%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO253+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:52:14 AM UTC 2026
% Result : Theorem 3.44s 1.45s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 8 unt; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 22 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( right_apart_point(X0,X1)
<=> left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_defns) ).
fof(f6,axiom,
! [X0,X1] :
( apart_point_and_line(X0,X1)
<=> ( left_apart_point(X0,X1)
| right_apart_point(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_defns) ).
fof(f20,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10_basics) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( ( apart_point_and_line(X0,X2)
& incident_point_and_line(X1,parallel_through_point(X2,X0)) )
=> apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( apart_point_and_line(X0,X2)
& incident_point_and_line(X1,parallel_through_point(X2,X0)) )
=> apart_point_and_line(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f40,plain,
~ ! [X0,X1,X2] :
( apart_point_and_line(X0,X2)
=> apart_point_and_line(X1,X2) ),
inference(pure_predicate_removal,[],[f38]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X1,X2)
& apart_point_and_line(X0,X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f59,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f76,plain,
( ~ apart_point_and_line(sK1,sK2)
& apart_point_and_line(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f41]) ).
fof(f77,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ right_apart_point(X0,X1) ) )
& ( left_apart_point(X0,X1)
| right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f78,plain,
! [X0,X1] :
( ( apart_point_and_line(X0,X1)
| ( ~ left_apart_point(X0,X1)
& ~ right_apart_point(X0,X1) ) )
& ( left_apart_point(X0,X1)
| right_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( right_apart_point(X0,X1)
| ~ left_apart_point(X0,reverse_line(X1)) )
& ( left_apart_point(X0,reverse_line(X1))
| ~ right_apart_point(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f80,plain,
apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f76]) ).
fof(f89,plain,
! [X0,X1] :
( right_apart_point(X0,X1)
| left_apart_point(X0,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f104,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f59]) ).
fof(f111,plain,
! [X0,X1] :
( ~ right_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f125,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,X1)
| left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
inference(resolution,[],[f89,f111]) ).
fof(f165,plain,
( left_apart_point(sK0,sK2)
| left_apart_point(sK0,reverse_line(sK2)) ),
inference(resolution,[],[f125,f80]) ).
fof(f167,definition,
( spl3_1
<=> left_apart_point(sK0,reverse_line(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f168,plain,
( left_apart_point(sK0,reverse_line(sK2))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,definition,
( spl3_2
<=> left_apart_point(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f171,plain,
( left_apart_point(sK0,sK2)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f165,f170,f167]) ).
fof(f173,plain,
( $false
| ~ spl3_2 ),
inference(resolution,[],[f171,f104]) ).
fof(f174,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f175,plain,
( $false
| ~ spl3_1 ),
inference(resolution,[],[f168,f104]) ).
fof(f176,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f175]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f172]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f174]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f176]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f177,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO253+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:55:36 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.44/1.45 % (3217008)Detected formulas, will run a generic FOF schedule.
% 3.44/1.45 % (3217017)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=366460668:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.45 % (3217013)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=874670296:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.45 % (3217019)dis-21_1_sil=8000:lcm=predicate:random_seed=3636850015: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)
% 3.44/1.45 % (3217016)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3011814587:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.45 % (3217014)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=1975962570:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.45 % (3217015)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=2494407810:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.45 % (3217016)Refutation not found, incomplete strategy
% 3.44/1.45 % (3217016)------------------------------
% 3.44/1.45 % (3217016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (3217016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (3217016)CaDiCaL version: 2.1.3
% 3.44/1.45 % (3217016)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.45 % (3217016)Time elapsed: 0.001 s
% 3.44/1.45 % (3217016)Peak memory usage: 87 MB
% 3.44/1.45 % (3217018)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3458147322:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.45 % (3217017)Instruction limit reached!
% 3.44/1.45 % (3217017)------------------------------
% 3.44/1.45 % (3217017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (3217017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (3217017)CaDiCaL version: 2.1.3
% 3.44/1.45 % (3217017)Termination reason: Instruction limit
% 3.44/1.45 % (3217017)Termination phase: Saturation
% 3.44/1.45 % (3217017)Time elapsed: 0.040 s
% 3.44/1.45 % (3217017)Peak memory usage: 88 MB
% 3.44/1.45 % (3217017)Instructions burned: 125 (million)
% 3.44/1.45 % (3217019)First to succeed.
% 3.44/1.45 % (3217018)Also succeeded, but the first one will report.
% 3.44/1.45 % (3217019)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3217008"
% 3.44/1.45 % (3217027)lrs+10_1_sil=8000:sp=occurrence:random_seed=399412549:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.44/1.45 % (3217027)Also succeeded, but the first one will report.
% 3.44/1.45 % (3217016)------------------------------
% 3.44/1.45 % (3217016)------------------------------
% 3.44/1.45 % (3217019)Refutation found. Thanks to Tanya!
% 3.44/1.45 % SZS status Theorem for theBenchmark
% 3.44/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.45 % (3217019)------------------------------
% 3.44/1.45 % (3217019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (3217019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (3217019)CaDiCaL version: 2.1.3
% 3.44/1.45 % (3217019)Termination reason: Refutation
% 3.44/1.45 % (3217019)Time elapsed: 0.004 s
% 3.44/1.45 % (3217019)Peak memory usage: 89 MB
% 3.44/1.45 % (3217019)Instructions burned: 3 (million)
% 3.44/1.45 % (3217019)------------------------------
% 3.44/1.45 % (3217019)------------------------------
% 3.44/1.45 % (3217008)Success in time 0.4 s
% 3.44/1.45 % Vampire exiting
%------------------------------------------------------------------------------