%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM312+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 : n019.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 12:18:18 PM UTC 2026
% Result : Theorem 0.17s 0.54s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 18 unt; 1 def)
% Number of atoms : 106 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 55 ~; 50 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 86 ( 0 sgn 85 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn5) ).
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(f294,axiom,
! [X0,X1,X2,X3] :
( ( sum(X0,X2,X3)
& sum(X1,X2,X3) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',unique_LHS) ).
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(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(f402,conjecture,
! [X0] :
( sum(X0,n3,n5)
=> X0 = n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_only_n2_n3_n5) ).
fof(f403,negated_conjecture,
~ ! [X0] :
( sum(X0,n3,n5)
=> X0 = n2 ),
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(f437,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ sum(X0,X2,X3)
| ~ sum(X1,X2,X3) ),
inference(ennf_transformation,[],[f294]) ).
fof(f438,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ sum(X0,X2,X3)
| ~ sum(X1,X2,X3) ),
inference(flattening,[],[f437]) ).
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] :
( n2 != X0
& sum(X0,n3,n5) ),
inference(ennf_transformation,[],[f403]) ).
fof(f453,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[],[f3]) ).
fof(f454,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[],[f4]) ).
fof(f456,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[],[f6]) ).
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(f746,plain,
! [X2,X3,X0,X1] :
( ~ sum(X1,X2,X3)
| ~ sum(X0,X2,X3)
| X0 = X1 ),
inference(cnf_transformation,[],[f438]) ).
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(f778,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f325]) ).
fof(f805,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[],[f352]) ).
fof(f855,plain,
sum(sK0,n3,n5),
inference(cnf_transformation,[],[f450]) ).
fof(f856,plain,
n2 != sK0,
inference(cnf_transformation,[],[f450]) ).
fof(f873,plain,
! [X0] :
( ~ sum(X0,n3,n5)
| sK0 = X0 ),
inference(resolution,[],[f746,f855]) ).
fof(f1215,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(f1500,plain,
! [X2,X3,X0,X1,X4] :
( ~ rdn_digit_add(rdnn(X0),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X4),rdnn(X2),rdnn(X0),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X2)))
| ~ rdn_translate(X3,rdn_pos(rdnn(X4)))
| ~ rdn_translate(n5,rdn_pos(rdnn(X1)))
| sK0 = X3 ),
inference(resolution,[],[f1215,f873]) ).
fof(f1511,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| sK0 = X2 ),
inference(resolution,[],[f1500,f805]) ).
fof(f1587,definition,
( spl1_28
<=> ! [X1] :
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| sK0 = X1 ) ),
introduced(definition,[new_symbols(definition,[spl1_28])],[avatar_definition]) ).
fof(f1588,plain,
( ! [X1] :
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| sK0 = X1 )
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f1587]) ).
fof(f1640,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| sK0 = X2 ),
inference(forward_subsumption_resolution,[],[f1511,f456]) ).
fof(f1856,plain,
! [X0] :
( ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| sK0 = X0 ),
inference(resolution,[],[f1640,f778]) ).
fof(f1865,plain,
! [X0] :
( ~ rdn_translate(X0,rdn_pos(rdnn(n2)))
| sK0 = X0 ),
inference(forward_subsumption_resolution,[],[f1856,f454]) ).
fof(f1876,plain,
spl1_28,
inference(avatar_split_clause,[],[f1865,f1587]) ).
fof(f1895,plain,
( n2 = sK0
| ~ spl1_28 ),
inference(resolution,[],[f1588,f453]) ).
fof(f1896,plain,
( $false
| ~ spl1_28 ),
inference(forward_subsumption_resolution,[],[f1895,f856]) ).
fof(f1897,plain,
~ spl1_28,
inference(avatar_contradiction_clause,[],[f1896]) ).
cnf(s32,plain,
spl1_28,
inference(sat_conversion,[],[f1876]) ).
cnf(s33,plain,
~ spl1_28,
inference(sat_conversion,[],[f1897]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s32,s33]) ).
fof(f1898,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM312+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n019.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 19:31:35 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.54 % (3357006)Will run a generic schedule for satisfiability detection.
% 0.17/0.54 % (3357014)dis+10_1_sil=32000:sp=arity:random_seed=1600173728:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.54 % (3357012)% WARNING: option uhcvi not known.
% 0.17/0.54 % (3357015)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2839312316:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.54 % (3357011)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=206971069_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.54 % (3357012)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1686188506:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.54 % (3357013)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1407950812:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.54 % (3357016)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=897473046:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.54 % (3357017)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3634275017:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.54 % (3357014)Instruction limit reached!
% 0.17/0.54 % (3357014)------------------------------
% 0.17/0.54 % (3357014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.54 % (3357014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.54 % (3357014)CaDiCaL version: 2.1.3
% 0.17/0.54 % (3357014)Termination reason: Instruction limit
% 0.17/0.54 % (3357014)Termination phase: Saturation
% 0.17/0.54 % (3357014)Time elapsed: 0.027 s
% 0.17/0.54 % (3357014)Peak memory usage: 13 MB
% 0.17/0.54 % (3357014)Instructions burned: 107 (million)
% 0.17/0.54 % TRYING [1]
% 0.17/0.54 % (3357025)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2271651325:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.54 % TRYING [2]
% 0.17/0.54 % TRYING [3]
% 0.17/0.54 % TRYING [1]
% 0.17/0.54 % (3357015) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3357006-3357015"...
% 0.17/0.54 % TRYING [2]
% 0.17/0.54 % (3357015)...printing done.
% 0.17/0.54 % (3357015)Refutation found. Thanks to Tanya!
% 0.17/0.54 % SZS status Theorem for theBenchmark
% 0.17/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.54 % (3357015)------------------------------
% 0.17/0.54 % (3357015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.54 % (3357015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.54 % (3357015)CaDiCaL version: 2.1.3
% 0.17/0.54 % (3357015)Termination reason: Refutation
% 0.17/0.54 % (3357015)Time elapsed: 0.053 s
% 0.17/0.54 % (3357015)Peak memory usage: 14 MB
% 0.17/0.54 % (3357015)Instructions burned: 101 (million)
% 0.17/0.54 % (3357006)Success in time 0.109 s
% 0.17/0.54 % Vampire exiting
%------------------------------------------------------------------------------