%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:18:20 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% 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 : 68 ( 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn4) ).
fof(f9,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',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/Axioms/NUM005+2.ax',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/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f346,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',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/Axioms/NUM005+2.ax',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(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(f441,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(f442,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,[],[f441]) ).
fof(f450,plain,
! [X0,X1] :
( ~ sum(X0,X1,n8)
| n4 != X0
| n4 != X1 ),
inference(ennf_transformation,[],[f403]) ).
fof(f455,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf_transformation,[],[f5]) ).
fof(f459,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[],[f9]) ).
fof(f739,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_pos(X5))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_pos(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f424]) ).
fof(f750,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,[],[f442]) ).
fof(f799,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f346]) ).
fof(f835,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[],[f382]) ).
fof(f855,plain,
! [X0,X1] :
( n4 != X1
| n4 != X0
| ~ sum(X0,X1,n8) ),
inference(cnf_transformation,[],[f450]) ).
fof(f857,plain,
! [X0] :
( n4 != X0
| ~ sum(X0,n4,n8) ),
inference(equality_resolution,[],[f855]) ).
fof(f858,plain,
~ sum(n4,n4,n8),
inference(equality_resolution,[],[f857]) ).
fof(f1172,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X6,X5,X4)
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))
| ~ rdn_translate(X4,rdn_pos(rdnn(X3)))
| ~ rdn_translate(X5,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X6,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(resolution,[],[f750,f739]) ).
fof(f1427,plain,
! [X2,X3,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X3),rdnn(X2),rdnn(X0),rdnn(n0))
| ~ rdn_translate(n4,rdn_pos(rdnn(X2)))
| ~ rdn_translate(n4,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n8,rdn_pos(rdnn(X1))) ),
inference(resolution,[],[f1172,f858]) ).
fof(f1452,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n8),rdnn(n0))
| ~ rdn_translate(n4,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n4,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n8,rdn_pos(rdnn(n8))) ),
inference(resolution,[],[f1427,f835]) ).
fof(f1548,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n8),rdnn(n0))
| ~ rdn_translate(n4,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n4,rdn_pos(rdnn(X0))) ),
inference(forward_subsumption_resolution,[],[f1452,f459]) ).
fof(f1756,plain,
( ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4))) ),
inference(resolution,[],[f1548,f799]) ).
fof(f1761,plain,
~ rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(duplicate_literal_removal,[],[f1756]) ).
fof(f1764,plain,
$false,
inference(forward_subsumption_resolution,[],[f1761,f455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM330+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n007.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 19:31:55 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.49 % (1732561)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (1732575)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4224818467:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (1732572)% WARNING: option uhcvi not known.
% 0.18/0.49 % (1732572)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1485065558:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (1732573)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1522510820:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (1732577)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3496188054:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % (1732576)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2287385934:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (1732574)dis+10_1_sil=32000:sp=arity:random_seed=2728655151:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (1732571)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1814170178_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (1732575) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1732561-1732575"...
% 0.18/0.49 % (1732575)...printing done.
% 0.18/0.49 % (1732575)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (1732575)------------------------------
% 0.18/0.49 % (1732575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (1732575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (1732575)CaDiCaL version: 2.1.3
% 0.18/0.49 % (1732575)Termination reason: Refutation
% 0.18/0.49 % (1732575)Time elapsed: 0.025 s
% 0.18/0.49 % (1732575)Peak memory usage: 13 MB
% 0.18/0.49 % (1732575)Instructions burned: 90 (million)
% 0.18/0.49 % (1732561)Success in time 0.062 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------