%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM523+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:24:39 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 13 unt; 3 def)
% Number of atoms : 186 ( 15 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 222 ( 96 ~; 95 |; 21 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 42 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( isPrime0(X2)
& doDivides0(X2,sdtasdt0(X0,X1)) )
=> ( doDivides0(X2,X0)
| doDivides0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).
fof(f40,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(f43,axiom,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(f44,conjecture,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f50]) ).
fof(f94,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f95,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f94]) ).
fof(f112,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f113,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f112]) ).
fof(f116,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(ennf_transformation,[],[f45]) ).
fof(f122,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f95]) ).
fof(f123,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f123]) ).
fof(f136,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f181,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ doDivides0(X2,sdtasdt0(X0,X1))
| doDivides0(X2,X1)
| ~ isPrime0(X2)
| doDivides0(X2,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f204,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f205,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f206,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f208,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f209,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f43]) ).
fof(f210,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(cnf_transformation,[],[f116]) ).
fof(f217,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f181]) ).
fof(f225,definition,
( spl4_1
<=> doDivides0(xp,xn) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f227,plain,
( ~ doDivides0(xp,xn)
| spl4_1 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f229,definition,
( spl4_2
<=> doDivides0(xp,sdtasdt0(xn,xn)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f230,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f232,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f210,f229,f225]) ).
fof(f306,definition,
( spl4_7
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f307,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f308,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| spl4_7 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f314,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(resolution,[],[f308,f136]) ).
fof(f315,plain,
( ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(duplicate_literal_removal,[],[f314]) ).
fof(f316,plain,
( $false
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f315,f205]) ).
fof(f317,plain,
spl4_7,
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f576,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f217,f136]) ).
fof(f596,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f576,f208]) ).
fof(f600,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f596,f307]) ).
fof(f613,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f600,f204]) ).
fof(f624,plain,
( spl4_2
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f613,f306,f229]) ).
fof(f1592,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| doDivides0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_2 ),
inference(resolution,[],[f200,f230]) ).
fof(f1609,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_2 ),
inference(duplicate_literal_removal,[],[f1592]) ).
fof(f1618,plain,
( ~ isPrime0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1609,f227]) ).
fof(f1625,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1618,f209]) ).
fof(f1629,plain,
( ~ aNaturalNumber0(xp)
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1625,f206]) ).
fof(f1630,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1629,f204]) ).
fof(f1631,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f1630]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f232]) ).
cnf(s7,plain,
spl4_7,
inference(sat_conversion,[],[f317]) ).
cnf(s16,plain,
( spl4_2
| ~ spl4_7 ),
inference(sat_conversion,[],[f624]) ).
cnf(s37,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f1631]) ).
cnf(s38,plain,
spl4_2,
inference(rat,[],[s16,s7]) ).
cnf(s39,plain,
spl4_1,
inference(rat,[],[s37,s38]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s1,s38,s39]) ).
fof(f1632,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM523+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:20:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.48 % (3718320)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3718325)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1976532138_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % (3718326)% WARNING: option uhcvi not known.
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (3718326)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4242074333:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3718327)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=519285590:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3718328)dis+10_1_sil=32000:sp=arity:random_seed=3981638985:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3718329)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3369708407:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3718331)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=310520581:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (3718330)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2242958747:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (3718328) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3718320-3718328"...
% 0.16/0.48 % (3718328)...printing done.
% 0.16/0.48 % (3718328)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3718328)------------------------------
% 0.16/0.48 % (3718328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3718328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3718328)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3718328)Termination reason: Refutation
% 0.16/0.48 % (3718328)Time elapsed: 0.029 s
% 0.16/0.48 % (3718328)Peak memory usage: 13 MB
% 0.16/0.48 % (3718328)Instructions burned: 46 (million)
% 0.16/0.48 % (3718320)Success in time 0.062 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------