%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:52:08 AM UTC 2026
% Result : Theorem 3.42s 1.37s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 14 unt; 1 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 94 ( 44 ~; 35 |; 10 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 48 ( 0 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] : ~ unequally_directed_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oag5) ).
fof(f11,axiom,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X1)
=> ( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oag6) ).
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/sandbox/benchmark/theBenchmark.p',oag9) ).
fof(f16,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oag11) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( ( ~ unequally_directed_lines(X0,reverse_line(X1))
& ~ unequally_directed_lines(X0,X2) )
=> ~ unequally_directed_lines(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ unequally_directed_lines(X0,reverse_line(X1))
& ~ unequally_directed_lines(X0,X2) )
=> ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f40,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f41,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(flattening,[],[f40]) ).
fof(f46,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(f47,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,[],[f46]) ).
fof(f49,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,X1)
& ~ left_convergent_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f70,plain,
? [X0,X1,X2] :
( unequally_directed_lines(X1,reverse_line(X2))
& ~ unequally_directed_lines(X0,reverse_line(X1))
& ~ unequally_directed_lines(X0,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
? [X0,X1,X2] :
( unequally_directed_lines(X1,reverse_line(X2))
& ~ unequally_directed_lines(X0,reverse_line(X1))
& ~ unequally_directed_lines(X0,X2) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
( unequally_directed_lines(sK1,reverse_line(sK2))
& ~ unequally_directed_lines(sK0,reverse_line(sK1))
& ~ unequally_directed_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f71]) ).
fof(f79,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f86,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,[],[f47]) ).
fof(f90,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f49]) ).
fof(f108,plain,
~ unequally_directed_lines(sK0,sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
~ unequally_directed_lines(sK0,reverse_line(sK1)),
inference(cnf_transformation,[],[f72]) ).
fof(f110,plain,
unequally_directed_lines(sK1,reverse_line(sK2)),
inference(cnf_transformation,[],[f72]) ).
fof(f111,plain,
! [X0] :
( unequally_directed_lines(sK1,X0)
| unequally_directed_lines(reverse_line(sK2),X0) ),
inference(resolution,[],[f80,f110]) ).
fof(f112,plain,
unequally_directed_lines(reverse_line(sK2),sK1),
inference(resolution,[],[f111,f79]) ).
fof(f144,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(forward_subsumption_resolution,[],[f86,f90]) ).
fof(f145,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[],[f144,f90]) ).
fof(f154,definition,
( spl3_2
<=> unequally_directed_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f155,plain,
( unequally_directed_lines(sK1,sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f156,plain,
( ~ unequally_directed_lines(sK1,sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f164,plain,
~ unequally_directed_lines(sK1,sK2),
inference(resolution,[],[f145,f110]) ).
fof(f203,plain,
( ! [X0] :
( unequally_directed_lines(sK1,X0)
| unequally_directed_lines(sK0,X0) )
| ~ spl3_2 ),
inference(resolution,[],[f155,f80]) ).
fof(f204,plain,
( unequally_directed_lines(sK0,sK2)
| ~ spl3_2 ),
inference(resolution,[],[f203,f164]) ).
fof(f209,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f204,f108]) ).
fof(f210,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f209]) ).
fof(f212,plain,
( unequally_directed_lines(reverse_line(sK2),sK0)
| spl3_2 ),
inference(resolution,[],[f156,f111]) ).
fof(f216,plain,
( ! [X0] :
( unequally_directed_lines(reverse_line(sK2),X0)
| unequally_directed_lines(sK0,X0) )
| spl3_2 ),
inference(resolution,[],[f212,f80]) ).
fof(f234,plain,
( ! [X0] :
( unequally_directed_lines(sK0,reverse_line(X0))
| ~ unequally_directed_lines(reverse_line(sK2),X0) )
| spl3_2 ),
inference(resolution,[],[f216,f145]) ).
fof(f486,plain,
( ~ unequally_directed_lines(reverse_line(sK2),sK1)
| spl3_2 ),
inference(resolution,[],[f234,f109]) ).
fof(f491,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f486,f112]) ).
fof(f492,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f491]) ).
cnf(s4,plain,
~ spl3_2,
inference(sat_conversion,[],[f210]) ).
cnf(s5,plain,
spl3_2,
inference(sat_conversion,[],[f492]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s4,s5]) ).
fof(f493,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO231+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 07:47:34 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.42/1.37 % (1700773)Detected formulas, will run a generic FOF schedule.
% 3.42/1.37 % (1700778)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=1979295704:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.42/1.37 % (1700783)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=150663217:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.42/1.37 % (1700782)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3358022588:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.42/1.37 % (1700781)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=127541727:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.42/1.37 % (1700780)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=4068565341:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.42/1.37 % (1700779)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=3686870328:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.42/1.37 % (1700783)First to succeed.
% 3.42/1.37 % (1700783)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1700773"
% 3.42/1.37 % (1700784)dis-21_1_sil=8000:lcm=predicate:random_seed=797388004: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)
% 3.42/1.37 % (1700782)Also succeeded, but the first one will report.
% 3.42/1.37 % (1700781)Also succeeded, but the first one will report.
% 3.42/1.37 % (1700784)Also succeeded, but the first one will report.
% 3.42/1.37 % (1700783)Refutation found. Thanks to Tanya!
% 3.42/1.37 % SZS status Theorem for theBenchmark
% 3.42/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.37 % (1700783)------------------------------
% 3.42/1.37 % (1700783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.37 % (1700783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.37 % (1700783)CaDiCaL version: 2.1.3
% 3.42/1.37 % (1700783)Termination reason: Refutation
% 3.42/1.37 % (1700783)Time elapsed: 0.013 s
% 3.42/1.37 % (1700783)Peak memory usage: 89 MB
% 3.42/1.37 % (1700783)Instructions burned: 14 (million)
% 3.42/1.37 % (1700783)------------------------------
% 3.42/1.37 % (1700783)------------------------------
% 3.42/1.37 % (1700773)Success in time 0.417 s
% 3.42/1.37 % Vampire exiting
%------------------------------------------------------------------------------