%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM323+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 12:18:19 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 21 unt; 1 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 47 ~; 35 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 70 ( 0 sgn 68 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn5) ).
fof(f135,axiom,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn7) ).
fof(f288,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( rdn_translate(X0,rdn_neg(X3))
& rdn_translate(X1,rdn_neg(X4))
& rdn_add_with_carry(rdnn(n0),X3,X4,X5)
& rdn_translate(X2,rdn_neg(X5)) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_neg_neg) ).
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(f327,axiom,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n5_n7_n0) ).
fof(f372,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n7_n0_n7_n0) ).
fof(f402,conjecture,
? [X0] : sum(X0,nn5,nn7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_nn5_nn7) ).
fof(f403,negated_conjecture,
~ ? [X0] : sum(X0,nn5,nn7),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f425,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_neg(X5)) ),
inference(ennf_transformation,[],[f288]) ).
fof(f426,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_neg(X5)) ),
inference(flattening,[],[f425]) ).
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,nn5,nn7),
inference(ennf_transformation,[],[f403]) ).
fof(f580,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[],[f130]) ).
fof(f583,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[],[f133]) ).
fof(f585,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(cnf_transformation,[],[f135]) ).
fof(f740,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rdn_add_with_carry(rdnn(n0),X3,X4,X5)
| ~ rdn_translate(X2,rdn_neg(X5))
| ~ rdn_translate(X1,rdn_neg(X4))
| ~ rdn_translate(X0,rdn_neg(X3))
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f426]) ).
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(f780,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f327]) ).
fof(f825,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[],[f372]) ).
fof(f855,plain,
! [X0] : ~ sum(X0,nn5,nn7),
inference(cnf_transformation,[],[f450]) ).
fof(f1168,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_neg(rdnn(X3)))
| ~ rdn_translate(X5,rdn_neg(rdnn(X1)))
| ~ rdn_translate(X6,rdn_neg(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(resolution,[],[f750,f740]) ).
fof(f1380,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(nn5,rdn_neg(rdnn(X2)))
| ~ rdn_translate(X3,rdn_neg(rdnn(X4)))
| ~ rdn_translate(nn7,rdn_neg(rdnn(X1))) ),
inference(resolution,[],[f1168,f855]) ).
fof(f1404,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n7),rdnn(n0))
| ~ rdn_translate(nn5,rdn_neg(rdnn(X1)))
| ~ rdn_translate(X2,rdn_neg(rdnn(X0)))
| ~ rdn_translate(nn7,rdn_neg(rdnn(n7))) ),
inference(resolution,[],[f1380,f825]) ).
fof(f1472,definition,
( spl0_16
<=> ! [X1] : ~ rdn_translate(X1,rdn_neg(rdnn(n2))) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f1473,plain,
( ! [X1] : ~ rdn_translate(X1,rdn_neg(rdnn(n2)))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1472]) ).
fof(f1513,plain,
! [X2,X0,X1] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n7),rdnn(n0))
| ~ rdn_translate(nn5,rdn_neg(rdnn(X1)))
| ~ rdn_translate(X2,rdn_neg(rdnn(X0))) ),
inference(forward_subsumption_resolution,[],[f1404,f585]) ).
fof(f1724,plain,
! [X0] :
( ~ rdn_translate(nn5,rdn_neg(rdnn(n5)))
| ~ rdn_translate(X0,rdn_neg(rdnn(n2))) ),
inference(resolution,[],[f1513,f780]) ).
fof(f1745,plain,
! [X0] : ~ rdn_translate(X0,rdn_neg(rdnn(n2))),
inference(forward_subsumption_resolution,[],[f1724,f583]) ).
fof(f1756,plain,
spl0_16,
inference(avatar_split_clause,[],[f1745,f1472]) ).
fof(f1761,plain,
( $false
| ~ spl0_16 ),
inference(resolution,[],[f1473,f580]) ).
fof(f1762,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[],[f1761]) ).
cnf(s26,plain,
spl0_16,
inference(sat_conversion,[],[f1756]) ).
cnf(s27,plain,
~ spl0_16,
inference(sat_conversion,[],[f1762]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s26,s27]) ).
fof(f1763,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM323+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n018.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 19:35:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.16/0.50 % (2678817)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (2678825)dis+10_1_sil=32000:sp=arity:random_seed=2948704971:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (2678823)% WARNING: option uhcvi not known.
% 0.16/0.50 % (2678822)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3529512020_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (2678826)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3452475060:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (2678823)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1034685148:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (2678824)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1407922886:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (2678828)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=22666175:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % (2678827)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4283369620:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (2678825)Instruction limit reached!
% 0.16/0.50 % (2678825)------------------------------
% 0.16/0.50 % (2678825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (2678825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (2678825)CaDiCaL version: 2.1.3
% 0.16/0.50 % (2678825)Termination reason: Instruction limit
% 0.16/0.50 % (2678825)Termination phase: Saturation
% 0.16/0.50 % (2678825)Time elapsed: 0.027 s
% 0.16/0.50 % (2678825)Peak memory usage: 13 MB
% 0.16/0.50 % (2678825)Instructions burned: 104 (million)
% 0.16/0.50 % (2678836)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1420158505:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % (2678826) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2678817-2678826"...
% 0.16/0.50 % (2678826)...printing done.
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % (2678826)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (2678826)------------------------------
% 0.16/0.50 % (2678826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (2678826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (2678826)CaDiCaL version: 2.1.3
% 0.16/0.50 % (2678826)Termination reason: Refutation
% 0.16/0.50 % (2678826)Time elapsed: 0.048 s
% 0.16/0.50 % (2678826)Peak memory usage: 14 MB
% 0.16/0.50 % (2678826)Instructions burned: 90 (million)
% 0.16/0.50 % (2678817)Success in time 0.094 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------