%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO022-3 : 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 : n026.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 09:51:14 AM UTC 2026
% Result : Unsatisfiable 2.55s 1.32s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 9 ( 6 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f20,axiom,
! [X2,X3,X0,X1] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f27,axiom,
equidistant(u,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
fof(f28,axiom,
equidistant(w,x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
fof(f29,negated_conjecture,
~ equidistant(u,v,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity) ).
fof(f86,plain,
! [X0,X1] :
( ~ equidistant(X0,X1,y,z)
| ~ equidistant(X0,X1,u,v) ),
inference(resolution,[],[f2,f29]) ).
fof(f94,plain,
~ equidistant(w,x,u,v),
inference(resolution,[],[f86,f28]) ).
fof(f106,plain,
~ equidistant(u,v,w,x),
inference(resolution,[],[f94,f20]) ).
fof(f113,plain,
$false,
inference(forward_subsumption_resolution,[],[f106,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:38:41 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.55/1.32 % (2469947)Input is clausal, will run a generic CNF schedule.
% 2.55/1.32 % (2469956)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2255508944:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.55/1.32 % (2469956)First to succeed.
% 2.55/1.32 % (2469956)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2469947"
% 2.55/1.32 % (2469953)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3650722437:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.55/1.32 % (2469955)lrs+10_1_sil=8000:sp=occurrence:random_seed=2481385647:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.55/1.32 % (2469954)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1601255255:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.55/1.32 % (2469952)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=2930679710:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.55/1.32 % (2469955)Also succeeded, but the first one will report.
% 2.55/1.32 % (2469958)dis-21_1_sil=8000:lcm=predicate:random_seed=737271775: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)
% 2.55/1.32 % (2469957)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1290784909:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.55/1.32 % (2469958)Also succeeded, but the first one will report.
% 2.55/1.32 % (2469957)Also succeeded, but the first one will report.
% 2.55/1.32 % (2469956)Refutation found. Thanks to Tanya!
% 2.55/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.55/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.32 % (2469956)------------------------------
% 2.55/1.32 % (2469956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (2469956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (2469956)CaDiCaL version: 2.1.3
% 2.55/1.32 % (2469956)Termination reason: Refutation
% 2.55/1.32 % (2469956)Time elapsed: 0.001 s
% 2.55/1.32 % (2469956)Peak memory usage: 88 MB
% 2.55/1.32 % (2469956)Instructions burned: 2 (million)
% 2.55/1.32 % (2469956)------------------------------
% 2.55/1.32 % (2469956)------------------------------
% 2.55/1.32 % (2469947)Success in time 0.267 s
% 2.55/1.32 % Vampire exiting
%------------------------------------------------------------------------------