%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:52:02 AM UTC 2026
% Result : Theorem 3.47s 1.44s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 95 ( 40 ~; 36 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 66 ( 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
fof(f3,axiom,
! [X0] : ~ convergent_lines(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
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',apart6) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f16,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
| unorthogonal_lines(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',oac1) ).
fof(f21,conjecture,
! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( unorthogonal_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| unorthogonal_lines(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
? [X0,X1,X2] :
( ~ distinct_lines(X0,X2)
& ~ unorthogonal_lines(X1,X2)
& unorthogonal_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f31,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f30]) ).
fof(f34,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(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f37,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
( ~ distinct_lines(sK0,sK2)
& ~ unorthogonal_lines(sK1,sK2)
& unorthogonal_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f24]) ).
fof(f39,plain,
unorthogonal_lines(sK0,sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f40,plain,
~ unorthogonal_lines(sK1,sK2),
inference(cnf_transformation,[],[f38]) ).
fof(f41,plain,
~ distinct_lines(sK0,sK2),
inference(cnf_transformation,[],[f38]) ).
fof(f43,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f50,plain,
! [X2,X0,X1] :
( unorthogonal_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1)
| ~ unorthogonal_lines(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
! [X0,X1] :
( unorthogonal_lines(X0,X1)
| convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f53,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0] : ~ convergent_lines(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f55,plain,
~ convergent_lines(sK0,sK2),
inference(resolution,[],[f43,f41]) ).
fof(f57,plain,
convergent_lines(sK1,sK2),
inference(resolution,[],[f52,f40]) ).
fof(f58,plain,
! [X0] :
( distinct_lines(X0,sK2)
| ~ distinct_lines(X0,sK0) ),
inference(resolution,[],[f45,f41]) ).
fof(f63,plain,
~ distinct_lines(sK2,sK0),
inference(resolution,[],[f58,f46]) ).
fof(f65,plain,
~ convergent_lines(sK2,sK0),
inference(resolution,[],[f63,f43]) ).
fof(f66,plain,
! [X0] :
( convergent_lines(X0,sK0)
| ~ convergent_lines(X0,sK2) ),
inference(resolution,[],[f65,f53]) ).
fof(f75,plain,
! [X0] :
( convergent_lines(X0,sK2)
| ~ convergent_lines(X0,sK1)
| ~ unorthogonal_lines(X0,sK1) ),
inference(resolution,[],[f50,f40]) ).
fof(f89,plain,
( ~ convergent_lines(sK0,sK1)
| ~ unorthogonal_lines(sK0,sK1) ),
inference(resolution,[],[f75,f55]) ).
fof(f90,plain,
~ convergent_lines(sK0,sK1),
inference(forward_subsumption_resolution,[],[f89,f39]) ).
fof(f93,plain,
! [X0] :
( convergent_lines(X0,sK1)
| ~ convergent_lines(X0,sK0) ),
inference(resolution,[],[f90,f53]) ).
fof(f102,plain,
~ convergent_lines(sK1,sK0),
inference(resolution,[],[f93,f54]) ).
fof(f104,plain,
~ convergent_lines(sK1,sK2),
inference(resolution,[],[f102,f66]) ).
fof(f106,plain,
$false,
inference(forward_subsumption_resolution,[],[f104,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.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 07:40:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.47/1.44 % (475772)Detected formulas, will run a generic FOF schedule.
% 3.47/1.44 % (475780)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=620593883:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.44 % (475780)Instruction limit reached!
% 3.47/1.44 % (475780)------------------------------
% 3.47/1.44 % (475780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (475780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (475780)CaDiCaL version: 2.1.3
% 3.47/1.44 % (475780)Termination reason: Instruction limit
% 3.47/1.44 % (475780)Termination phase: Saturation
% 3.47/1.44 % (475780)Time elapsed: 0.027 s
% 3.47/1.44 % (475780)Peak memory usage: 88 MB
% 3.47/1.44 % (475780)Instructions burned: 111 (million)
% 3.47/1.44 % (475782)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1321172276:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.44 % (475783)dis-21_1_sil=8000:lcm=predicate:random_seed=2442421446: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)
% 3.47/1.44 % (475779)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=4249991513:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.44 % (475781)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=520213893:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.44 % (475778)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=826184494:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.44 % (475777)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=2222688263:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.44 % (475781)First to succeed.
% 3.47/1.44 % (475781)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-475772"
% 3.47/1.44 % (475783)Also succeeded, but the first one will report.
% 3.47/1.44 % (475782)Also succeeded, but the first one will report.
% 3.47/1.44 % (475785)lrs+10_1_sil=8000:sp=occurrence:random_seed=3575560638:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.47/1.44 % (475785)Also succeeded, but the first one will report.
% 3.47/1.44 % (475781)Refutation found. Thanks to Tanya!
% 3.47/1.44 % SZS status Theorem for theBenchmark
% 3.47/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.44 % (475781)------------------------------
% 3.47/1.44 % (475781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.44 % (475781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.44 % (475781)CaDiCaL version: 2.1.3
% 3.47/1.44 % (475781)Termination reason: Refutation
% 3.47/1.44 % (475781)Time elapsed: 0.003 s
% 3.47/1.44 % (475781)Peak memory usage: 88 MB
% 3.47/1.44 % (475781)Instructions burned: 2 (million)
% 3.47/1.44 % (475781)------------------------------
% 3.47/1.44 % (475781)------------------------------
% 3.47/1.44 % (475772)Success in time 0.404 s
% 3.47/1.44 % Vampire exiting
%------------------------------------------------------------------------------