%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO236+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 : n013.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 09:52:10 AM UTC 2026
% Result : Theorem 2.59s 1.24s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 28 ( 11 ~; 3 |; 12 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 18 ( 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X0,X1] :
~ ( left_apart_point(X0,X1)
| left_apart_point(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( ( left_apart_point(X0,X1)
& right_apart_point(X0,X2) )
=> ( unequally_directed_lines(X1,X2)
| distinct_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( left_apart_point(X0,X1)
& right_apart_point(X0,X2) )
=> ( unequally_directed_lines(X1,X2)
| distinct_lines(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f41,plain,
? [X0,X1,X2] :
( ~ unequally_directed_lines(X1,X2)
& ~ distinct_lines(X1,X2)
& left_apart_point(X0,X1)
& right_apart_point(X0,X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f42,plain,
? [X0,X1,X2] :
( ~ unequally_directed_lines(X1,X2)
& ~ distinct_lines(X1,X2)
& left_apart_point(X0,X1)
& right_apart_point(X0,X2) ),
inference(flattening,[],[f41]) ).
fof(f50,plain,
! [X0,X1] :
( ~ left_apart_point(X0,X1)
& ~ left_apart_point(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f69,plain,
( ~ unequally_directed_lines(sK1,sK2)
& ~ distinct_lines(sK1,sK2)
& left_apart_point(sK0,sK1)
& right_apart_point(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f42]) ).
fof(f72,plain,
left_apart_point(sK0,sK1),
inference(cnf_transformation,[],[f69]) ).
fof(f87,plain,
! [X0,X1] : ~ left_apart_point(X0,X1),
inference(cnf_transformation,[],[f50]) ).
fof(f105,plain,
$false,
inference(resolution,[],[f87,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO236+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 07:47:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 2.59/1.24 % (4091053)Detected formulas, will run a generic FOF schedule.
% 2.59/1.24 % (4091062)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1215983:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.24 % (4091062)First to succeed.
% 2.59/1.24 % (4091062)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4091053"
% 2.59/1.24 % (4091058)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=1515800299:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.24 % (4091061)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4201838985:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.24 % (4091060)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=1108525772:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.24 % (4091059)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=1592352192:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.24 % (4091061)Also succeeded, but the first one will report.
% 2.59/1.24 % (4091064)dis-21_1_sil=8000:lcm=predicate:random_seed=678196976: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)
% 2.59/1.24 % (4091063)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2550267901:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.24 % (4091064)Also succeeded, but the first one will report.
% 2.59/1.24 % (4091063)Also succeeded, but the first one will report.
% 2.59/1.24 % (4091062)Refutation found. Thanks to Tanya!
% 2.59/1.24 % SZS status Theorem for theBenchmark
% 2.59/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.24 % (4091062)------------------------------
% 2.59/1.24 % (4091062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.24 % (4091062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.24 % (4091062)CaDiCaL version: 2.1.3
% 2.59/1.24 % (4091062)Termination reason: Refutation
% 2.59/1.24 % (4091062)Time elapsed: 0.001 s
% 2.59/1.24 % (4091062)Peak memory usage: 88 MB
% 2.59/1.24 % (4091062)Instructions burned: 1 (million)
% 2.59/1.24 % (4091062)------------------------------
% 2.59/1.24 % (4091062)------------------------------
% 2.59/1.24 % (4091053)Success in time 0.299 s
% 2.59/1.24 % Vampire exiting
%------------------------------------------------------------------------------