%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO206+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 09:52:00 AM UTC 2026
% Result : Theorem 2.37s 1.20s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 36 ~; 30 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/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/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(f15,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cup1) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,parallel_through_point(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,parallel_through_point(X2,X0)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
? [X0,X1,X2] :
( distinct_lines(X1,parallel_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( distinct_lines(X1,parallel_through_point(X2,X0))
& ~ apart_point_and_line(X0,X1)
& ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f20]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] :
( convergent_lines(X0,X2)
| convergent_lines(X1,X2)
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
( distinct_lines(sK1,parallel_through_point(sK2,sK0))
& ~ apart_point_and_line(sK0,sK1)
& ~ convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f30,plain,
~ convergent_lines(sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f31,plain,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f29]) ).
fof(f32,plain,
distinct_lines(sK1,parallel_through_point(sK2,sK0)),
inference(cnf_transformation,[],[f29]) ).
fof(f33,plain,
! [X2,X0,X1] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
! [X0,X1] : ~ apart_point_and_line(X0,parallel_through_point(X1,X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f39,plain,
! [X0,X1] : ~ convergent_lines(parallel_through_point(X1,X0),X1),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| convergent_lines(X0,X2)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0] :
( convergent_lines(X0,sK2)
| ~ convergent_lines(X0,sK1) ),
inference(resolution,[],[f40,f30]) ).
fof(f51,plain,
! [X0] :
( apart_point_and_line(sK0,X0)
| convergent_lines(X0,sK1)
| ~ distinct_lines(X0,sK1) ),
inference(resolution,[],[f33,f31]) ).
fof(f55,plain,
! [X0] : ~ convergent_lines(parallel_through_point(sK2,X0),sK1),
inference(resolution,[],[f48,f39]) ).
fof(f58,plain,
! [X0] :
( convergent_lines(parallel_through_point(X0,sK0),sK1)
| ~ distinct_lines(parallel_through_point(X0,sK0),sK1) ),
inference(resolution,[],[f51,f38]) ).
fof(f72,plain,
~ distinct_lines(parallel_through_point(sK2,sK0),sK1),
inference(resolution,[],[f58,f55]) ).
fof(f75,plain,
! [X0] :
( ~ distinct_lines(X0,parallel_through_point(sK2,sK0))
| distinct_lines(X0,sK1) ),
inference(resolution,[],[f72,f36]) ).
fof(f84,plain,
distinct_lines(sK1,sK1),
inference(resolution,[],[f75,f32]) ).
fof(f88,plain,
$false,
inference(forward_subsumption_resolution,[],[f84,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 07:39:44 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.37/1.20 % (3209206)Detected formulas, will run a generic FOF schedule.
% 2.37/1.20 % (3209215)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=365903778:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.37/1.20 % (3209215)First to succeed.
% 2.37/1.20 % (3209215)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3209206"
% 2.37/1.20 % (3209216)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3846020287:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.37/1.20 % (3209217)dis-21_1_sil=8000:lcm=predicate:random_seed=3785065176: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)
% 2.37/1.20 % (3209212)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=436811936:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.37/1.20 % (3209211)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=2694293857:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.37/1.20 % (3209213)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=3754285924:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.37/1.20 % (3209216)Also succeeded, but the first one will report.
% 2.37/1.20 % (3209214)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1878393021:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.37/1.20 % (3209214)Also succeeded, but the first one will report.
% 2.37/1.20 % (3209217)Also succeeded, but the first one will report.
% 2.37/1.20 % (3209215)Refutation found. Thanks to Tanya!
% 2.37/1.20 % SZS status Theorem for theBenchmark
% 2.37/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 2.37/1.20 % (3209215)------------------------------
% 2.37/1.20 % (3209215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/1.20 % (3209215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/1.20 % (3209215)CaDiCaL version: 2.1.3
% 2.37/1.20 % (3209215)Termination reason: Refutation
% 2.37/1.20 % (3209215)Time elapsed: 0.001 s
% 2.37/1.20 % (3209215)Peak memory usage: 88 MB
% 2.37/1.20 % (3209215)Instructions burned: 2 (million)
% 2.37/1.20 % (3209215)------------------------------
% 2.37/1.20 % (3209215)------------------------------
% 2.37/1.20 % (3209206)Success in time 0.27 s
% 2.37/1.20 % Vampire exiting
%------------------------------------------------------------------------------