%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO221+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 : n026.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 09:54:06 AM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 14 unt; 2 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 75 ( 30 ~; 34 |; 2 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 52 !; 3 ?)
% 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(f36,conjecture,
! [X0,X1,X2] :
( incident_point_and_line(X1,orthogonal_through_point(X2,X0))
=> equal_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( incident_point_and_line(X1,orthogonal_through_point(X2,X0))
=> equal_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( incident_point_and_line(X0,X1)
=> ~ apart_point_and_line(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f63,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(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(flattening,[],[f63]) ).
fof(f78,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f79,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| ~ incident_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0,X1,X2] :
( ~ equal_lines(orthogonal_through_point(X2,X0),orthogonal_through_point(X2,X1))
& incident_point_and_line(X1,orthogonal_through_point(X2,X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f81,plain,
( ~ equal_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1))
& incident_point_and_line(sK1,orthogonal_through_point(sK2,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f80]) ).
fof(f105,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f106,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f107,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,[],[f64]) ).
fof(f118,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f119,plain,
! [X0,X1] :
( ~ incident_point_and_line(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
incident_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f81]) ).
fof(f121,plain,
~ equal_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(cnf_transformation,[],[f81]) ).
fof(f123,plain,
distinct_lines(orthogonal_through_point(sK2,sK0),orthogonal_through_point(sK2,sK1)),
inference(resolution,[],[f118,f121]) ).
fof(f125,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0)),
inference(resolution,[],[f119,f120]) ).
fof(f211,plain,
! [X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK1),X1)
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) ),
inference(resolution,[],[f107,f123]) ).
fof(f222,definition,
( spl3_1
<=> ! [X1] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f223,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(sK2,sK1),X1)
| unorthogonal_lines(orthogonal_through_point(sK2,sK0),X1) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,definition,
( spl3_2
<=> ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK0))
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f226,plain,
( ! [X0] :
( apart_point_and_line(X0,orthogonal_through_point(sK2,sK1))
| apart_point_and_line(X0,orthogonal_through_point(sK2,sK0)) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f211,f225,f222]) ).
fof(f229,plain,
( apart_point_and_line(sK1,orthogonal_through_point(sK2,sK0))
| ~ spl3_2 ),
inference(resolution,[],[f226,f106]) ).
fof(f234,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f229,f125]) ).
fof(f235,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f246,plain,
( unorthogonal_lines(orthogonal_through_point(sK2,sK0),sK2)
| ~ spl3_1 ),
inference(resolution,[],[f223,f105]) ).
fof(f253,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f246,f105]) ).
fof(f254,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f253]) ).
cnf(s2,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f228]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f235]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f254]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s3,s4]) ).
fof(f255,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO221+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:45:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.15/0.46 % (2505943)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2505954)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2194425441:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (2505949)% WARNING: option uhcvi not known.
% 0.15/0.46 % (2505949)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=15855257:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (2505948)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1317816002_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (2505950)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1279318371:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (2505951)dis+10_1_sil=32000:sp=arity:random_seed=3278864727:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (2505952)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2754610590:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (2505953)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4110904785:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % TRYING [3]
% 0.15/0.46 % TRYING [4]
% 0.15/0.46 % (2505951) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2505943-2505951"...
% 0.15/0.46 % (2505953) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2505943-2505953"...
% 0.15/0.46 % (2505951)...printing done.
% 0.15/0.46 % TRYING [5]
% 0.15/0.46 % (2505953)...printing done.
% 0.15/0.46 % (2505951)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (2505951)------------------------------
% 0.15/0.46 % (2505951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (2505951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (2505951)CaDiCaL version: 2.1.3
% 0.15/0.46 % (2505951)Termination reason: Refutation
% 0.15/0.46 % (2505951)Time elapsed: 0.005 s
% 0.15/0.46 % (2505951)Peak memory usage: 12 MB
% 0.15/0.46 % (2505951)Instructions burned: 7 (million)
% 0.15/0.46 % (2505943)Success in time 0.043 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------