%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO184+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:51:51 AM UTC 2026
% Result : Theorem 3.41s 1.37s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 12 unt; 2 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 48 ~; 48 |; 22 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 43 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f13,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) )
=> ~ distinct_lines(X2,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) )
=> ~ distinct_lines(X2,line_connecting(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f25]) ).
fof(f32,plain,
? [X0,X1,X2,X3] :
( distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( distinct_lines(X2,line_connecting(X0,X1))
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( distinct_lines(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f33]) ).
fof(f35,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f49,plain,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f74,plain,
! [X0,X1] :
( ~ distinct_lines(X1,X0)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK1,X0)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0) ),
inference(resolution,[],[f45,f52]) ).
fof(f80,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(resolution,[],[f74,f53]) ).
fof(f104,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,sK2)
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f80,f49]) ).
fof(f107,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f104,f50]) ).
fof(f110,definition,
( spl4_5
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f112,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f114,definition,
( spl4_6
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f116,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f107,f114,f110]) ).
fof(f129,plain,
( distinct_points(sK0,sK0)
| ~ distinct_points(sK0,sK1)
| ~ spl4_5 ),
inference(resolution,[],[f112,f42]) ).
fof(f135,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f129,f35]) ).
fof(f136,plain,
( $false
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f135,f52]) ).
fof(f137,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f136]) ).
fof(f139,plain,
( distinct_points(sK1,sK1)
| ~ distinct_points(sK0,sK1)
| ~ spl4_6 ),
inference(resolution,[],[f116,f41]) ).
fof(f144,plain,
( ~ distinct_points(sK0,sK1)
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f139,f35]) ).
fof(f145,plain,
( $false
| ~ spl4_6 ),
inference(forward_subsumption_resolution,[],[f144,f52]) ).
fof(f146,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f145]) ).
cnf(s4,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f117]) ).
cnf(s5,plain,
~ spl4_5,
inference(sat_conversion,[],[f137]) ).
cnf(s6,plain,
~ spl4_6,
inference(sat_conversion,[],[f146]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s6,s5]) ).
fof(f147,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO184+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.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 07:28:35 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.41/1.37 % (3069370)Detected formulas, will run a generic FOF schedule.
% 3.41/1.37 % (3069375)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=2887116578:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.41/1.37 % (3069377)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=2556512496:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.41/1.37 % (3069379)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3569949958:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.41/1.37 % (3069378)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1265126922:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.41/1.37 % (3069376)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=3123512710:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.41/1.37 % (3069380)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3914697617:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.41/1.37 % (3069380)First to succeed.
% 3.41/1.37 % (3069380)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3069370"
% 3.41/1.37 % (3069378)Also succeeded, but the first one will report.
% 3.41/1.37 % (3069379)Also succeeded, but the first one will report.
% 3.41/1.37 % (3069381)dis-21_1_sil=8000:lcm=predicate:random_seed=1873414222: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)
% 3.41/1.37 % (3069381)Also succeeded, but the first one will report.
% 3.41/1.37 % (3069380)Refutation found. Thanks to Tanya!
% 3.41/1.37 % SZS status Theorem for theBenchmark
% 3.41/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.41/1.37 % (3069380)------------------------------
% 3.41/1.37 % (3069380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.37 % (3069380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.37 % (3069380)CaDiCaL version: 2.1.3
% 3.41/1.37 % (3069380)Termination reason: Refutation
% 3.41/1.37 % (3069380)Time elapsed: 0.004 s
% 3.41/1.37 % (3069380)Peak memory usage: 89 MB
% 3.41/1.37 % (3069380)Instructions burned: 4 (million)
% 3.41/1.37 % (3069380)------------------------------
% 3.41/1.37 % (3069380)------------------------------
% 3.41/1.37 % (3069370)Success in time 0.42 s
% 3.41/1.37 % Vampire exiting
%------------------------------------------------------------------------------