%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM330+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:12:11 PM UTC 2026
% Result : Theorem 3.50s 1.38s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 77 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 48 ~; 38 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 70 ( 66 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn4) ).
fof(f9,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn8) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',add_digit_digit_digit) ).
fof(f346,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n4_n4_n8_n0) ).
fof(f382,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit_add_n8_n0_n8_n0) ).
fof(f402,conjecture,
? [X0,X1] :
( sum(X0,X1,n8)
& X0 = n4
& X1 = n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_n4_n4_n8) ).
fof(f403,negated_conjecture,
~ ? [X0,X1] :
( sum(X0,X1,n8)
& X0 = n4
& X1 = n4 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
! [X0,X1] :
( ~ sum(X0,X1,n8)
| n4 != X0
| n4 != X1 ),
inference(ennf_transformation,[],[f403]) ).
fof(f425,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(f426,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,[],[f425]) ).
fof(f448,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(f449,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,[],[f448]) ).
fof(f453,plain,
! [X0,X1] :
( ~ sum(X0,X1,n8)
| n4 != X0
| n4 != X1 ),
inference(cnf_transformation,[],[f406]) ).
fof(f476,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f346]) ).
fof(f490,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf_transformation,[],[f5]) ).
fof(f496,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,[],[f426]) ).
fof(f506,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f382]) ).
fof(f521,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[],[f9]) ).
fof(f598,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,[],[f449]) ).
fof(f600,plain,
! [X1] :
( ~ sum(n4,X1,n8)
| n4 != X1 ),
inference(equality_resolution,[],[f453]) ).
fof(f601,plain,
~ sum(n4,n4,n8),
inference(equality_resolution,[],[f600]) ).
fof(f654,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,[],[f598,f496]) ).
fof(f692,plain,
! [X2,X3,X0,X1] :
( ~ rdn_translate(n4,rdn_pos(rdnn(X2)))
| ~ rdn_translate(n4,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n8,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0)) ),
inference(resolution,[],[f654,f601]) ).
fof(f693,plain,
! [X2,X0,X1] :
( ~ rdn_translate(n4,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n4,rdn_pos(rdnn(X1)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(n8),rdnn(n0)) ),
inference(resolution,[],[f692,f521]) ).
fof(f696,plain,
! [X0,X1] :
( ~ rdn_translate(n4,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n4),rdnn(X0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(n8),rdnn(n0)) ),
inference(resolution,[],[f693,f490]) ).
fof(f700,plain,
! [X0] :
( ~ rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(X0),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(n8),rdnn(n0)) ),
inference(resolution,[],[f696,f490]) ).
fof(f702,plain,
~ rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(resolution,[],[f700,f506]) ).
fof(f704,plain,
$false,
inference(resolution,[],[f702,f476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM330+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 19:33:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.50/1.38 % (118562)Detected formulas, will run a generic FOF schedule.
% 3.50/1.38 % (118570)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3138796432:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.38 % (118570)Refutation not found, incomplete strategy
% 3.50/1.38 % (118570)------------------------------
% 3.50/1.38 % (118570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (118570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (118570)CaDiCaL version: 2.1.3
% 3.50/1.38 % (118570)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.38 % (118570)Time elapsed: 0.001 s
% 3.50/1.38 % (118570)Peak memory usage: 88 MB
% 3.50/1.38 % (118570)Instructions burned: 2 (million)
% 3.50/1.38 % (118572)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1018567105:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.38 % (118567)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=1468036750:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.38 % (118568)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=2885375852:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.38 % (118569)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=1028319410:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.38 % (118571)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1249057391:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.38 % (118573)dis-21_1_sil=8000:lcm=predicate:random_seed=3734584003: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)
% 3.50/1.38 % (118573)First to succeed.
% 3.50/1.38 % (118573)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-118562"
% 3.50/1.38 % (118572)Also succeeded, but the first one will report.
% 3.50/1.38 % (118571)Instruction limit reached!
% 3.50/1.38 % (118571)------------------------------
% 3.50/1.38 % (118571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (118571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (118571)CaDiCaL version: 2.1.3
% 3.50/1.38 % (118571)Termination reason: Instruction limit
% 3.50/1.38 % (118571)Termination phase: Saturation
% 3.50/1.38 % (118571)Time elapsed: 0.067 s
% 3.50/1.38 % (118571)Peak memory usage: 88 MB
% 3.50/1.38 % (118571)Instructions burned: 120 (million)
% 3.50/1.38 % (118570)------------------------------
% 3.50/1.38 % (118570)------------------------------
% 3.50/1.38 % (118582)lrs+10_1_sil=32000:urr=on:br=off:random_seed=905464489:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.50/1.38 % (118581)lrs+10_1_sil=8000:sp=occurrence:random_seed=50706568:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.50/1.38 % (118582)Refutation not found, incomplete strategy
% 3.50/1.38 % (118582)------------------------------
% 3.50/1.38 % (118582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (118582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (118582)CaDiCaL version: 2.1.3
% 3.50/1.38 % (118582)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.38 % (118582)Time elapsed: 0.002 s
% 3.50/1.38 % (118582)Peak memory usage: 88 MB
% 3.50/1.38 % (118582)Instructions burned: 6 (million)
% 3.50/1.38 % (118581)Refutation not found, incomplete strategy
% 3.50/1.38 % (118581)------------------------------
% 3.50/1.38 % (118581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (118581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (118581)CaDiCaL version: 2.1.3
% 3.50/1.38 % (118581)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.38 % (118581)Time elapsed: 0.010 s
% 3.50/1.38 % (118581)Peak memory usage: 88 MB
% 3.50/1.38 % (118581)Instructions burned: 16 (million)
% 3.50/1.38 % (118573)Refutation found. Thanks to Tanya!
% 3.50/1.38 % SZS status Theorem for theBenchmark
% 3.50/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.38 % (118573)------------------------------
% 3.50/1.38 % (118573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (118573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (118573)CaDiCaL version: 2.1.3
% 3.50/1.38 % (118573)Termination reason: Refutation
% 3.50/1.38 % (118573)Time elapsed: 0.010 s
% 3.50/1.38 % (118573)Peak memory usage: 88 MB
% 3.50/1.38 % (118573)Instructions burned: 16 (million)
% 3.50/1.38 % (118573)------------------------------
% 3.50/1.38 % (118573)------------------------------
% 3.50/1.38 % (118562)Success in time 0.441 s
% 3.50/1.38 % Vampire exiting
%------------------------------------------------------------------------------