%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO223+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 : n009.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 09:54:07 AM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 26 unt; 4 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 49 ~; 67 |; 7 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 82 !; 2 ?)
% 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(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f16,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(f18,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f19,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+3.ax',oac1) ).
fof(f20,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f21,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(f22,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/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(f23,conjecture,
! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f24,negated_conjecture,
~ ! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f29,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f29]) ).
fof(f45,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,[],[f19]) ).
fof(f46,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,[],[f45]) ).
fof(f47,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,[],[f22]) ).
fof(f48,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,[],[f47]) ).
fof(f49,plain,
? [X0,X1] : distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f24]) ).
fof(f52,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f64,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f15]) ).
fof(f65,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f67,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f72,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f20]) ).
fof(f73,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f49]) ).
fof(f76,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f67,f72]) ).
fof(f104,plain,
! [X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X0) ),
inference(resolution,[],[f55,f52]) ).
fof(f169,definition,
( spl2_3
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X0,parallel_through_point(sK1,sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f170,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X0,parallel_through_point(sK1,sK0)) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f184,plain,
( apart_point_and_line(sK0,parallel_through_point(sK1,sK0))
| ~ spl2_3 ),
inference(resolution,[],[f170,f73]) ).
fof(f187,plain,
( $false
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f184,f65]) ).
fof(f188,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f240,plain,
! [X0,X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| unorthogonal_lines(parallel_through_point(sK1,sK0),X0)
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| apart_point_and_line(X1,parallel_through_point(sK1,sK0)) ),
inference(resolution,[],[f74,f75]) ).
fof(f259,definition,
( spl2_6
<=> ! [X0] :
( unorthogonal_lines(parallel_through_point(sK1,sK0),X0)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f260,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| unorthogonal_lines(parallel_through_point(sK1,sK0),X0) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( spl2_3
| spl2_6 ),
inference(avatar_split_clause,[],[f240,f259,f169]) ).
fof(f263,plain,
( unorthogonal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| ~ spl2_6 ),
inference(resolution,[],[f260,f72]) ).
fof(f271,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| convergent_lines(parallel_through_point(sK1,sK0),X0) )
| ~ spl2_6 ),
inference(resolution,[],[f263,f71]) ).
fof(f276,definition,
( spl2_7
<=> convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f278,plain,
( ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| spl2_7 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f288,definition,
( spl2_10
<=> ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(parallel_through_point(sK1,sK0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f289,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(parallel_through_point(sK1,sK0),X0) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( ~ spl2_7
| spl2_10
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f271,f259,f288,f276]) ).
fof(f338,plain,
! [X0,X1] : ~ convergent_lines(X0,parallel_through_point(X0,X1)),
inference(resolution,[],[f104,f64]) ).
fof(f342,plain,
( ~ convergent_lines(orthogonal_through_point(sK1,sK0),parallel_through_point(sK1,sK0))
| spl2_7 ),
inference(resolution,[],[f104,f278]) ).
fof(f343,plain,
( ! [X0] :
( ~ convergent_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(X0,parallel_through_point(sK1,sK0)) )
| spl2_7 ),
inference(resolution,[],[f342,f55]) ).
fof(f606,plain,
( convergent_lines(sK1,parallel_through_point(sK1,sK0))
| spl2_7 ),
inference(resolution,[],[f343,f76]) ).
fof(f620,plain,
( $false
| spl2_7 ),
inference(forward_subsumption_resolution,[],[f606,f338]) ).
fof(f621,plain,
spl2_7,
inference(avatar_contradiction_clause,[],[f620]) ).
fof(f814,plain,
( convergent_lines(parallel_through_point(sK1,sK0),sK1)
| ~ spl2_10 ),
inference(resolution,[],[f289,f72]) ).
fof(f822,plain,
( $false
| ~ spl2_10 ),
inference(forward_subsumption_resolution,[],[f814,f64]) ).
fof(f823,plain,
~ spl2_10,
inference(avatar_contradiction_clause,[],[f822]) ).
cnf(s3,plain,
~ spl2_3,
inference(sat_conversion,[],[f188]) ).
cnf(s6,plain,
( spl2_3
| spl2_6 ),
inference(sat_conversion,[],[f262]) ).
cnf(s9,plain,
( ~ spl2_6
| ~ spl2_7
| spl2_10 ),
inference(sat_conversion,[],[f290]) ).
cnf(s10,plain,
spl2_7,
inference(sat_conversion,[],[f621]) ).
cnf(s11,plain,
~ spl2_10,
inference(sat_conversion,[],[f823]) ).
cnf(s12,plain,
~ spl2_6,
inference(rat,[],[s9,s11,s10]) ).
cnf(s13,plain,
spl2_3,
inference(rat,[],[s6,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s13]) ).
fof(f824,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.35 % Computer : n009.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 07:43:30 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 Running first-order model finding
% 0.12/0.39 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
% 0.12/0.46 % (1699008)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (1699018)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2800576433:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.46 % (1699014)% WARNING: option uhcvi not known.
% 0.12/0.46 % (1699015)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3036188026:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.46 % (1699013)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=540674184_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.46 % (1699014)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1582826167:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.46 % (1699019)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=626259173:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.46 % (1699016)dis+10_1_sil=32000:sp=arity:random_seed=3798706451:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.46 % (1699017)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1357877908:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.46 % TRYING [1]
% 0.12/0.46 % TRYING [2]
% 0.12/0.46 % TRYING [3]
% 0.12/0.46 % TRYING [4]
% 0.12/0.46 % TRYING [5]
% 0.12/0.46 % TRYING [6]
% 0.12/0.46 % TRYING [7]
% 0.12/0.46 % (1699017) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1699008-1699017"...
% 0.12/0.46 % (1699018)Instruction limit reached!
% 0.12/0.46 % (1699018)------------------------------
% 0.12/0.46 % (1699018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (1699018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (1699018)CaDiCaL version: 2.1.3
% 0.12/0.46 % (1699018)Termination reason: Instruction limit
% 0.12/0.46 % (1699018)Termination phase: Saturation
% 0.12/0.46 % (1699018)Time elapsed: 0.039 s
% 0.12/0.46 % (1699018)Peak memory usage: 12 MB
% 0.12/0.46 % (1699018)Instructions burned: 133 (million)
% 0.12/0.46 % (1699017)...printing done.
% 0.12/0.46 % (1699017)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.47 % (1699017)------------------------------
% 0.12/0.47 % (1699017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.47 % (1699017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.47 % (1699017)CaDiCaL version: 2.1.3
% 0.12/0.47 % (1699017)Termination reason: Refutation
% 0.12/0.47 % (1699017)Time elapsed: 0.031 s
% 0.12/0.47 % (1699017)Peak memory usage: 12 MB
% 0.12/0.47 % (1699017)Instructions burned: 58 (million)
% 0.12/0.47 % (1699008)Success in time 0.07 s
% 0.12/0.47 % Vampire exiting
%------------------------------------------------------------------------------