%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM328+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 : n018.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 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 16 unt; 2 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 56 ~; 43 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 76 ( 0 sgn 72 !; 4 ?)
% 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,X1] : sum(X0,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_something_anotherthing_firstthing) ).
fof(f403,negated_conjecture,
~ ? [X0,X1] : sum(X0,X1,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,X1] : ~ sum(X0,X1,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,X1] : ~ sum(X0,X1,X0),
inference(cnf_transformation,[],[f450]) ).
fof(f1299,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(f1532,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X5),rdnn(X4),rdnn(X0),rdnn(n0))
| ~ rdn_translate(X3,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X1))) ),
inference(resolution,[],[f1299,f855]) ).
fof(f1770,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(X0),rdnn(n0))
| ~ rdn_translate(X1,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0))) ),
inference(resolution,[],[f1532,f845]) ).
fof(f1772,definition,
( spl0_1
<=> ! [X1] : ~ rdn_translate(X1,rdn_pos(rdnn(n0))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1773,plain,
( ! [X1] : ~ rdn_translate(X1,rdn_pos(rdnn(n0)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1772]) ).
fof(f1775,definition,
( spl0_2
<=> ! [X2,X0] :
( ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(X0),rdnn(n0))
| ~ rdn_translate(X2,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1776,plain,
( ! [X2,X0] :
( ~ rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(X0),rdnn(n0))
| ~ rdn_translate(X2,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0))) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1775]) ).
fof(f1777,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1770,f1775,f1772]) ).
fof(f1915,plain,
( ! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n9)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n9))) )
| ~ spl0_2 ),
inference(resolution,[],[f1776,f845]) ).
fof(f1916,plain,
( ! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n9)))
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f1915]) ).
fof(f1917,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f1916,f460]) ).
fof(f1918,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1917]) ).
fof(f1919,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f1773,f451]) ).
fof(f1920,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1919]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1777]) ).
cnf(s29,plain,
~ spl0_2,
inference(sat_conversion,[],[f1918]) ).
cnf(s30,plain,
~ spl0_1,
inference(sat_conversion,[],[f1920]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s1,s29,s30]) ).
fof(f1921,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM328+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 19:35:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.17/0.48 % (2679234)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (2679243)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2065502798:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (2679240)% WARNING: option uhcvi not known.
% 0.17/0.48 % (2679239)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3146667297_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (2679240)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2794629140:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (2679241)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=249984316:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (2679242)dis+10_1_sil=32000:sp=arity:random_seed=929253441:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (2679244)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3129600171:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (2679245)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4032586735:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (2679243) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2679234-2679243"...
% 0.17/0.48 % (2679243)...printing done.
% 0.17/0.48 % (2679243)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (2679243)------------------------------
% 0.17/0.48 % (2679243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2679243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2679243)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2679243)Termination reason: Refutation
% 0.17/0.48 % (2679243)Time elapsed: 0.032 s
% 0.17/0.48 % (2679243)Peak memory usage: 14 MB
% 0.17/0.48 % (2679243)Instructions burned: 111 (million)
% 0.17/0.48 % (2679234)Success in time 0.067 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------