%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO234+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 : n013.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 09:52:09 AM UTC 2026
% Result : Theorem 2.39s 1.22s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 16 unt; 5 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 196 ( 77 ~; 97 |; 13 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 69 ( 0 sgn 63 !; 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(f12,axiom,
! [X0,X1,X2] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> ( ( unequally_directed_lines(X0,X2)
& unequally_directed_lines(X0,reverse_line(X2)) )
| ( unequally_directed_lines(X1,X2)
& unequally_directed_lines(X1,reverse_line(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oag7) ).
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(f35,plain,
? [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X2)
& ~ unequally_directed_lines(X1,reverse_line(X2))
& unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ~ unequally_directed_lines(X0,X2)
& ~ unequally_directed_lines(X1,reverse_line(X2))
& unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f35]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( unequally_directed_lines(X0,X2)
& unequally_directed_lines(X0,reverse_line(X2)) )
| ( unequally_directed_lines(X1,X2)
& unequally_directed_lines(X1,reverse_line(X2)) )
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( unequally_directed_lines(X0,X2)
& unequally_directed_lines(X0,reverse_line(X2)) )
| ( unequally_directed_lines(X1,X2)
& unequally_directed_lines(X1,reverse_line(X2)) )
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f48]) ).
fof(f53,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f54,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f72,plain,
( ~ unequally_directed_lines(sK0,sK2)
& ~ unequally_directed_lines(sK1,reverse_line(sK2))
& unequally_directed_lines(sK0,reverse_line(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f36]) ).
fof(f73,plain,
unequally_directed_lines(sK0,reverse_line(sK1)),
inference(cnf_transformation,[],[f72]) ).
fof(f74,plain,
~ unequally_directed_lines(sK1,reverse_line(sK2)),
inference(cnf_transformation,[],[f72]) ).
fof(f75,plain,
~ unequally_directed_lines(sK0,sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f88,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,reverse_line(X2))
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f89,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f95,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f96,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f114,plain,
! [X0] :
( unequally_directed_lines(X0,sK2)
| ~ unequally_directed_lines(X0,sK0) ),
inference(resolution,[],[f95,f75]) ).
fof(f115,plain,
! [X0] :
( unequally_directed_lines(X0,reverse_line(sK2))
| ~ unequally_directed_lines(X0,sK1) ),
inference(resolution,[],[f95,f74]) ).
fof(f116,plain,
~ unequally_directed_lines(sK2,sK0),
inference(resolution,[],[f114,f96]) ).
fof(f119,plain,
! [X0] :
( ~ unequally_directed_lines(X0,sK2)
| unequally_directed_lines(X0,sK0) ),
inference(resolution,[],[f116,f95]) ).
fof(f125,plain,
! [X0,X1] :
( unequally_directed_lines(X1,sK2)
| unequally_directed_lines(X0,sK0)
| ~ unequally_directed_lines(X1,X0) ),
inference(resolution,[],[f119,f95]) ).
fof(f137,definition,
( spl3_3
<=> unequally_directed_lines(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f140,plain,
~ unequally_directed_lines(reverse_line(sK2),sK1),
inference(resolution,[],[f115,f96]) ).
fof(f152,plain,
! [X0] :
( unequally_directed_lines(X0,sK0)
| ~ unequally_directed_lines(sK2,X0) ),
inference(resolution,[],[f125,f96]) ).
fof(f156,plain,
! [X0,X1] :
( ~ unequally_directed_lines(reverse_line(X1),reverse_line(X0))
| ~ unequally_directed_lines(reverse_line(X1),X0)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[],[f88,f96]) ).
fof(f168,plain,
! [X0] :
( ~ unequally_directed_lines(X0,reverse_line(sK1))
| ~ unequally_directed_lines(X0,sK1)
| unequally_directed_lines(X0,sK2) ),
inference(resolution,[],[f89,f74]) ).
fof(f217,plain,
( ~ unequally_directed_lines(sK0,sK1)
| unequally_directed_lines(sK0,sK2) ),
inference(resolution,[],[f168,f73]) ).
fof(f223,definition,
( spl3_8
<=> unequally_directed_lines(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f224,plain,
( unequally_directed_lines(sK0,sK2)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f226,definition,
( spl3_9
<=> unequally_directed_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f227,plain,
( ~ unequally_directed_lines(sK0,sK1)
| spl3_9 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( spl3_8
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f217,f226,f223]) ).
fof(f229,plain,
( ! [X0] :
( unequally_directed_lines(X0,sK1)
| ~ unequally_directed_lines(X0,sK0) )
| spl3_9 ),
inference(resolution,[],[f227,f95]) ).
fof(f230,plain,
( ~ unequally_directed_lines(sK1,sK0)
| spl3_9 ),
inference(resolution,[],[f229,f96]) ).
fof(f231,plain,
( ~ unequally_directed_lines(reverse_line(sK2),sK0)
| spl3_9 ),
inference(resolution,[],[f229,f140]) ).
fof(f237,plain,
( ~ unequally_directed_lines(sK2,sK1)
| spl3_9 ),
inference(resolution,[],[f230,f152]) ).
fof(f244,plain,
( ! [X0] :
( ~ unequally_directed_lines(X0,reverse_line(sK2))
| unequally_directed_lines(X0,sK0) )
| spl3_9 ),
inference(resolution,[],[f231,f95]) ).
fof(f278,plain,
( ! [X0,X1] :
( unequally_directed_lines(X1,reverse_line(sK2))
| unequally_directed_lines(X0,sK0)
| ~ unequally_directed_lines(X1,X0) )
| spl3_9 ),
inference(resolution,[],[f244,f95]) ).
fof(f302,plain,
( ! [X0] :
( unequally_directed_lines(X0,sK0)
| ~ unequally_directed_lines(sK1,X0) )
| spl3_9 ),
inference(resolution,[],[f278,f74]) ).
fof(f308,plain,
( ~ unequally_directed_lines(sK1,sK2)
| spl3_3 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f310,definition,
( spl3_11
<=> ! [X0] :
( unequally_directed_lines(X0,sK0)
| ~ unequally_directed_lines(sK1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f311,plain,
( ! [X0] :
( unequally_directed_lines(X0,sK0)
| ~ unequally_directed_lines(sK1,X0) )
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f313,plain,
( spl3_11
| spl3_9 ),
inference(avatar_split_clause,[],[f302,f226,f310]) ).
fof(f317,plain,
( $false
| ~ spl3_8 ),
inference(resolution,[],[f224,f75]) ).
fof(f319,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f320,plain,
( ! [X0] :
( unequally_directed_lines(X0,sK1)
| ~ unequally_directed_lines(X0,sK0) )
| spl3_9 ),
inference(resolution,[],[f227,f95]) ).
fof(f323,plain,
( ! [X0] :
( ~ unequally_directed_lines(X0,sK1)
| unequally_directed_lines(X0,sK0) )
| spl3_9 ),
inference(resolution,[],[f230,f95]) ).
fof(f325,plain,
( ~ unequally_directed_lines(reverse_line(sK2),sK0)
| spl3_9 ),
inference(resolution,[],[f320,f140]) ).
fof(f332,plain,
( ! [X0] :
( ~ unequally_directed_lines(X0,sK2)
| unequally_directed_lines(X0,sK1) )
| spl3_9 ),
inference(resolution,[],[f237,f95]) ).
fof(f334,plain,
( ~ unequally_directed_lines(sK2,reverse_line(sK2))
| spl3_9 ),
inference(resolution,[],[f325,f152]) ).
fof(f351,plain,
( ! [X0] :
( unequally_directed_lines(X0,reverse_line(sK2))
| ~ unequally_directed_lines(X0,sK2) )
| spl3_9 ),
inference(resolution,[],[f334,f95]) ).
fof(f386,plain,
( ~ unequally_directed_lines(sK1,sK2)
| ~ spl3_11 ),
inference(resolution,[],[f311,f116]) ).
fof(f387,plain,
( ~ spl3_3
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f386,f310,f137]) ).
fof(f407,plain,
( ! [X0] :
( unequally_directed_lines(X0,sK2)
| ~ unequally_directed_lines(X0,sK1) )
| spl3_3 ),
inference(resolution,[],[f308,f95]) ).
fof(f435,plain,
( ! [X0,X1] :
( unequally_directed_lines(X1,sK2)
| unequally_directed_lines(X0,sK1)
| ~ unequally_directed_lines(X1,X0) )
| spl3_9 ),
inference(resolution,[],[f332,f95]) ).
fof(f703,definition,
( spl3_17
<=> unequally_directed_lines(sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f704,plain,
( unequally_directed_lines(sK2,sK0)
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f929,plain,
( ! [X0] :
( unequally_directed_lines(X0,sK1)
| ~ unequally_directed_lines(sK0,X0) )
| spl3_9 ),
inference(resolution,[],[f435,f75]) ).
fof(f1786,plain,
( $false
| ~ spl3_17 ),
inference(resolution,[],[f704,f116]) ).
fof(f1787,plain,
~ spl3_17,
inference(avatar_contradiction_clause,[],[f1786]) ).
fof(f3423,plain,
( ! [X0] :
( ~ unequally_directed_lines(reverse_line(X0),sK2)
| unequally_directed_lines(sK2,X0)
| ~ unequally_directed_lines(reverse_line(X0),sK2) )
| spl3_9 ),
inference(resolution,[],[f156,f351]) ).
fof(f3440,plain,
( ! [X0] :
( ~ unequally_directed_lines(reverse_line(X0),sK2)
| unequally_directed_lines(sK2,X0) )
| spl3_9 ),
inference(duplicate_literal_removal,[],[f3423]) ).
fof(f3442,plain,
( ! [X0] :
( ~ unequally_directed_lines(reverse_line(X0),sK1)
| unequally_directed_lines(sK2,X0) )
| spl3_3
| spl3_9 ),
inference(resolution,[],[f3440,f407]) ).
fof(f3478,plain,
( ! [X0] :
( ~ unequally_directed_lines(sK0,reverse_line(X0))
| unequally_directed_lines(sK2,X0) )
| spl3_3
| spl3_9 ),
inference(resolution,[],[f3442,f929]) ).
fof(f3604,plain,
( unequally_directed_lines(sK2,sK1)
| spl3_3
| spl3_9 ),
inference(resolution,[],[f3478,f73]) ).
fof(f3637,plain,
( unequally_directed_lines(sK2,sK0)
| spl3_3
| spl3_9 ),
inference(resolution,[],[f3604,f323]) ).
fof(f3639,plain,
( spl3_17
| spl3_3
| spl3_9 ),
inference(avatar_split_clause,[],[f3637,f226,f137,f703]) ).
cnf(s5,plain,
( spl3_8
| ~ spl3_9 ),
inference(sat_conversion,[],[f228]) ).
cnf(s8,plain,
( spl3_9
| spl3_11 ),
inference(sat_conversion,[],[f313]) ).
cnf(s9,plain,
~ spl3_8,
inference(sat_conversion,[],[f319]) ).
cnf(s11,plain,
( ~ spl3_3
| ~ spl3_11 ),
inference(sat_conversion,[],[f387]) ).
cnf(s172,plain,
~ spl3_17,
inference(sat_conversion,[],[f1787]) ).
cnf(s418,plain,
( spl3_3
| spl3_9
| spl3_17 ),
inference(sat_conversion,[],[f3639]) ).
cnf(s458,plain,
~ spl3_9,
inference(rat,[],[s5,s9]) ).
cnf(s459,plain,
spl3_3,
inference(rat,[],[s418,s172,s458]) ).
cnf(s558,plain,
spl3_11,
inference(rat,[],[s8,s458]) ).
cnf(s560,plain,
$false,
inference(rat,[],[s11,s558,s459]) ).
fof(f3640,plain,
$false,
inference(avatar_sat_refutation,[],[s560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO234+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n013.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 07:47:22 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 2.39/1.22 % (4090649)Detected formulas, will run a generic FOF schedule.
% 2.39/1.22 % (4090660)dis-21_1_sil=8000:lcm=predicate:random_seed=2648447483: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)
% 2.39/1.22 % (4090660)First to succeed.
% 2.39/1.22 % (4090660)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4090649"
% 2.39/1.22 % (4090656)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=2292148457:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.39/1.22 % (4090657)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2124037029:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.39/1.22 % (4090659)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4288663763:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.39/1.22 % (4090655)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=2340741716:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.39/1.22 % (4090654)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=1882960777:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.39/1.22 % (4090658)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2526426907:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.39/1.22 % (4090659)Also succeeded, but the first one will report.
% 2.39/1.22 % (4090658)Also succeeded, but the first one will report.
% 2.39/1.22 % (4090657)Also succeeded, but the first one will report.
% 2.39/1.22 % (4090660)Refutation found. Thanks to Tanya!
% 2.39/1.22 % SZS status Theorem for theBenchmark
% 2.39/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.01/1.41 % (4090660)------------------------------
% 3.01/1.41 % (4090660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.01/1.41 % (4090660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.01/1.41 % (4090660)CaDiCaL version: 2.1.3
% 3.01/1.41 % (4090660)Termination reason: Refutation
% 3.01/1.41 % (4090660)Time elapsed: 0.026 s
% 3.01/1.41 % (4090660)Peak memory usage: 90 MB
% 3.01/1.41 % (4090660)Instructions burned: 74 (million)
% 3.01/1.41 % (4090660)------------------------------
% 3.01/1.41 % (4090660)------------------------------
% 3.01/1.41 % (4090649)Success in time 0.336 s
% 3.01/1.41 % Vampire exiting
%------------------------------------------------------------------------------