%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO192+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 : n002.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 09:51:54 AM UTC 2026
% Result : Theorem 0.16s 1.20s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 10 unt; 2 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 101 ( 41 ~; 42 |; 8 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : ~ distinct_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
fof(f5,axiom,
! [X0,X1,X2] :
( distinct_lines(X0,X1)
=> ( distinct_lines(X0,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
fof(f9,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
fof(f10,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f36,conjecture,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X0,X2)
& distinct_lines(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f37,negated_conjecture,
~ ! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( apart_point_and_line(intersection_point(X0,X1),X2)
=> ( distinct_lines(X0,X2)
& distinct_lines(X1,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ( ~ distinct_lines(X0,X2)
| ~ distinct_lines(X1,X2) )
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ( ~ distinct_lines(X0,X2)
| ~ distinct_lines(X1,X2) )
& apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f38]) ).
fof(f42,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f43,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f51,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f52,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f51]) ).
fof(f55,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f56,plain,
! [X0,X1,X2] :
( distinct_lines(X0,X2)
| distinct_lines(X1,X2)
| ~ distinct_lines(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f78,plain,
( ( ~ distinct_lines(sK0,sK2)
| ~ distinct_lines(sK1,sK2) )
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f39]) ).
fof(f79,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f80,plain,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f78]) ).
fof(f81,plain,
( ~ distinct_lines(sK0,sK2)
| ~ distinct_lines(sK1,sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f83,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f84,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f89,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f91,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| distinct_lines(X0,X2)
| ~ distinct_lines(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f92,plain,
! [X0] : ~ distinct_lines(X0,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f119,definition,
( spl3_1
<=> distinct_lines(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f120,plain,
( ~ distinct_lines(sK1,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,definition,
( spl3_2
<=> distinct_lines(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f123,plain,
( ~ distinct_lines(sK0,sK2)
| spl3_2 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f81,f122,f119]) ).
fof(f136,plain,
( ! [X0] :
( distinct_lines(X0,sK2)
| ~ distinct_lines(X0,sK1) )
| spl3_1 ),
inference(resolution,[],[f91,f120]) ).
fof(f140,plain,
( ~ distinct_lines(sK2,sK1)
| spl3_1 ),
inference(resolution,[],[f136,f92]) ).
fof(f143,plain,
( ! [X0] :
( ~ apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK1) )
| spl3_1 ),
inference(resolution,[],[f140,f89]) ).
fof(f152,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK1)
| spl3_1 ),
inference(resolution,[],[f143,f80]) ).
fof(f155,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_1 ),
inference(resolution,[],[f152,f83]) ).
fof(f158,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f155,f79]) ).
fof(f159,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f158]) ).
fof(f160,plain,
( ! [X0] :
( distinct_lines(X0,sK2)
| ~ distinct_lines(X0,sK0) )
| spl3_2 ),
inference(resolution,[],[f123,f91]) ).
fof(f163,plain,
( ~ distinct_lines(sK2,sK0)
| spl3_2 ),
inference(resolution,[],[f160,f92]) ).
fof(f169,plain,
( ! [X0] :
( ~ apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0) )
| spl3_2 ),
inference(resolution,[],[f163,f89]) ).
fof(f180,plain,
( apart_point_and_line(intersection_point(sK0,sK1),sK0)
| spl3_2 ),
inference(resolution,[],[f169,f80]) ).
fof(f189,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_2 ),
inference(resolution,[],[f180,f84]) ).
fof(f192,plain,
( $false
| spl3_2 ),
inference(resolution,[],[f189,f79]) ).
fof(f194,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f192]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f124]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f159]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f194]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f195,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO192+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 07:33:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.16/1.20 % (3207075)Detected formulas, will run a generic FOF schedule.
% 0.16/1.20 % (3207086)dis-21_1_sil=8000:lcm=predicate:random_seed=3250235665: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)
% 0.16/1.20 % (3207086)First to succeed.
% 0.16/1.20 % (3207086)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3207075"
% 0.16/1.20 % (3207085)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2332746526:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.20 % (3207084)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3500027221:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.20 % (3207081)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=3490257673:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.20 % (3207083)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1030741673:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.20 % (3207080)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=1720201265:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.20 % (3207082)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=2261450422:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.20 % (3207084)Also succeeded, but the first one will report.
% 0.16/1.20 % (3207085)Also succeeded, but the first one will report.
% 0.16/1.20 % (3207083)Also succeeded, but the first one will report.
% 0.16/1.20 % (3207086)Refutation found. Thanks to Tanya!
% 0.16/1.20 % SZS status Theorem for theBenchmark
% 0.16/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.20 % (3207086)------------------------------
% 0.16/1.20 % (3207086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.20 % (3207086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.20 % (3207086)CaDiCaL version: 2.1.3
% 0.16/1.20 % (3207086)Termination reason: Refutation
% 0.16/1.20 % (3207086)Time elapsed: 0.002 s
% 0.16/1.20 % (3207086)Peak memory usage: 89 MB
% 0.16/1.20 % (3207086)Instructions burned: 4 (million)
% 0.16/1.20 % (3207086)------------------------------
% 0.16/1.20 % (3207086)------------------------------
% 0.16/1.20 % (3207075)Success in time 0.272 s
% 0.16/1.20 % Vampire exiting
%------------------------------------------------------------------------------