%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO255+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 : n010.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 09:52:15 AM UTC 2026
% Result : Theorem 2.91s 1.26s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 17 unt; 2 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 173 ( 69 ~; 57 |; 37 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 75 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
<=> ( distinct_points(X1,X2)
& ~ ( left_apart_point(X1,X0)
| left_apart_point(X1,reverse_line(X0)) )
& ~ ( left_apart_point(X2,X0)
| left_apart_point(X2,reverse_line(X0)) )
& ~ unequally_directed_lines(X0,line_connecting(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bf_def) ).
fof(f10,axiom,
! [X0] : ~ unequally_directed_lines(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',oag7) ).
fof(f13,axiom,
! [X0,X1] :
( ( line(X0)
& line(X1) )
=> ( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag8) ).
fof(f20,axiom,
! [X0] :
( line(X0)
=> line(reverse_line(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco4) ).
fof(f25,axiom,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco9) ).
fof(f32,conjecture,
! [X0,X1,X2] :
( ( line(X0)
& distinct_points(X1,X2) )
=> ~ ( before_on_line(X0,X1,X2)
& before_on_line(X0,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f33,negated_conjecture,
~ ! [X0,X1,X2] :
( ( line(X0)
& distinct_points(X1,X2) )
=> ~ ( before_on_line(X0,X1,X2)
& before_on_line(X0,X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( before_on_line(X0,X1,X2)
=> ( distinct_points(X1,X2)
& ~ ( left_apart_point(X1,X0)
| left_apart_point(X1,reverse_line(X0)) )
& ~ ( left_apart_point(X2,X0)
| left_apart_point(X2,reverse_line(X0)) )
& ~ unequally_directed_lines(X0,line_connecting(X1,X2)) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f36,plain,
? [X0,X1,X2] :
( before_on_line(X0,X1,X2)
& before_on_line(X0,X2,X1)
& line(X0)
& distinct_points(X1,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f37,plain,
? [X0,X1,X2] :
( before_on_line(X0,X1,X2)
& before_on_line(X0,X2,X1)
& line(X0)
& distinct_points(X1,X2) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( distinct_points(X1,X2)
& ~ left_apart_point(X1,X0)
& ~ left_apart_point(X1,reverse_line(X0))
& ~ left_apart_point(X2,X0)
& ~ left_apart_point(X2,reverse_line(X0))
& ~ unequally_directed_lines(X0,line_connecting(X1,X2)) )
| ~ before_on_line(X0,X1,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( distinct_points(X1,X2)
& ~ left_apart_point(X1,X0)
& ~ left_apart_point(X1,reverse_line(X0))
& ~ left_apart_point(X2,X0)
& ~ left_apart_point(X2,reverse_line(X0))
& ~ unequally_directed_lines(X0,line_connecting(X1,X2)) )
| ~ before_on_line(X0,X1,X2) ),
inference(flattening,[],[f38]) ).
fof(f51,plain,
! [X0] :
( line(reverse_line(X0))
| ~ line(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f56,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| ~ line(X0)
| ~ line(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f57,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1))
| ~ line(X0)
| ~ line(X1) ),
inference(flattening,[],[f56]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f69,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f70,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f75,plain,
( before_on_line(sK0,sK1,sK2)
& before_on_line(sK0,sK2,sK1)
& line(sK0)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f37]) ).
fof(f77,plain,
line(sK0),
inference(cnf_transformation,[],[f75]) ).
fof(f78,plain,
before_on_line(sK0,sK2,sK1),
inference(cnf_transformation,[],[f75]) ).
fof(f79,plain,
before_on_line(sK0,sK1,sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ before_on_line(X0,X1,X2)
| ~ unequally_directed_lines(X0,line_connecting(X1,X2)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f94,plain,
! [X0] :
( line(reverse_line(X0))
| ~ line(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f97,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1)
| ~ line(X0)
| ~ line(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f99,plain,
! [X0,X1] : ~ unequally_directed_lines(line_connecting(X0,X1),reverse_line(line_connecting(X1,X0))),
inference(cnf_transformation,[],[f25]) ).
fof(f107,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,[],[f65]) ).
fof(f114,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X0,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f115,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f123,plain,
~ unequally_directed_lines(sK0,line_connecting(sK2,sK1)),
inference(resolution,[],[f80,f78]) ).
fof(f124,plain,
~ unequally_directed_lines(sK0,line_connecting(sK1,sK2)),
inference(resolution,[],[f80,f79]) ).
fof(f128,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,reverse_line(line_connecting(X1,X2)))
| ~ unequally_directed_lines(X0,line_connecting(X2,X1)) ),
inference(resolution,[],[f114,f99]) ).
fof(f129,plain,
! [X0] :
( unequally_directed_lines(X0,line_connecting(sK2,sK1))
| ~ unequally_directed_lines(X0,sK0) ),
inference(resolution,[],[f114,f123]) ).
fof(f130,plain,
! [X0] :
( unequally_directed_lines(X0,line_connecting(sK1,sK2))
| ~ unequally_directed_lines(X0,sK0) ),
inference(resolution,[],[f114,f124]) ).
fof(f132,plain,
~ unequally_directed_lines(line_connecting(sK2,sK1),sK0),
inference(resolution,[],[f129,f115]) ).
fof(f139,plain,
! [X0] :
( ~ line(reverse_line(X0))
| unequally_directed_lines(reverse_line(X0),X0)
| ~ line(X0) ),
inference(resolution,[],[f97,f115]) ).
fof(f154,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,[],[f107,f115]) ).
fof(f212,plain,
! [X0] :
( unequally_directed_lines(reverse_line(X0),X0)
| ~ line(X0)
| ~ line(X0) ),
inference(resolution,[],[f139,f94]) ).
fof(f213,plain,
! [X0] :
( ~ line(X0)
| unequally_directed_lines(reverse_line(X0),X0) ),
inference(duplicate_literal_removal,[],[f212]) ).
fof(f235,plain,
! [X2,X0,X1] :
( unequally_directed_lines(line_connecting(X1,X2),X0)
| ~ unequally_directed_lines(reverse_line(X0),line_connecting(X1,X2))
| ~ unequally_directed_lines(reverse_line(X0),line_connecting(X2,X1)) ),
inference(resolution,[],[f154,f128]) ).
fof(f334,plain,
unequally_directed_lines(reverse_line(sK0),sK0),
inference(resolution,[],[f213,f77]) ).
fof(f439,plain,
( ~ unequally_directed_lines(reverse_line(sK0),line_connecting(sK2,sK1))
| ~ unequally_directed_lines(reverse_line(sK0),line_connecting(sK1,sK2)) ),
inference(resolution,[],[f235,f132]) ).
fof(f442,definition,
( spl3_8
<=> unequally_directed_lines(reverse_line(sK0),line_connecting(sK2,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f443,plain,
( ~ unequally_directed_lines(reverse_line(sK0),line_connecting(sK2,sK1))
| spl3_8 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f445,definition,
( spl3_9
<=> unequally_directed_lines(reverse_line(sK0),line_connecting(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f446,plain,
( ~ unequally_directed_lines(reverse_line(sK0),line_connecting(sK1,sK2))
| spl3_9 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f448,plain,
( ~ spl3_9
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f439,f442,f445]) ).
fof(f450,plain,
( ~ unequally_directed_lines(reverse_line(sK0),sK0)
| spl3_8 ),
inference(resolution,[],[f443,f129]) ).
fof(f452,plain,
( $false
| spl3_8 ),
inference(resolution,[],[f450,f334]) ).
fof(f455,plain,
spl3_8,
inference(avatar_contradiction_clause,[],[f452]) ).
fof(f457,plain,
( ~ unequally_directed_lines(reverse_line(sK0),sK0)
| spl3_9 ),
inference(resolution,[],[f446,f130]) ).
fof(f461,plain,
( $false
| spl3_9 ),
inference(resolution,[],[f457,f334]) ).
fof(f464,plain,
spl3_9,
inference(avatar_contradiction_clause,[],[f461]) ).
cnf(s6,plain,
( ~ spl3_8
| ~ spl3_9 ),
inference(sat_conversion,[],[f448]) ).
cnf(s7,plain,
spl3_8,
inference(sat_conversion,[],[f455]) ).
cnf(s8,plain,
spl3_9,
inference(sat_conversion,[],[f464]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s6,s8,s7]) ).
fof(f465,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO255+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:53:47 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.91/1.26 % (619725)Detected formulas, will run a generic FOF schedule.
% 2.91/1.26 % (619734)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3785578404:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.91/1.26 % (619733)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=760207289:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.91/1.26 % (619733)Refutation not found, incomplete strategy
% 2.91/1.26 % (619733)------------------------------
% 2.91/1.26 % (619733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.26 % (619733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.26 % (619733)CaDiCaL version: 2.1.3
% 2.91/1.26 % (619733)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.26 % (619733)Time elapsed: 0.001 s
% 2.91/1.26 % (619733)Peak memory usage: 88 MB
% 2.91/1.26 % (619734)Instruction limit reached!
% 2.91/1.26 % (619734)------------------------------
% 2.91/1.26 % (619734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.26 % (619734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.26 % (619734)CaDiCaL version: 2.1.3
% 2.91/1.26 % (619734)Termination reason: Instruction limit
% 2.91/1.26 % (619734)Termination phase: Saturation
% 2.91/1.26 % (619734)Time elapsed: 0.039 s
% 2.91/1.26 % (619734)Peak memory usage: 88 MB
% 2.91/1.26 % (619734)Instructions burned: 119 (million)
% 2.91/1.26 % (619735)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2974297901:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.91/1.26 % (619730)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=3811306817:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.91/1.26 % (619732)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=2977480313:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.91/1.26 % (619731)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=522908345:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.91/1.26 % (619736)dis-21_1_sil=8000:lcm=predicate:random_seed=3138224300: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)
% 2.91/1.26 % (619736)First to succeed.
% 2.91/1.26 % (619736)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-619725"
% 2.91/1.26 % (619735)Also succeeded, but the first one will report.
% 2.91/1.26 % (619743)lrs+10_1_sil=8000:sp=occurrence:random_seed=2499521279:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.91/1.26 % (619743)Also succeeded, but the first one will report.
% 2.91/1.26 % (619733)------------------------------
% 2.91/1.26 % (619733)------------------------------
% 2.91/1.26 % (619736)Refutation found. Thanks to Tanya!
% 2.91/1.26 % SZS status Theorem for theBenchmark
% 2.91/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.46 % (619736)------------------------------
% 3.52/1.46 % (619736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.46 % (619736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.46 % (619736)CaDiCaL version: 2.1.3
% 3.52/1.46 % (619736)Termination reason: Refutation
% 3.52/1.46 % (619736)Time elapsed: 0.009 s
% 3.52/1.46 % (619736)Peak memory usage: 89 MB
% 3.52/1.46 % (619736)Instructions burned: 11 (million)
% 3.52/1.46 % (619736)------------------------------
% 3.52/1.46 % (619736)------------------------------
% 3.52/1.46 % (619725)Success in time 0.417 s
% 3.52/1.46 % Vampire exiting
%------------------------------------------------------------------------------