%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO208+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:52:01 AM UTC 2026
% Result : Theorem 2.74s 1.35s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 2 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 33 ~; 22 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 0 sgn 21 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
=> ( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cup1) ).
fof(f16,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) )
=> ~ distinct_lines(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
? [X0,X1,X2] :
( distinct_lines(X1,X2)
& ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( distinct_lines(X1,X2)
& ~ apart_point_and_line(X0,X1)
& ~ apart_point_and_line(X0,X2)
& ~ convergent_lines(X1,X2) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(flattening,[],[f20]) ).
fof(f35,plain,
( distinct_lines(sK1,sK2)
& ~ apart_point_and_line(sK0,sK1)
& ~ apart_point_and_line(sK0,sK2)
& ~ convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f36,plain,
~ convergent_lines(sK1,sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f37,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f38,plain,
~ apart_point_and_line(sK0,sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f39,plain,
distinct_lines(sK1,sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f40,plain,
! [X2,X0,X1] :
( convergent_lines(X1,X2)
| apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X1)
| ~ distinct_lines(X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f69,plain,
! [X0] :
( apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK1)
| ~ distinct_lines(sK1,sK2) ),
inference(resolution,[],[f40,f36]) ).
fof(f76,definition,
( spl3_2
<=> ! [X0] :
( apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f77,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK1) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl3_3
<=> distinct_lines(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f81,plain,
( ~ distinct_lines(sK1,sK2)
| spl3_3 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( ~ spl3_3
| spl3_2 ),
inference(avatar_split_clause,[],[f69,f76,f80]) ).
fof(f83,plain,
( $false
| spl3_3 ),
inference(resolution,[],[f81,f39]) ).
fof(f86,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f83]) ).
fof(f89,plain,
( apart_point_and_line(sK0,sK1)
| ~ spl3_2 ),
inference(resolution,[],[f77,f37]) ).
fof(f90,plain,
( $false
| ~ spl3_2 ),
inference(resolution,[],[f89,f38]) ).
fof(f91,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f90]) ).
cnf(s2,plain,
( spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
spl3_3,
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
~ spl3_2,
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s3,s4]) ).
fof(f92,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO208+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.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 07:37:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.74/1.35 % (2660157)Detected formulas, will run a generic FOF schedule.
% 2.74/1.35 % (2660168)dis-21_1_sil=8000:lcm=predicate:random_seed=3002493031: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)
% 2.74/1.35 % (2660168)First to succeed.
% 2.74/1.35 % (2660168)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2660157"
% 2.74/1.35 % (2660166)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=534500219:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.35 % (2660163)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=1353853517:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.35 % (2660165)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2347497374:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.35 % (2660164)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=2341177099:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.35 % (2660162)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=1698208990:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.35 % (2660167)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1723285126:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.35 % (2660166)Also succeeded, but the first one will report.
% 2.74/1.35 % (2660165)Also succeeded, but the first one will report.
% 2.74/1.35 % (2660167)Also succeeded, but the first one will report.
% 2.74/1.35 % (2660168)Refutation found. Thanks to Tanya!
% 2.74/1.35 % SZS status Theorem for theBenchmark
% 2.74/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.35 % (2660168)------------------------------
% 2.74/1.35 % (2660168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.35 % (2660168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.35 % (2660168)CaDiCaL version: 2.1.3
% 2.74/1.35 % (2660168)Termination reason: Refutation
% 2.74/1.35 % (2660168)Time elapsed: 0.002 s
% 2.74/1.35 % (2660168)Peak memory usage: 89 MB
% 2.74/1.35 % (2660168)Instructions burned: 1 (million)
% 2.74/1.35 % (2660168)------------------------------
% 2.74/1.35 % (2660168)------------------------------
% 2.74/1.35 % (2660157)Success in time 0.304 s
% 2.74/1.35 % Vampire exiting
%------------------------------------------------------------------------------