%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 2.69s 1.26s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 26 unt; 4 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 53 ~; 72 |; 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 : 90 ( 0 sgn 88 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',apart6) ).
fof(f13,axiom,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
fof(f14,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
fof(f16,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
fof(f17,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/theBenchmark.p',oac1) ).
fof(f18,axiom,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
fof(f19,axiom,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
fof(f20,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/theBenchmark.p',ouo1) ).
fof(f21,conjecture,
! [X0,X1] : ~ distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f22,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)],[f21]) ).
fof(f23,plain,
? [X0,X1] : distinct_lines(parallel_through_point(X1,X0),orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
inference(ennf_transformation,[],[f22]) ).
fof(f24,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,[],[f20]) ).
fof(f25,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,[],[f24]) ).
fof(f37,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,[],[f17]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f40,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
distinct_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)],[f23]) ).
fof(f44,plain,
distinct_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
inference(cnf_transformation,[],[f43]) ).
fof(f45,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,[],[f25]) ).
fof(f52,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f53,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f13]) ).
fof(f54,plain,
! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f55,plain,
! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f18]) ).
fof(f59,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f61,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f62,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f63,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f67,plain,
! [X0,X1] : convergent_lines(orthogonal_through_point(X0,X1),X0),
inference(resolution,[],[f61,f55]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ convergent_lines(X0,parallel_through_point(X1,X2))
| convergent_lines(X0,X1) ),
inference(resolution,[],[f62,f53]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( convergent_lines(X2,parallel_through_point(X1,X3))
| convergent_lines(X0,X1)
| ~ convergent_lines(X2,X0) ),
inference(resolution,[],[f72,f62]) ).
fof(f84,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(f85,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,[],[f84]) ).
fof(f87,plain,
( apart_point_and_line(sK0,parallel_through_point(sK1,sK0))
| ~ spl2_2 ),
inference(resolution,[],[f85,f54]) ).
fof(f88,plain,
( $false
| ~ spl2_2 ),
inference(resolution,[],[f87,f52]) ).
fof(f89,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f88]) ).
fof(f99,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,[],[f59,f55]) ).
fof(f107,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,[],[f45,f44]) ).
fof(f112,definition,
( spl2_3
<=> ! [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_3])],[avatar_definition]) ).
fof(f113,plain,
( ! [X1] :
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X1)
| unorthogonal_lines(parallel_through_point(sK1,sK0),X1) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f107,f84,f112]) ).
fof(f115,plain,
( unorthogonal_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| ~ spl2_3 ),
inference(resolution,[],[f113,f55]) ).
fof(f133,definition,
( spl2_5
<=> convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f134,plain,
( ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| spl2_5 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f138,plain,
( ! [X0] :
( ~ convergent_lines(X0,parallel_through_point(sK1,sK0))
| convergent_lines(X0,orthogonal_through_point(sK1,sK0)) )
| spl2_5 ),
inference(resolution,[],[f134,f62]) ).
fof(f144,plain,
( ! [X0,X1] :
( convergent_lines(X0,orthogonal_through_point(sK1,sK0))
| convergent_lines(X1,sK1)
| ~ convergent_lines(X0,X1) )
| spl2_5 ),
inference(resolution,[],[f138,f75]) ).
fof(f176,plain,
( ! [X0] :
( ~ convergent_lines(orthogonal_through_point(sK1,sK0),X0)
| convergent_lines(X0,sK1) )
| spl2_5 ),
inference(resolution,[],[f144,f63]) ).
fof(f184,plain,
( convergent_lines(sK1,sK1)
| spl2_5 ),
inference(resolution,[],[f176,f67]) ).
fof(f194,plain,
( $false
| spl2_5 ),
inference(resolution,[],[f184,f63]) ).
fof(f195,plain,
spl2_5,
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f212,plain,
( ~ convergent_lines(parallel_through_point(sK1,sK0),orthogonal_through_point(sK1,sK0))
| convergent_lines(parallel_through_point(sK1,sK0),sK1)
| ~ spl2_3 ),
inference(resolution,[],[f99,f115]) ).
fof(f215,definition,
( spl2_9
<=> convergent_lines(parallel_through_point(sK1,sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f216,plain,
( convergent_lines(parallel_through_point(sK1,sK0),sK1)
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f217,plain,
( spl2_9
| ~ spl2_5
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f212,f112,f133,f215]) ).
fof(f220,plain,
( $false
| ~ spl2_9 ),
inference(resolution,[],[f216,f53]) ).
fof(f222,plain,
~ spl2_9,
inference(avatar_contradiction_clause,[],[f220]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f89]) ).
cnf(s3,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f114]) ).
cnf(s7,plain,
spl2_5,
inference(sat_conversion,[],[f195]) ).
cnf(s8,plain,
( ~ spl2_3
| ~ spl2_5
| spl2_9 ),
inference(sat_conversion,[],[f217]) ).
cnf(s9,plain,
~ spl2_9,
inference(sat_conversion,[],[f222]) ).
cnf(s10,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
~ spl2_3,
inference(rat,[],[s10,s7]) ).
cnf(s12,plain,
spl2_2,
inference(rat,[],[s3,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s12]) ).
fof(f223,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n002.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 07:46:07 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.69/1.25 % (3212206)Detected formulas, will run a generic FOF schedule.
% 2.69/1.25 % (3212213)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=1079472741:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.25 % (3212214)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2292702321:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.25 % (3212216)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=19403848:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.25 % (3212211)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=2735657580:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.25 % (3212217)dis-21_1_sil=8000:lcm=predicate:random_seed=2749186117: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)
% 2.69/1.25 % (3212215)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3412321803:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.25 % (3212212)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=2700399534:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.25 % (3212217)First to succeed.
% 2.69/1.25 % (3212217)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3212206"
% 2.69/1.25 % (3212215)Also succeeded, but the first one will report.
% 2.69/1.25 % (3212214)Instruction limit reached!
% 2.69/1.25 % (3212214)------------------------------
% 2.69/1.25 % (3212214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.25 % (3212214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.25 % (3212214)CaDiCaL version: 2.1.3
% 2.69/1.25 % (3212214)Termination reason: Instruction limit
% 2.69/1.25 % (3212214)Termination phase: Saturation
% 2.69/1.25 % (3212214)Time elapsed: 0.056 s
% 2.69/1.25 % (3212214)Peak memory usage: 88 MB
% 2.69/1.25 % (3212214)Instructions burned: 109 (million)
% 2.69/1.26 % (3212216)Instruction limit reached!
% 2.69/1.26 % (3212216)------------------------------
% 2.69/1.26 % (3212216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.26 % (3212216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.26 % (3212216)CaDiCaL version: 2.1.3
% 2.69/1.26 % (3212216)Termination reason: Instruction limit
% 2.69/1.26 % (3212216)Termination phase: Saturation
% 2.69/1.26 % (3212216)Time elapsed: 0.093 s
% 2.69/1.26 % (3212216)Peak memory usage: 89 MB
% 2.69/1.26 % (3212216)Instructions burned: 139 (million)
% 2.69/1.26 % (3212225)lrs+10_1_sil=8000:sp=occurrence:random_seed=1512603809:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.69/1.26 % (3212226)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2299188007:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.69/1.26 % (3212217)Refutation found. Thanks to Tanya!
% 2.69/1.26 % SZS status Theorem for theBenchmark
% 2.69/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.45 % (3212217)------------------------------
% 3.49/1.45 % (3212217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.45 % (3212217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.45 % (3212217)CaDiCaL version: 2.1.3
% 3.49/1.45 % (3212217)Termination reason: Refutation
% 3.49/1.45 % (3212217)Time elapsed: 0.005 s
% 3.49/1.45 % (3212217)Peak memory usage: 89 MB
% 3.49/1.45 % (3212217)Instructions burned: 6 (million)
% 3.49/1.45 % (3212217)------------------------------
% 3.49/1.45 % (3212217)------------------------------
% 3.49/1.45 % (3212206)Success in time 0.414 s
% 3.49/1.45 % Vampire exiting
%------------------------------------------------------------------------------