%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO223+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 : n019.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 0.37s 0.49s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 24 unt; 2 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 137 ( 50 ~; 70 |; 8 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 114 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(f15,axiom,
! [X0,X1] :
( distinct_lines(X0,X1)
=> convergent_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(f19,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(f20,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/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( ~ unorthogonal_lines(X0,X1)
& ~ unorthogonal_lines(X0,X2) )
=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(f36,conjecture,
! [X0,X1] : equal_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] : equal_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
=> equal_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f32]) ).
fof(f41,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f57,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f60,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,[],[f20]) ).
fof(f61,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,[],[f60]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f77,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f78,plain,
? [X0,X1] : ~ equal_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f37]) ).
fof(f79,plain,
~ equal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f78]) ).
fof(f81,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f82,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f84,plain,
! [X2,X0,X1] :
( ~ distinct_lines(X0,X1)
| distinct_lines(X1,X2)
| distinct_lines(X0,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,X1)
| convergent_lines(X1,X2)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f94,plain,
! [X0,X1] :
( ~ distinct_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f95,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f98,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,X1)
| unorthogonal_lines(X1,X2)
| ~ convergent_lines(X0,X1)
| convergent_lines(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f103,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f116,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
~ equal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f98,f103]) ).
fof(f119,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(resolution,[],[f116,f117]) ).
fof(f121,plain,
! [X0] :
( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| distinct_lines(parallel_through_point(sK1,sK0),X0) ),
inference(resolution,[],[f84,f119]) ).
fof(f122,plain,
! [X2,X0,X1] :
( convergent_lines(orthogonal_through_point(X0,X2),X1)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f85,f118]) ).
fof(f125,plain,
! [X0,X1] :
( distinct_lines(parallel_through_point(sK1,sK0),X0)
| distinct_lines(X0,X1)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1) ),
inference(resolution,[],[f121,f84]) ).
fof(f138,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X0,orthogonal_through_point(X1,X2))
| unorthogonal_lines(X0,X1) ),
inference(resolution,[],[f111,f118]) ).
fof(f147,plain,
! [X0,X1] :
( distinct_lines(parallel_through_point(sK1,sK0),X0)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| convergent_lines(X0,X1) ),
inference(resolution,[],[f125,f94]) ).
fof(f282,plain,
! [X0,X1] : convergent_lines(X0,orthogonal_through_point(X0,X1)),
inference(resolution,[],[f122,f82]) ).
fof(f301,plain,
! [X2,X3,X0,X1] :
( ~ convergent_lines(X0,orthogonal_through_point(X1,X2))
| unorthogonal_lines(orthogonal_through_point(X1,X2),X3)
| unorthogonal_lines(X0,X1)
| unorthogonal_lines(X0,X3) ),
inference(resolution,[],[f138,f99]) ).
fof(f794,plain,
! [X0,X1] :
( distinct_lines(parallel_through_point(sK1,sK0),parallel_through_point(X0,X1))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(resolution,[],[f147,f95]) ).
fof(f842,plain,
! [X0,X1] :
( convergent_lines(parallel_through_point(sK1,sK0),parallel_through_point(X0,X1))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
inference(resolution,[],[f794,f94]) ).
fof(f881,plain,
distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1),
inference(resolution,[],[f842,f82]) ).
fof(f920,plain,
! [X0] :
( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| distinct_lines(sK1,X0) ),
inference(resolution,[],[f881,f84]) ).
fof(f923,definition,
( spl2_10
<=> ! [X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| unorthogonal_lines(sK1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f924,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| unorthogonal_lines(sK1,X1) )
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f1035,plain,
distinct_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(resolution,[],[f920,f81]) ).
fof(f1067,plain,
convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(resolution,[],[f1035,f94]) ).
fof(f1101,plain,
! [X0] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
| unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
| unorthogonal_lines(sK1,X0) ),
inference(resolution,[],[f1067,f301]) ).
fof(f1111,definition,
( spl2_20
<=> unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f1113,plain,
( unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1119,plain,
( spl2_20
| spl2_10 ),
inference(avatar_split_clause,[],[f1101,f923,f1111]) ).
fof(f1553,plain,
( unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
| ~ spl2_10 ),
inference(resolution,[],[f924,f103]) ).
fof(f1560,plain,
( spl2_20
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f1553,f923,f1111]) ).
fof(f1619,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| ~ convergent_lines(sK1,orthogonal_through_point(sK1,sK0))
| convergent_lines(sK1,X0) )
| ~ spl2_20 ),
inference(resolution,[],[f1113,f101]) ).
fof(f1624,plain,
( ! [X0] :
( unorthogonal_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(sK1,X0) )
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f1619,f282]) ).
fof(f1711,plain,
( convergent_lines(sK1,sK1)
| ~ spl2_20 ),
inference(resolution,[],[f1624,f103]) ).
fof(f1724,plain,
( $false
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f1711,f82]) ).
fof(f1725,plain,
~ spl2_20,
inference(avatar_contradiction_clause,[],[f1724]) ).
cnf(s23,plain,
( spl2_10
| spl2_20 ),
inference(sat_conversion,[],[f1119]) ).
cnf(s33,plain,
( ~ spl2_10
| spl2_20 ),
inference(sat_conversion,[],[f1560]) ).
cnf(s43,plain,
~ spl2_20,
inference(sat_conversion,[],[f1725]) ).
cnf(s44,plain,
~ spl2_10,
inference(rat,[],[s33,s43]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s23,s43,s44]) ).
fof(f1726,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:44:03 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 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
% 0.37/0.49 % (2772498)Will run a generic schedule for satisfiability detection.
% 0.37/0.49 % (2772504)% WARNING: option uhcvi not known.
% 0.37/0.49 % (2772504)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2491424446:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.37/0.49 % (2772507)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2609073370:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.37/0.49 % (2772503)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2826758056_2999 on theBenchmark for (2999ds/0Mi)
% 0.37/0.49 % (2772505)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2611839193:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.37/0.49 % (2772506)dis+10_1_sil=32000:sp=arity:random_seed=2622574186:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.37/0.49 % (2772508)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4108575848:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.37/0.49 % (2772509)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2598805653:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.37/0.49 % TRYING [1]
% 0.37/0.49 % TRYING [2]
% 0.37/0.49 % TRYING [3]
% 0.37/0.49 % TRYING [4]
% 0.37/0.49 % TRYING [5]
% 0.37/0.49 % TRYING [6]
% 0.37/0.49 % TRYING [7]
% 0.37/0.49 % (2772506) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2772498-2772506"...
% 0.37/0.49 % (2772506)...printing done.
% 0.37/0.49 % (2772506)Refutation found. Thanks to Tanya!
% 0.37/0.49 % SZS status Theorem for theBenchmark
% 0.37/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.49 % (2772506)------------------------------
% 0.37/0.49 % (2772506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.49 % (2772506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.49 % (2772506)CaDiCaL version: 2.1.3
% 0.37/0.49 % (2772506)Termination reason: Refutation
% 0.37/0.49 % (2772506)Time elapsed: 0.044 s
% 0.37/0.49 % (2772506)Peak memory usage: 12 MB
% 0.37/0.49 % (2772506)Instructions burned: 73 (million)
% 0.37/0.49 % (2772498)Success in time 0.083 s
% 0.37/0.49 % Vampire exiting
%------------------------------------------------------------------------------