%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 09:51:15 AM UTC 2026
% Result : Unsatisfiable 3.23s 1.26s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 15 unt; 4 def)
% Number of atoms : 62 ( 5 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 56 ( 27 ~; 25 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f21,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f43,axiom,
! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X0,X1,X3)
| ~ equidistant(X1,X2,X1,X3)
| X0 = X1
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
fof(f44,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f45,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f46,negated_conjecture,
w != extension(u,v,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_an_extension) ).
fof(f54,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( sQ0_eqProxy(X2,X3)
| ~ between(X0,X1,X3)
| ~ equidistant(X1,X2,X1,X3)
| sQ0_eqProxy(X0,X1)
| ~ between(X0,X1,X2) ),
inference(equality_proxy_replacement,[],[f43,f54,f54]) ).
fof(f60,plain,
~ sQ0_eqProxy(u,v),
inference(equality_proxy_replacement,[],[f45,f54]) ).
fof(f61,plain,
~ sQ0_eqProxy(w,extension(u,v,v,w)),
inference(equality_proxy_replacement,[],[f46,f54]) ).
fof(f194,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ equidistant(X1,w,X1,extension(u,v,v,w))
| ~ between(X0,X1,extension(u,v,v,w))
| ~ between(X0,X1,w) ),
inference(resolution,[],[f59,f61]) ).
fof(f258,plain,
( ~ equidistant(v,w,v,extension(u,v,v,w))
| ~ between(u,v,extension(u,v,v,w))
| ~ between(u,v,w) ),
inference(resolution,[],[f194,f60]) ).
fof(f272,definition,
( spl1_4
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f273,plain,
( ~ between(u,v,w)
| spl1_4 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,definition,
( spl1_5
<=> between(u,v,extension(u,v,v,w)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f276,plain,
( ~ between(u,v,extension(u,v,v,w))
| spl1_5 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f278,definition,
( spl1_6
<=> equidistant(v,w,v,extension(u,v,v,w)) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f279,plain,
( ~ equidistant(v,w,v,extension(u,v,v,w))
| spl1_6 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( ~ spl1_4
| ~ spl1_5
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f258,f278,f275,f272]) ).
fof(f282,plain,
( ~ equidistant(v,extension(u,v,v,w),v,w)
| spl1_6 ),
inference(resolution,[],[f279,f21]) ).
fof(f291,plain,
( $false
| spl1_6 ),
inference(resolution,[],[f282,f5]) ).
fof(f302,plain,
spl1_6,
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f303,plain,
( $false
| spl1_4 ),
inference(resolution,[],[f273,f44]) ).
fof(f304,plain,
spl1_4,
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f305,plain,
( $false
| spl1_5 ),
inference(resolution,[],[f276,f4]) ).
fof(f306,plain,
spl1_5,
inference(avatar_contradiction_clause,[],[f305]) ).
cnf(s2,plain,
( ~ spl1_4
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f280]) ).
cnf(s3,plain,
spl1_6,
inference(sat_conversion,[],[f302]) ).
cnf(s4,plain,
spl1_4,
inference(sat_conversion,[],[f304]) ).
cnf(s5,plain,
spl1_5,
inference(sat_conversion,[],[f306]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s3,s5,s4]) ).
fof(f307,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 % Computer : n005.cluster.edu
% 0.16/0.46 % Model : x86_64 x86_64
% 0.16/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.46 % Memory : 8046.5625MB
% 0.16/0.46 % OS : Linux 6.8.0-71-generic
% 0.16/0.46 % CPULimit : 300
% 0.16/0.46 % WCLimit : 300
% 0.16/0.46 % DateTime : Sun Sep 27 06:37:18 UTC 2026
% 0.16/0.46 % CPUTime :
% 0.16/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 3.23/1.26 % (3631142)Input is clausal, will run a generic CNF schedule.
% 3.23/1.26 % (3631168)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1824560911:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.23/1.26 % (3631169)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2704873287:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.23/1.26 % (3631166)lrs+10_1_sil=8000:sp=occurrence:random_seed=3633522470:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.23/1.26 % (3631164)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3628157090:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.23/1.26 % (3631171)dis-21_1_sil=8000:lcm=predicate:random_seed=1453569595:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.23/1.26 % (3631165)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=468552467:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.23/1.26 % (3631162)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=2903212954:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.23/1.26 % (3631171)First to succeed.
% 3.23/1.26 % (3631171)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3631142"
% 3.23/1.26 % (3631169)Also succeeded, but the first one will report.
% 3.23/1.26 % (3631166)Also succeeded, but the first one will report.
% 3.23/1.26 % (3631168)Also succeeded, but the first one will report.
% 3.23/1.26 % (3631171)Refutation found. Thanks to Tanya!
% 3.23/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.23/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.23/1.26 % (3631171)------------------------------
% 3.23/1.26 % (3631171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.26 % (3631171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.26 % (3631171)CaDiCaL version: 2.1.3
% 3.23/1.26 % (3631171)Termination reason: Refutation
% 3.23/1.26 % (3631171)Time elapsed: 0.005 s
% 3.23/1.26 % (3631171)Peak memory usage: 89 MB
% 3.23/1.26 % (3631171)Instructions burned: 7 (million)
% 3.23/1.26 % (3631171)------------------------------
% 3.23/1.26 % (3631171)------------------------------
% 3.23/1.26 % (3631142)Success in time 0.391 s
% 3.23/1.26 % Vampire exiting
%------------------------------------------------------------------------------