%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:52:18 AM UTC 2026
% Result : Theorem 3.60s 1.50s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 33 ~; 24 |; 2 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 55 ( 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
fof(f4,axiom,
! [X0,X1] :
( equally_directed_lines(X0,X1)
<=> ~ unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_defns) ).
fof(f5,axiom,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
<=> ~ unequally_directed_opposite_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_defns) ).
fof(f15,axiom,
! [X0] : equally_directed_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_basics) ).
fof(f18,axiom,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_basics) ).
fof(f19,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/sandbox/benchmark/theBenchmark.p',ax9_basics) ).
fof(f21,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
fof(f37,conjecture,
! [X0] : equally_directed_opposite_lines(X0,reverse_line(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0] : equally_directed_opposite_lines(X0,reverse_line(X0)),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equally_directed_lines(X0,X1)
=> ~ unequally_directed_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
=> equally_directed_opposite_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f43,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
=> unequally_directed_lines(X0,reverse_line(X1)) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f44,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f47,plain,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
| unequally_directed_opposite_lines(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
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(ennf_transformation,[],[f19]) ).
fof(f58,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,[],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,X1)
& ~ left_convergent_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f82,plain,
? [X0] : ~ equally_directed_opposite_lines(X0,reverse_line(X0)),
inference(ennf_transformation,[],[f38]) ).
fof(f83,plain,
~ equally_directed_opposite_lines(sK0,reverse_line(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f86,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f87,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| equally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f94,plain,
! [X0] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f100,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f101,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,[],[f58]) ).
fof(f105,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f60]) ).
fof(f123,plain,
~ equally_directed_opposite_lines(sK0,reverse_line(sK0)),
inference(cnf_transformation,[],[f83]) ).
fof(f135,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(forward_subsumption_resolution,[],[f101,f105]) ).
fof(f136,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[],[f135,f105]) ).
fof(f140,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[],[f136,f84]) ).
fof(f143,plain,
! [X0,X1] :
( equally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[],[f140,f87]) ).
fof(f144,plain,
~ unequally_directed_lines(sK0,reverse_line(sK0)),
inference(resolution,[],[f143,f123]) ).
fof(f162,plain,
unequally_directed_lines(sK0,sK0),
inference(resolution,[],[f144,f100]) ).
fof(f166,plain,
~ equally_directed_lines(sK0,sK0),
inference(resolution,[],[f162,f86]) ).
fof(f167,plain,
$false,
inference(forward_subsumption_resolution,[],[f166,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO269+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 % Computer : n006.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Sun Sep 27 07:56:26 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 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
% 3.60/1.50 % (2668222)Detected formulas, will run a generic FOF schedule.
% 3.60/1.50 % (2668231)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2387225863:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.50 % (2668231)Refutation not found, incomplete strategy
% 3.60/1.50 % (2668231)------------------------------
% 3.60/1.50 % (2668231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.50 % (2668231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.50 % (2668231)CaDiCaL version: 2.1.3
% 3.60/1.50 % (2668231)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.50 % (2668231)Time elapsed: 0.001 s
% 3.60/1.50 % (2668231)Peak memory usage: 88 MB
% 3.60/1.50 % (2668227)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=92217728:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.50 % (2668228)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=38058986:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.50 % (2668229)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=1943317669:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.50 % (2668230)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2622771499:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.50 % (2668233)dis-21_1_sil=8000:lcm=predicate:random_seed=1973581052: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)
% 3.60/1.50 % (2668232)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2615186323:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.50 % (2668230)Refutation not found, incomplete strategy
% 3.60/1.50 % (2668230)------------------------------
% 3.60/1.50 % (2668230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.50 % (2668230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.50 % (2668230)CaDiCaL version: 2.1.3
% 3.60/1.50 % (2668230)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.50 % (2668230)Time elapsed: 0.001 s
% 3.60/1.50 % (2668230)Peak memory usage: 87 MB
% 3.60/1.50 % (2668232)First to succeed.
% 3.60/1.50 % (2668233)Also succeeded, but the first one will report.
% 3.60/1.50 % (2668232)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2668222"
% 3.60/1.50 % (2668231)------------------------------
% 3.60/1.50 % (2668231)------------------------------
% 3.60/1.50 % (2668230)------------------------------
% 3.60/1.50 % (2668230)------------------------------
% 3.60/1.50 % (2668241)lrs+10_1_sil=8000:sp=occurrence:random_seed=829175901:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.60/1.50 % (2668232)Refutation found. Thanks to Tanya!
% 3.60/1.50 % SZS status Theorem for theBenchmark
% 3.60/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.50 % (2668232)------------------------------
% 3.60/1.50 % (2668232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.50 % (2668232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.50 % (2668232)CaDiCaL version: 2.1.3
% 3.60/1.50 % (2668232)Termination reason: Refutation
% 3.60/1.50 % (2668232)Time elapsed: 0.004 s
% 3.60/1.50 % (2668232)Peak memory usage: 88 MB
% 3.60/1.50 % (2668232)Instructions burned: 3 (million)
% 3.60/1.50 % (2668232)------------------------------
% 3.60/1.50 % (2668232)------------------------------
% 3.60/1.50 % (2668222)Success in time 0.432 s
% 3.60/1.50 % Vampire exiting
%------------------------------------------------------------------------------