%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM327+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:18:20 PM UTC 2026
% Result : Theorem 0.07s 0.39s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 64 ( 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 : 4 ( 4 usr; 2 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/Axioms/NUM005+0.ax',rdn0) ).
fof(f10,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn9) ).
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/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/sandbox/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(f392,axiom,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n9_n0_n9_n0) ).
fof(f402,conjecture,
? [X0] : sum(X0,n0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_zero_identity) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,n0,X0),
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] : ~ sum(X0,n0,X0),
inference(ennf_transformation,[],[f403]) ).
fof(f451,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f460,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(cnf_transformation,[],[f10]) ).
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(f845,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(cnf_transformation,[],[f392]) ).
fof(f855,plain,
! [X0] : ~ sum(X0,n0,X0),
inference(cnf_transformation,[],[f450]) ).
fof(f1179,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(f1410,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X3),rdnn(X0),rdnn(n0))
| ~ rdn_translate(n0,rdn_pos(rdnn(X3)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X1))) ),
inference(resolution,[],[f1179,f855]) ).
fof(f1448,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(X0),rdnn(n0))
| ~ rdn_translate(n0,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X1,rdn_pos(rdnn(X0))) ),
inference(resolution,[],[f1410,f845]) ).
fof(f1449,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(X0),rdnn(n0))
| ~ rdn_translate(X1,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X1,rdn_pos(rdnn(X0))) ),
inference(forward_subsumption_resolution,[],[f1448,f451]) ).
fof(f1503,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n9))) ),
inference(resolution,[],[f1449,f845]) ).
fof(f1504,plain,
! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n9))),
inference(duplicate_literal_removal,[],[f1503]) ).
fof(f1505,plain,
$false,
inference(resolution,[],[f1504,f460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM327+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 19:33:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 Running first-order model finding
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.39 % (2688335)Will run a generic schedule for satisfiability detection.
% 0.07/0.39 % (2688341)% WARNING: option uhcvi not known.
% 0.07/0.39 % (2688340)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3211949981_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.39 % (2688346)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1372513078:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.39 % (2688342)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3074414565:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.39 % (2688343)dis+10_1_sil=32000:sp=arity:random_seed=1624582250:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.39 % (2688341)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3618499817:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.39 % (2688344)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3543234102:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.39 % (2688345)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=75598814:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.39 % TRYING [1]
% 0.07/0.39 % TRYING [2]
% 0.07/0.39 % (2688344) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2688335-2688344"...
% 0.07/0.39 % (2688344)...printing done.
% 0.07/0.39 % (2688344)Refutation found. Thanks to Tanya!
% 0.07/0.39 % SZS status Theorem for theBenchmark
% 0.07/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.39 % (2688344)------------------------------
% 0.07/0.39 % (2688344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.39 % (2688344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.39 % (2688344)CaDiCaL version: 2.1.3
% 0.07/0.39 % (2688344)Termination reason: Refutation
% 0.07/0.39 % (2688344)Time elapsed: 0.022 s
% 0.07/0.39 % (2688344)Peak memory usage: 13 MB
% 0.07/0.39 % (2688344)Instructions burned: 77 (million)
% 0.07/0.39 % (2688335)Success in time 0.052 s
% 0.07/0.39 % Vampire exiting
%------------------------------------------------------------------------------