%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM322+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:12:10 PM UTC 2026
% Result : Theorem 2.31s 0.93s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 7 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 17 ( 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn5) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdnn5) ).
fof(f291,axiom,
! [X0,X1,X2] :
( ( rdn_translate(X0,rdn_pos(X2))
& rdn_translate(X1,rdn_neg(X2)) )
=> sum(X0,X1,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_posx_negx) ).
fof(f402,conjecture,
? [X0] : sum(n5,nn5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n5_nn5_what) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(n5,nn5,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f410,plain,
! [X0] : ~ sum(n5,nn5,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f413,plain,
! [X0,X1,X2] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(ennf_transformation,[],[f291]) ).
fof(f414,plain,
! [X0,X1,X2] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(flattening,[],[f413]) ).
fof(f415,plain,
! [X0] : ~ sum(n5,nn5,X0),
inference(cnf_transformation,[],[f410]) ).
fof(f417,plain,
! [X2,X0,X1] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(cnf_transformation,[],[f414]) ).
fof(f418,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f419,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f422,plain,
! [X0] :
( ~ rdn_translate(nn5,rdn_neg(X0))
| ~ rdn_translate(n5,rdn_pos(X0)) ),
inference(resolution,[],[f417,f415]) ).
fof(f424,plain,
~ rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(resolution,[],[f422,f419]) ).
fof(f425,plain,
$false,
inference(forward_subsumption_resolution,[],[f424,f418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM322+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 19:32:20 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 Running first-order theorem proving
% 0.07/0.34 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
% 2.31/0.93 % (2687058)Detected formulas, will run a generic FOF schedule.
% 2.31/0.93 % (2687064)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=2351246933:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.31/0.93 % (2687065)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=3311527300:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.31/0.93 % (2687063)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=3169754667:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.31/0.93 % (2687069)dis-21_1_sil=8000:lcm=predicate:random_seed=1273595599: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)
% 2.31/0.93 % (2687068)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1087394339:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.31/0.93 % (2687066)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1025049115:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.31/0.93 % (2687067)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3382839863:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.31/0.93 % (2687066)Refutation not found, incomplete strategy
% 2.31/0.93 % (2687066)------------------------------
% 2.31/0.93 % (2687066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.93 % (2687067)First to succeed.
% 2.31/0.93 % (2687066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.93 % (2687066)CaDiCaL version: 2.1.3
% 2.31/0.93 % (2687066)Termination reason: Refutation not found, incomplete strategy
% 2.31/0.93 % (2687066)Time elapsed: 0.001 s
% 2.31/0.93 % (2687066)Peak memory usage: 87 MB
% 2.31/0.93 % (2687066)Instructions burned: 2 (million)
% 2.31/0.93 % (2687067)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2687058"
% 2.31/0.93 % (2687069)Also succeeded, but the first one will report.
% 2.31/0.93 % (2687068)Also succeeded, but the first one will report.
% 2.31/0.93 % (2687066)------------------------------
% 2.31/0.93 % (2687066)------------------------------
% 2.31/0.93 % (2687067)Refutation found. Thanks to Tanya!
% 2.31/0.93 % SZS status Theorem for theBenchmark
% 2.31/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.93 % (2687067)------------------------------
% 2.31/0.93 % (2687067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.93 % (2687067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.93 % (2687067)CaDiCaL version: 2.1.3
% 2.31/0.93 % (2687067)Termination reason: Refutation
% 2.31/0.93 % (2687067)Time elapsed: 0.001 s
% 2.31/0.93 % (2687067)Peak memory usage: 88 MB
% 2.31/0.93 % (2687067)Instructions burned: 2 (million)
% 2.31/0.93 % (2687067)------------------------------
% 2.31/0.93 % (2687067)------------------------------
% 2.31/0.93 % (2687058)Success in time 0.301 s
% 2.31/0.93 % Vampire exiting
%------------------------------------------------------------------------------