%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 09:52:06 AM UTC 2026
% Result : Theorem 1.77s 1.13s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 26 unt; 4 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 57 ~; 73 |; 8 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 98 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f6,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( convergent_lines(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f16,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
fof(f17,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
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/sandbox2/benchmark/theBenchmark.p',oac1) ).
fof(f21,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
fof(f22,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/benchmark/theBenchmark.p',ouo1) ).
fof(f24,axiom,
! [X0,X1] :
~ ( ~ convergent_lines(X0,X1)
& ~ unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
fof(f32,axiom,
! [X0,X1] :
( equal_lines(X0,X1)
<=> ~ distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/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(f39,plain,
? [X0,X1] : ~ equal_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f37]) ).
fof(f44,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f67,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f68,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(f69,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,[],[f68]) ).
fof(f73,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f74,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f73]) ).
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)],[f39]) ).
fof(f80,plain,
~ equal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f79]) ).
fof(f82,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f83,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f16]) ).
fof(f85,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f86,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f21]) ).
fof(f87,plain,
! [X0,X1] :
( equal_lines(X0,X1)
| distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f90,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,[],[f50]) ).
fof(f104,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f107,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f113,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f118,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(resolution,[],[f87,f80]) ).
fof(f119,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f104,f86]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,parallel_through_point(X1,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[],[f112,f83]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( convergent_lines(X2,parallel_through_point(X1,X3))
| convergent_lines(X0,X1)
| ~ convergent_lines(X2,X0) ),
inference(resolution,[],[f131,f112]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ unorthogonal_lines(X0,orthogonal_through_point(X1,X2))
| ~ convergent_lines(X0,orthogonal_through_point(X1,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[],[f107,f86]) ).
fof(f185,plain,
! [X0,X1] :
( apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
| unorthogonal_lines(parallel_through_point(sK1,sK0),X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| apart_point_and_line(X0,parallel_through_point(sK1,sK0)) ),
inference(resolution,[],[f90,f118]) ).
fof(f190,definition,
( spl2_1
<=> ! [X1] :
( unorthogonal_lines(parallel_through_point(sK1,sK0),X1)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f191,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| unorthogonal_lines(parallel_through_point(sK1,sK0),X1) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,definition,
( spl2_2
<=> ! [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_2])],[avatar_definition]) ).
fof(f194,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_2 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f195,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f185,f193,f190]) ).
fof(f196,plain,
( apart_point_and_line(sK0,parallel_through_point(sK1,sK0))
| ~ spl2_2 ),
inference(resolution,[],[f194,f85]) ).
fof(f200,plain,
( $false
| ~ spl2_2 ),
inference(resolution,[],[f196,f82]) ).
fof(f202,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f200]) ).
fof(f203,plain,
( unorthogonal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| ~ spl2_1 ),
inference(resolution,[],[f191,f86]) ).
fof(f211,definition,
( spl2_4
<=> convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f212,plain,
( ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| spl2_4 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f1316,plain,
( ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| convergent_lines(parallel_through_point(sK1,sK0),sK1)
| ~ spl2_1 ),
inference(resolution,[],[f178,f203]) ).
fof(f1328,definition,
( spl2_48
<=> convergent_lines(parallel_through_point(sK1,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_48])],[avatar_definition]) ).
fof(f1329,plain,
( convergent_lines(parallel_through_point(sK1,sK0),sK1)
| ~ spl2_48 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f1330,plain,
( spl2_48
| ~ spl2_4
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f1316,f190,f211,f1328]) ).
fof(f1331,plain,
( $false
| ~ spl2_48 ),
inference(resolution,[],[f1329,f83]) ).
fof(f1333,plain,
~ spl2_48,
inference(avatar_contradiction_clause,[],[f1331]) ).
fof(f1349,plain,
( ! [X0] :
( ~ convergent_lines(X0,parallel_through_point(sK1,sK0))
| convergent_lines(X0,orthogonal_through_point(sK1,sK0)) )
| spl2_4 ),
inference(resolution,[],[f212,f112]) ).
fof(f1414,plain,
( ! [X0,X1] :
( convergent_lines(X0,orthogonal_through_point(sK1,sK0))
| convergent_lines(X1,sK1)
| ~ convergent_lines(X0,X1) )
| spl2_4 ),
inference(resolution,[],[f1349,f135]) ).
fof(f1532,plain,
( ! [X0] :
( ~ convergent_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(X0,sK1) )
| spl2_4 ),
inference(resolution,[],[f1414,f113]) ).
fof(f1540,plain,
( convergent_lines(sK1,sK1)
| spl2_4 ),
inference(resolution,[],[f1532,f119]) ).
fof(f1569,plain,
( $false
| spl2_4 ),
inference(resolution,[],[f1540,f113]) ).
fof(f1570,plain,
spl2_4,
inference(avatar_contradiction_clause,[],[f1569]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f195]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f202]) ).
cnf(s66,plain,
( ~ spl2_1
| ~ spl2_4
| spl2_48 ),
inference(sat_conversion,[],[f1330]) ).
cnf(s67,plain,
~ spl2_48,
inference(sat_conversion,[],[f1333]) ).
cnf(s78,plain,
spl2_4,
inference(sat_conversion,[],[f1570]) ).
cnf(s79,plain,
~ spl2_1,
inference(rat,[],[s66,s67,s78]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s1,s2,s79]) ).
fof(f1571,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 07:44:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.77/1.13 % (1699925)Detected formulas, will run a generic FOF schedule.
% 1.77/1.13 % (1699936)dis-21_1_sil=8000:lcm=predicate:random_seed=1942568329:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.77/1.13 % (1699936)First to succeed.
% 1.77/1.13 % (1699936)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1699925"
% 1.77/1.13 % (1699934)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2789457399:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.77/1.13 % (1699934)Also succeeded, but the first one will report.
% 1.77/1.13 % (1699930)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1738241324:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.77/1.13 % (1699932)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4058513467:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.77/1.13 % (1699931)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=711001828:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.77/1.13 % (1699933)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3880372707:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.77/1.13 % (1699933)Refutation not found, incomplete strategy
% 1.77/1.13 % (1699933)------------------------------
% 1.77/1.13 % (1699933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.77/1.13 % (1699933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/1.13 % (1699933)CaDiCaL version: 2.1.3
% 1.77/1.13 % (1699933)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.13 % (1699933)Time elapsed: 0.001 s
% 1.77/1.13 % (1699933)Peak memory usage: 86 MB
% 1.77/1.13 % (1699935)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=911657773:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.77/1.13 % (1699935)Also succeeded, but the first one will report.
% 1.77/1.13 % (1699936)Refutation found. Thanks to Tanya!
% 1.77/1.13 % SZS status Theorem for theBenchmark
% 1.77/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.32 % (1699936)------------------------------
% 2.67/1.32 % (1699936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.32 % (1699936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.32 % (1699936)CaDiCaL version: 2.1.3
% 2.67/1.32 % (1699936)Termination reason: Refutation
% 2.67/1.32 % (1699936)Time elapsed: 0.021 s
% 2.67/1.32 % (1699936)Peak memory usage: 89 MB
% 2.67/1.32 % (1699936)Instructions burned: 56 (million)
% 2.67/1.32 % (1699936)------------------------------
% 2.67/1.32 % (1699936)------------------------------
% 2.67/1.32 % (1699925)Success in time 0.291 s
% 2.67/1.32 % Vampire exiting
%------------------------------------------------------------------------------