%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM476+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:24:27 PM UTC 2026
% Result : Theorem 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 139 ( 22 unt; 11 def)
% Number of atoms : 387 ( 87 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 404 ( 156 ~; 179 |; 37 &)
% ( 20 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 57 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,conjecture,
( ( xl != sz00
=> ? [X0] :
( X0 = sdtsldt0(xm,xl)
& ? [X1] :
( X1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtlseqdt0(X0,X1)
& ? [X2] :
( X2 = sdtmndt0(X1,X0)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& xn = sdtasdt0(xl,X2) ) ) ) )
=> doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ ( ( xl != sz00
=> ? [X0] :
( X0 = sdtsldt0(xm,xl)
& ? [X1] :
( X1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtlseqdt0(X0,X1)
& ? [X2] :
( X2 = sdtmndt0(X1,X0)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& xn = sdtasdt0(xl,X2) ) ) ) )
=> doDivides0(xl,xn) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f40,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f39]) ).
fof(f47,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f53,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f66,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f66]) ).
fof(f87,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f88,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f90,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f89]) ).
fof(f95,plain,
( ~ doDivides0(xl,xn)
& ( ? [X0] :
( X0 = sdtsldt0(xm,xl)
& ? [X1] :
( X1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtlseqdt0(X0,X1)
& ? [X2] :
( X2 = sdtmndt0(X1,X0)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& xn = sdtasdt0(xl,X2) ) ) )
| sz00 = xl ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f96,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f99,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f103,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f109,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f142,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sK1(X0,X1)) = X1
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f143,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK1(X0,X1))
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f150,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f151,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f152,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f153,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f154,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f155,plain,
( sz00 = xl
| xn = sdtasdt0(xl,sK4) ),
inference(cnf_transformation,[],[f95]) ).
fof(f157,plain,
( sz00 = xl
| sK4 = sdtmndt0(sK3,sK2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
( sz00 = xl
| sdtlseqdt0(sK2,sK3) ),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
( sz00 = xl
| sdtsldt0(sdtpldt0(xm,xn),xl) = sK3 ),
inference(cnf_transformation,[],[f95]) ).
fof(f160,plain,
( sz00 = xl
| sdtsldt0(xm,xl) = sK2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f161,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[],[f95]) ).
fof(f164,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f124]) ).
fof(f167,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f144]) ).
fof(f169,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f146]) ).
fof(f173,definition,
( spl5_1
<=> xn = sdtasdt0(xl,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f175,plain,
( xn = sdtasdt0(xl,sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f177,definition,
( spl5_2
<=> sz00 = xl ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f178,plain,
( sz00 != xl
| spl5_2 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f179,plain,
( sz00 = xl
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f155,f177,f173]) ).
fof(f187,definition,
( spl5_4
<=> sK4 = sdtmndt0(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f189,plain,
( sK4 = sdtmndt0(sK3,sK2)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f157,f177,f187]) ).
fof(f192,definition,
( spl5_5
<=> sdtlseqdt0(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f194,plain,
( sdtlseqdt0(sK2,sK3)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( spl5_5
| spl5_2 ),
inference(avatar_split_clause,[],[f158,f177,f192]) ).
fof(f197,definition,
( spl5_6
<=> sdtsldt0(sdtpldt0(xm,xn),xl) = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f199,plain,
( sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f200,plain,
( spl5_6
| spl5_2 ),
inference(avatar_split_clause,[],[f159,f177,f197]) ).
fof(f202,definition,
( spl5_7
<=> sdtsldt0(xm,xl) = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f204,plain,
( sdtsldt0(xm,xl) = sK2
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f205,plain,
( spl5_7
| spl5_2 ),
inference(avatar_split_clause,[],[f160,f177,f202]) ).
fof(f206,plain,
( ~ doDivides0(sz00,xn)
| ~ spl5_2 ),
inference(superposition,[],[f161,f179]) ).
fof(f208,plain,
( doDivides0(sz00,xm)
| ~ spl5_2 ),
inference(superposition,[],[f154,f179]) ).
fof(f214,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[],[f103,f150]) ).
fof(f314,plain,
( ~ aNaturalNumber0(sz00)
| aNaturalNumber0(sK1(sz00,xm))
| ~ aNaturalNumber0(xm)
| ~ spl5_2 ),
inference(resolution,[],[f143,f208]) ).
fof(f319,plain,
( aNaturalNumber0(sK1(sz00,xm))
| ~ aNaturalNumber0(xm)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f314,f96]) ).
fof(f322,definition,
( spl5_8
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f323,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f324,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| spl5_8 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f331,plain,
( aNaturalNumber0(sK1(sz00,xm))
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f319,f151]) ).
fof(f335,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl5_8 ),
inference(resolution,[],[f324,f99]) ).
fof(f336,plain,
( ~ aNaturalNumber0(xn)
| spl5_8 ),
inference(forward_subsumption_resolution,[],[f335,f151]) ).
fof(f337,plain,
( $false
| spl5_8 ),
inference(forward_subsumption_resolution,[],[f336,f150]) ).
fof(f338,plain,
spl5_8,
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f384,definition,
( spl5_12
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
fof(f385,plain,
( sz00 != xm
| spl5_12 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f386,plain,
( sz00 = xm
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f410,plain,
( sz00 = sdtasdt0(sz00,sK1(sz00,xm))
| ~ spl5_2 ),
inference(resolution,[],[f331,f109]) ).
fof(f616,plain,
( ~ aNaturalNumber0(sz00)
| xm = sdtasdt0(sz00,sK1(sz00,xm))
| ~ aNaturalNumber0(xm)
| ~ spl5_2 ),
inference(resolution,[],[f142,f208]) ).
fof(f624,plain,
( xm = sdtasdt0(sz00,sK1(sz00,xm))
| ~ aNaturalNumber0(xm)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f616,f96]) ).
fof(f628,plain,
( xm = sdtasdt0(sz00,sK1(sz00,xm))
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f624,f151]) ).
fof(f631,plain,
( sz00 = xm
| ~ spl5_2 ),
inference(forward_demodulation,[],[f628,f410]) ).
fof(f633,plain,
( $false
| ~ spl5_2
| spl5_12 ),
inference(forward_subsumption_resolution,[],[f631,f385]) ).
fof(f634,plain,
( ~ spl5_2
| spl5_12 ),
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f711,plain,
( ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK3)
| aNaturalNumber0(sdtmndt0(sK3,sK2))
| ~ spl5_5 ),
inference(resolution,[],[f194,f164]) ).
fof(f714,definition,
( spl5_23
<=> aNaturalNumber0(sK3) ),
introduced(definition,[new_symbols(definition,[spl5_23])],[avatar_definition]) ).
fof(f722,definition,
( spl5_25
<=> aNaturalNumber0(sK2) ),
introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition]) ).
fof(f724,plain,
( ~ aNaturalNumber0(sK2)
| spl5_25 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f726,plain,
( aNaturalNumber0(sK4)
| ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK3)
| ~ spl5_4
| ~ spl5_5 ),
inference(forward_demodulation,[],[f711,f189]) ).
fof(f733,definition,
( spl5_27
<=> aNaturalNumber0(sK4) ),
introduced(definition,[new_symbols(definition,[spl5_27])],[avatar_definition]) ).
fof(f736,plain,
( ~ spl5_23
| ~ spl5_25
| spl5_27
| ~ spl5_4
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f726,f192,f187,f733,f722,f714]) ).
fof(f737,plain,
( doDivides0(xl,xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xn)
| ~ spl5_1 ),
inference(superposition,[],[f167,f175]) ).
fof(f741,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xn)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f737,f161]) ).
fof(f751,plain,
( ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xn)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f741,f152]) ).
fof(f752,plain,
( ~ aNaturalNumber0(sK4)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f751,f150]) ).
fof(f753,plain,
( ~ spl5_27
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f752,f173,f733]) ).
fof(f810,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(resolution,[],[f169,f154]) ).
fof(f811,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| sz00 = xl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(resolution,[],[f169,f153]) ).
fof(f815,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| sz00 = xl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)) ),
inference(forward_subsumption_resolution,[],[f811,f152]) ).
fof(f816,plain,
( ~ aNaturalNumber0(xm)
| sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f810,f152]) ).
fof(f817,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f815,f323]) ).
fof(f818,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f816,f151]) ).
fof(f819,plain,
( aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| spl5_2
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f817,f178]) ).
fof(f820,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f818,f178]) ).
fof(f830,plain,
( aNaturalNumber0(sK3)
| spl5_2
| ~ spl5_6
| ~ spl5_8 ),
inference(forward_demodulation,[],[f819,f199]) ).
fof(f831,plain,
( aNaturalNumber0(sK2)
| spl5_2
| ~ spl5_7 ),
inference(forward_demodulation,[],[f820,f204]) ).
fof(f832,plain,
( spl5_23
| spl5_2
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f830,f322,f197,f177,f714]) ).
fof(f833,plain,
( $false
| spl5_2
| ~ spl5_7
| spl5_25 ),
inference(forward_subsumption_resolution,[],[f831,f724]) ).
fof(f834,plain,
( spl5_2
| ~ spl5_7
| spl5_25 ),
inference(avatar_contradiction_clause,[],[f833]) ).
fof(f851,plain,
( doDivides0(sz00,sdtpldt0(xm,xn))
| ~ spl5_2 ),
inference(superposition,[],[f153,f179]) ).
fof(f855,plain,
( doDivides0(sz00,sdtpldt0(sz00,xn))
| ~ spl5_2
| ~ spl5_12 ),
inference(forward_demodulation,[],[f851,f386]) ).
fof(f856,plain,
( doDivides0(sz00,xn)
| ~ spl5_2
| ~ spl5_12 ),
inference(forward_demodulation,[],[f855,f214]) ).
fof(f857,plain,
( $false
| ~ spl5_2
| ~ spl5_12 ),
inference(forward_subsumption_resolution,[],[f856,f206]) ).
fof(f858,plain,
( ~ spl5_2
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f857]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f180]) ).
cnf(s3,plain,
( spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f190]) ).
cnf(s4,plain,
( spl5_2
| spl5_5 ),
inference(sat_conversion,[],[f195]) ).
cnf(s5,plain,
( spl5_2
| spl5_6 ),
inference(sat_conversion,[],[f200]) ).
cnf(s6,plain,
( spl5_2
| spl5_7 ),
inference(sat_conversion,[],[f205]) ).
cnf(s9,plain,
spl5_8,
inference(sat_conversion,[],[f338]) ).
cnf(s19,plain,
( ~ spl5_2
| spl5_12 ),
inference(sat_conversion,[],[f634]) ).
cnf(s25,plain,
( ~ spl5_4
| ~ spl5_5
| ~ spl5_23
| ~ spl5_25
| spl5_27 ),
inference(sat_conversion,[],[f736]) ).
cnf(s27,plain,
( ~ spl5_1
| ~ spl5_27 ),
inference(sat_conversion,[],[f753]) ).
cnf(s32,plain,
( spl5_2
| ~ spl5_6
| ~ spl5_8
| spl5_23 ),
inference(sat_conversion,[],[f832]) ).
cnf(s33,plain,
( spl5_2
| ~ spl5_7
| spl5_25 ),
inference(sat_conversion,[],[f834]) ).
cnf(s38,plain,
( ~ spl5_2
| ~ spl5_12 ),
inference(sat_conversion,[],[f858]) ).
cnf(s41,plain,
~ spl5_2,
inference(rat,[],[s19,s38]) ).
cnf(s42,plain,
spl5_7,
inference(rat,[],[s6,s41]) ).
cnf(s43,plain,
spl5_6,
inference(rat,[],[s5,s41]) ).
cnf(s44,plain,
spl5_5,
inference(rat,[],[s4,s41]) ).
cnf(s45,plain,
spl5_4,
inference(rat,[],[s3,s41]) ).
cnf(s47,plain,
spl5_1,
inference(rat,[],[s1,s41]) ).
cnf(s48,plain,
spl5_25,
inference(rat,[],[s33,s41,s42]) ).
cnf(s49,plain,
spl5_23,
inference(rat,[],[s32,s41,s9,s43]) ).
cnf(s50,plain,
spl5_27,
inference(rat,[],[s25,s44,s48,s49,s45]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s27,s50,s47]) ).
fof(f859,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM476+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:05:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.16/0.49 % (518108)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (518113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1047655286_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % (518114)% WARNING: option uhcvi not known.
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % (518114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4004847328:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (518116)dis+10_1_sil=32000:sp=arity:random_seed=2837761141:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (518115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3602775759:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (518117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1609066895:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (518118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3683991839:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % TRYING [5]
% 0.16/0.49 % (518117) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-518108-518117"...
% 0.16/0.49 % (518119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2714717120:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (518117)...printing done.
% 0.16/0.49 % (518117)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Theorem for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (518117)------------------------------
% 0.16/0.49 % (518117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (518117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (518117)CaDiCaL version: 2.1.3
% 0.16/0.49 % (518117)Termination reason: Refutation
% 0.16/0.49 % (518117)Time elapsed: 0.018 s
% 0.16/0.49 % (518117)Peak memory usage: 13 MB
% 0.16/0.49 % (518117)Instructions burned: 27 (million)
% 0.16/0.49 % (518108)Success in time 0.07 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------