%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO261+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 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 09:52:16 AM UTC 2026
% Result : Theorem 0.16s 1.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 29 ~; 18 |; 18 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 52 ( 42 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
<=> ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con_def) ).
fof(f14,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag9) ).
fof(f16,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag11) ).
fof(f32,conjecture,
! [X0,X1,X2,X3,X4] :
( ( between_on_line(X0,X2,X3,X4)
& convergent_lines(X0,X1)
& ~ apart_point_and_line(X3,X1) )
=> divides_points(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( between_on_line(X0,X2,X3,X4)
& convergent_lines(X0,X1)
& ~ apart_point_and_line(X3,X1) )
=> divides_points(X1,X2,X4) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f37,plain,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f40,plain,
! [X0,X1] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f56,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f57,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f56]) ).
fof(f59,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,X1)
& ~ left_convergent_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f80,plain,
? [X0,X1,X2,X3,X4] :
( ~ divides_points(X1,X2,X4)
& between_on_line(X0,X2,X3,X4)
& convergent_lines(X0,X1)
& ~ apart_point_and_line(X3,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
? [X0,X1,X2,X3,X4] :
( ~ divides_points(X1,X2,X4)
& between_on_line(X0,X2,X3,X4)
& convergent_lines(X0,X1)
& ~ apart_point_and_line(X3,X1) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
( ~ divides_points(sK1,sK2,sK4)
& between_on_line(sK0,sK2,sK3,sK4)
& convergent_lines(sK0,sK1)
& ~ apart_point_and_line(sK3,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f81]) ).
fof(f85,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f86,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f110,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f114,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f59]) ).
fof(f133,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f82]) ).
fof(f176,plain,
! [X0,X1] :
( left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(forward_subsumption_resolution,[],[f110,f114]) ).
fof(f177,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[],[f176,f114]) ).
fof(f179,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f177,f85]) ).
fof(f183,plain,
! [X0,X1] : ~ convergent_lines(X0,X1),
inference(forward_subsumption_resolution,[],[f179,f86]) ).
fof(f217,plain,
$false,
inference(resolution,[],[f183,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO261+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:55:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.65/1.50 % (1703656)Detected formulas, will run a generic FOF schedule.
% 3.65/1.50 % (1703665)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4017810730:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.65/1.50 % (1703665)Instruction limit reached!
% 3.65/1.50 % (1703665)------------------------------
% 3.65/1.50 % (1703665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.50 % (1703665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.50 % (1703665)CaDiCaL version: 2.1.3
% 3.65/1.50 % (1703665)Termination reason: Instruction limit
% 3.65/1.50 % (1703665)Termination phase: Saturation
% 3.65/1.50 % (1703665)Time elapsed: 0.037 s
% 3.65/1.50 % (1703665)Peak memory usage: 88 MB
% 3.65/1.50 % (1703665)Instructions burned: 119 (million)
% 3.65/1.50 % (1703662)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=3358326841:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.65/1.50 % (1703663)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=1358529280:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.65/1.50 % (1703664)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=170147479:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.65/1.50 % (1703666)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=873227910:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.65/1.50 % (1703667)dis-21_1_sil=8000:lcm=predicate:random_seed=2020149760: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)
% 3.65/1.50 % (1703661)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=80267722:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.65/1.50 % (1703664)Refutation not found, incomplete strategy
% 3.65/1.50 % (1703664)------------------------------
% 3.65/1.50 % (1703664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (1703664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (1703664)CaDiCaL version: 2.1.3
% 0.16/1.50 % (1703664)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.50 % (1703664)Time elapsed: 0.001 s
% 0.16/1.50 % (1703664)Peak memory usage: 86 MB
% 0.16/1.50 % (1703666)First to succeed.
% 0.16/1.50 % (1703666)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1703656"
% 0.16/1.50 % (1703667)Also succeeded, but the first one will report.
% 0.16/1.50 % (1703669)lrs+10_1_sil=8000:sp=occurrence:random_seed=2741573715:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.16/1.50 % (1703669)Also succeeded, but the first one will report.
% 0.16/1.50 % (1703664)------------------------------
% 0.16/1.50 % (1703664)------------------------------
% 0.16/1.50 % (1703666)Refutation found. Thanks to Tanya!
% 0.16/1.50 % SZS status Theorem for theBenchmark
% 0.16/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (1703666)------------------------------
% 0.16/1.50 % (1703666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (1703666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (1703666)CaDiCaL version: 2.1.3
% 0.16/1.50 % (1703666)Termination reason: Refutation
% 0.16/1.50 % (1703666)Time elapsed: 0.005 s
% 0.16/1.50 % (1703666)Peak memory usage: 88 MB
% 0.16/1.50 % (1703666)Instructions burned: 5 (million)
% 0.16/1.50 % (1703666)------------------------------
% 0.16/1.50 % (1703666)------------------------------
% 0.16/1.50 % (1703656)Success in time 0.438 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------