%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM329+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 : n007.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 12:12:11 PM UTC 2026
% Result : Theorem 2.60s 1.35s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 41 ~; 33 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 66 ( 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn0) ).
fof(f287,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X0,rdn_pos(X3))
& rdn_translate(X1,rdn_pos(X4))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X2,rdn_pos(X5)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_entry_point_pos_pos) ).
fof(f297,axiom,
! [X0,X1,X2,X3,X4] :
( ( rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
& rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f302,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit_add_n0_n0_n0_n0) ).
fof(f402,conjecture,
? [X0] : sum(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotent_element) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,X0,X0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
! [X0] : ~ sum(X0,X0,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f423,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(ennf_transformation,[],[f287]) ).
fof(f424,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(flattening,[],[f423]) ).
fof(f444,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0)) ),
inference(ennf_transformation,[],[f297]) ).
fof(f445,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0)) ),
inference(flattening,[],[f444]) ).
fof(f453,plain,
! [X0] : ~ sum(X0,X0,X0),
inference(cnf_transformation,[],[f406]) ).
fof(f462,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X0,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(X5)) ),
inference(cnf_transformation,[],[f424]) ).
fof(f476,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f540,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[],[f302]) ).
fof(f560,plain,
! [X2,X3,X0,X1,X4] :
( rdn_add_with_carry(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(X3))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X0),rdnn(X3),rdnn(n0)) ),
inference(cnf_transformation,[],[f445]) ).
fof(f653,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X4,X5,X6)
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))
| ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
| ~ rdn_translate(X5,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_translate(X6,rdn_pos(rdnn(X3))) ),
inference(resolution,[],[f560,f462]) ).
fof(f691,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_translate(X2,rdn_pos(rdnn(X3)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X3),rdnn(X4),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0)) ),
inference(resolution,[],[f653,f453]) ).
fof(f692,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n0,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n0,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(n0),rdnn(X0),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X1),rdnn(n0)) ),
inference(resolution,[],[f691,f476]) ).
fof(f726,plain,
! [X0,X1] :
( ~ rdn_translate(n0,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(resolution,[],[f692,f476]) ).
fof(f730,plain,
! [X0] :
( ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n0),rdnn(n0)) ),
inference(resolution,[],[f726,f476]) ).
fof(f732,plain,
~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(factoring,[],[f730]) ).
fof(f734,plain,
$false,
inference(resolution,[],[f732,f540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM329+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 19:31:55 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.60/1.35 % (1732640)Detected formulas, will run a generic FOF schedule.
% 2.60/1.35 % (1732761)dis-21_1_sil=8000:lcm=predicate:random_seed=855731529: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)
% 2.60/1.35 % (1732761)First to succeed.
% 2.60/1.35 % (1732761)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1732640"
% 2.60/1.35 % (1732755)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=1483366303:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.35 % (1732758)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2776629685:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.35 % (1732754)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=3602816111:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.35 % (1732757)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1889927716:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.35 % (1732756)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=1862501536:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.35 % (1732757)Refutation not found, incomplete strategy
% 2.60/1.35 % (1732757)------------------------------
% 2.60/1.35 % (1732757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.35 % (1732757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.35 % (1732757)CaDiCaL version: 2.1.3
% 2.60/1.35 % (1732757)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.35 % (1732757)Time elapsed: 0.001 s
% 2.60/1.35 % (1732757)Peak memory usage: 87 MB
% 2.60/1.35 % (1732757)Instructions burned: 1 (million)
% 2.60/1.35 % (1732758)Refutation not found, incomplete strategy
% 2.60/1.35 % (1732758)------------------------------
% 2.60/1.35 % (1732758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.35 % (1732758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.35 % (1732758)CaDiCaL version: 2.1.3
% 2.60/1.35 % (1732758)Termination reason: Refutation not found, incomplete strategy
% 2.60/1.35 % (1732758)Time elapsed: 0.002 s
% 2.60/1.35 % (1732758)Peak memory usage: 88 MB
% 2.60/1.35 % (1732758)Instructions burned: 1 (million)
% 2.60/1.35 % (1732759)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2297969175:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.35 % (1732759)Also succeeded, but the first one will report.
% 2.60/1.35 % (1732761)Refutation found. Thanks to Tanya!
% 2.60/1.35 % SZS status Theorem for theBenchmark
% 2.60/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.35 % (1732761)------------------------------
% 2.60/1.35 % (1732761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.35 % (1732761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.35 % (1732761)CaDiCaL version: 2.1.3
% 2.60/1.35 % (1732761)Termination reason: Refutation
% 2.60/1.35 % (1732761)Time elapsed: 0.006 s
% 2.60/1.35 % (1732761)Peak memory usage: 88 MB
% 2.60/1.35 % (1732761)Instructions burned: 17 (million)
% 2.60/1.35 % (1732761)------------------------------
% 2.60/1.35 % (1732761)------------------------------
% 2.60/1.35 % (1732640)Success in time 0.283 s
% 2.60/1.35 % Vampire exiting
%------------------------------------------------------------------------------