%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM326+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 2.35s 0.95s
% Output : Refutation 2.35s
% 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 : 19 ( 17 !; 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(X0,nn5,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_nn5_n0) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,nn5,n0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f455,plain,
! [X0] : ~ sum(X0,nn5,n0),
inference(ennf_transformation,[],[f403]) ).
fof(f458,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(f459,plain,
! [X0,X1,X2] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(flattening,[],[f458]) ).
fof(f460,plain,
! [X0] : ~ sum(X0,nn5,n0),
inference(cnf_transformation,[],[f455]) ).
fof(f463,plain,
! [X2,X0,X1] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(cnf_transformation,[],[f459]) ).
fof(f464,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f466,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
fof(f472,plain,
! [X0,X1] :
( ~ rdn_translate(nn5,rdn_neg(X1))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[],[f463,f460]) ).
fof(f474,plain,
! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n5))),
inference(resolution,[],[f472,f464]) ).
fof(f477,plain,
$false,
inference(resolution,[],[f474,f466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM326+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 19:33:04 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 2.35/0.95 % (2687918)Detected formulas, will run a generic FOF schedule.
% 2.35/0.95 % (2687928)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3792002167:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.35/0.95 % (2687924)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=356819505:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.35/0.95 % (2687926)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1878062577:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.35/0.95 % (2687925)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=95425565:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.35/0.95 % (2687929)dis-21_1_sil=8000:lcm=predicate:random_seed=3896778398: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)
% 2.35/0.95 % (2687923)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=3577713455:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.35/0.95 % (2687927)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1676091223:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.35/0.95 % (2687926)Refutation not found, incomplete strategy
% 2.35/0.95 % (2687926)------------------------------
% 2.35/0.95 % (2687926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.95 % (2687926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.95 % (2687926)CaDiCaL version: 2.1.3
% 2.35/0.95 % (2687926)Termination reason: Refutation not found, incomplete strategy
% 2.35/0.95 % (2687926)Time elapsed: 0.001 s
% 2.35/0.95 % (2687926)Peak memory usage: 87 MB
% 2.35/0.95 % (2687926)Instructions burned: 2 (million)
% 2.35/0.95 % (2687927)First to succeed.
% 2.35/0.95 % (2687927)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2687918"
% 2.35/0.95 % (2687929)Also succeeded, but the first one will report.
% 2.35/0.95 % (2687928)Also succeeded, but the first one will report.
% 2.35/0.95 % (2687926)------------------------------
% 2.35/0.95 % (2687926)------------------------------
% 2.35/0.95 % (2687927)Refutation found. Thanks to Tanya!
% 2.35/0.95 % SZS status Theorem for theBenchmark
% 2.35/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.95 % (2687927)------------------------------
% 2.35/0.95 % (2687927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.95 % (2687927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.95 % (2687927)CaDiCaL version: 2.1.3
% 2.35/0.95 % (2687927)Termination reason: Refutation
% 2.35/0.95 % (2687927)Time elapsed: 0.001 s
% 2.35/0.95 % (2687927)Peak memory usage: 88 MB
% 2.35/0.95 % (2687927)Instructions burned: 2 (million)
% 2.35/0.95 % (2687927)------------------------------
% 2.35/0.95 % (2687927)------------------------------
% 2.35/0.95 % (2687918)Success in time 0.308 s
% 2.35/0.95 % Vampire exiting
%------------------------------------------------------------------------------