [X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| unorthogonal_lines(sK1,X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1)
| apart_point_and_line(X0,sK1) ),
inference(resolution,[],[f110,f128]) ).
fof(f229,definition,
( spl3_3
<=> ! [X1] :
( unorthogonal_lines(sK1,X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f230,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1)
| unorthogonal_lines(sK1,X1) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f232,definition,
( spl3_4
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| apart_point_and_line(X0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f233,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| apart_point_and_line(X0,sK1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f214,f232,f229]) ).
fof(f251,plain,
( unorthogonal_lines(sK1,sK2)
| ~ spl3_3 ),
inference(resolution,[],[f230,f108]) ).
fof(f258,plain,
( $false
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f251,f130]) ).
fof(f259,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f260,plain,
( apart_point_and_line(sK0,sK1)
| ~ spl3_4 ),
inference(resolution,[],[f233,f109]) ).
fof(f265,plain,
( $false
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f260,f129]) ).
fof(f266,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f265]) ).
cnf(s3,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f234]) ).
cnf(s4,plain,
~ spl3_3,
inference(sat_conversion,[],[f259]) ).
cnf(s5,plain,
~ spl3_4,
inference(sat_conversion,[],[f266]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f267,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 07:36:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.38 Running first-order model finding
% 0.14/0.38 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.44 % (1076272)Will run a generic schedule for satisfiability detection.
% 0.14/0.44 % (1076277)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=248441697_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.44 % TRYING [1]
% 0.14/0.44 % TRYING [2]
% 0.14/0.44 % TRYING [3]
% 0.14/0.44 % TRYING [4]
% 0.14/0.44 % TRYING [5]
% 0.14/0.44 % (1076278)% WARNING: option uhcvi not known.
% 0.14/0.44 % TRYING [6]
% 0.14/0.44 % (1076278)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3382602512:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.44 % (1076279)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=407152978:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.44 % (1076280)dis+10_1_sil=32000:sp=arity:random_seed=906060208:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.44 % (1076281)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3331550299:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.44 % (1076282)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=831597820:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.44 % (1076283)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3691097283:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.44 % (1076280) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1076272-1076280"...
% 0.14/0.44 % TRYING [7]
% 0.14/0.44 % (1076280)...printing done.
% 0.14/0.44 % (1076280)Refutation found. Thanks to Tanya!
% 0.14/0.44 % SZS status Theorem for theBenchmark
% 0.14/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.44 % (1076280)------------------------------
% 0.14/0.44 % (1076280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.44 % (1076280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.44 % (1076280)CaDiCaL version: 2.1.3
% 0.14/0.44 % (1076280)Termination reason: Refutation
% 0.14/0.44 % (1076280)Time elapsed: 0.005 s
% 0.14/0.44 % (1076280)Peak memory usage: 12 MB
% 0.14/0.44 % (1076280)Instructions burned: 6 (million)
% 0.14/0.44 % (1076272)Success in time 0.046 s
% 0.14/0.44 % Vampire exiting
%------------------------------------------------------------------------------