%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM480+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:15:22 PM UTC 2026
% Result : Theorem 4.56s 1.53s
% Output : Refutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 118 ( 32 unt; 8 def)
% Number of atoms : 375 ( 93 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 466 ( 209 ~; 216 |; 25 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 83 !; 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(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
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(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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f36,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).
fof(f37,axiom,
( xl != sz00
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).
fof(f38,axiom,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).
fof(f40,conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f41,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f44,plain,
sdtsldt0(sdtasdt0(xn,xm),xl) != sdtasdt0(xn,sdtsldt0(xm,xl)),
inference(flattening,[],[f41]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f48]) ).
fof(f55,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f56,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f58,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f57]) ).
fof(f90,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f91,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f90]) ).
fof(f92,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(f93,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,[],[f92]) ).
fof(f107,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,[],[f91]) ).
fof(f108,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,[],[f107]) ).
fof(f109,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))],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f93]) ).
fof(f111,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f110]) ).
fof(f116,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f160,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f161,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f162,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f168,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f36]) ).
fof(f169,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f36]) ).
fof(f170,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f37]) ).
fof(f171,plain,
sz00 != xl,
inference(cnf_transformation,[],[f37]) ).
fof(f172,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f38]) ).
fof(f174,plain,
sdtsldt0(sdtasdt0(xn,xm),xl) != sdtasdt0(xn,sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f44]) ).
fof(f181,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f160]) ).
fof(f182,plain,
! [X2,X0] :
( ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sz00 = X0
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f163]) ).
fof(f183,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f162]) ).
fof(f184,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f161]) ).
fof(f185,definition,
sF2 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f186,plain,
sdtasdt0(xn,xm) = sF2,
inference(reorient_equations,[],[f185]) ).
fof(f187,definition,
sF3 = sdtsldt0(sF2,xl),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f188,plain,
sdtsldt0(sF2,xl) = sF3,
inference(reorient_equations,[],[f187]) ).
fof(f189,definition,
sF4 = sdtsldt0(xm,xl),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f190,plain,
sdtsldt0(xm,xl) = sF4,
inference(reorient_equations,[],[f189]) ).
fof(f191,definition,
sF5 = sdtasdt0(xn,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f192,plain,
sdtasdt0(xn,sF4) = sF5,
inference(reorient_equations,[],[f191]) ).
fof(f193,plain,
sF3 != sF5,
inference(definition_folding,[],[f174,f192,f190,f188,f186]) ).
fof(f201,definition,
( spl6_1
<=> aNaturalNumber0(sF5) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f202,plain,
( aNaturalNumber0(sF5)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
( ~ aNaturalNumber0(sF5)
| spl6_1 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f213,definition,
( spl6_4
<=> aNaturalNumber0(sF4) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f214,plain,
( aNaturalNumber0(sF4)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f215,plain,
( ~ aNaturalNumber0(sF4)
| spl6_4 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f222,definition,
( spl6_6
<=> aNaturalNumber0(sF2) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f223,plain,
( aNaturalNumber0(sF2)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f234,plain,
( aNaturalNumber0(sF5)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sF4) ),
inference(superposition,[],[f116,f192]) ).
fof(f235,plain,
( aNaturalNumber0(sF2)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f116,f186]) ).
fof(f236,plain,
( aNaturalNumber0(sF2)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f235,f172]) ).
fof(f237,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sF4)
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f234,f203]) ).
fof(f238,plain,
aNaturalNumber0(sF2),
inference(forward_subsumption_resolution,[],[f236,f168]) ).
fof(f239,plain,
( ~ aNaturalNumber0(sF4)
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f237,f172]) ).
fof(f240,plain,
spl6_6,
inference(avatar_split_clause,[],[f238,f222]) ).
fof(f241,plain,
( ~ spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f239,f201,f213]) ).
fof(f255,plain,
( sz00 = xl
| xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f170,f184]) ).
fof(f256,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f255,f171]) ).
fof(f257,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f256,f169]) ).
fof(f258,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f257,f168]) ).
fof(f259,plain,
xm = sdtasdt0(xl,sF4),
inference(forward_demodulation,[],[f258,f190]) ).
fof(f262,plain,
( aNaturalNumber0(sF4)
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f183,f190]) ).
fof(f265,plain,
( sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f262,f215]) ).
fof(f267,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f265,f171]) ).
fof(f269,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f267,f170]) ).
fof(f271,definition,
( spl6_9
<=> doDivides0(xl,sF2) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f272,plain,
( doDivides0(xl,sF2)
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( ~ doDivides0(xl,sF2)
| spl6_9 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f279,plain,
( ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f269,f169]) ).
fof(f280,plain,
( $false
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f279,f168]) ).
fof(f281,plain,
spl6_4,
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f324,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xn) = sdtasdt0(xn,X0) ),
inference(resolution,[],[f121,f172]) ).
fof(f332,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[],[f324,f168]) ).
fof(f335,plain,
( sdtasdt0(xn,sF4) = sdtasdt0(sF4,xn)
| ~ spl6_4 ),
inference(resolution,[],[f324,f214]) ).
fof(f337,plain,
( sF5 = sdtasdt0(sF4,xn)
| ~ spl6_4 ),
inference(forward_demodulation,[],[f335,f192]) ).
fof(f338,plain,
sF2 = sdtasdt0(xm,xn),
inference(forward_demodulation,[],[f332,f186]) ).
fof(f400,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),xn) = sdtasdt0(X0,sdtasdt0(X1,xn)) ),
inference(resolution,[],[f122,f172]) ).
fof(f411,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,sF4),xn) = sdtasdt0(X0,sdtasdt0(sF4,xn)) )
| ~ spl6_4 ),
inference(resolution,[],[f400,f214]) ).
fof(f414,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sF5) = sdtasdt0(sdtasdt0(X0,sF4),xn) )
| ~ spl6_4 ),
inference(forward_demodulation,[],[f411,f337]) ).
fof(f420,plain,
( sdtasdt0(xl,sF5) = sdtasdt0(sdtasdt0(xl,sF4),xn)
| ~ spl6_4 ),
inference(resolution,[],[f414,f169]) ).
fof(f428,plain,
( sdtasdt0(xm,xn) = sdtasdt0(xl,sF5)
| ~ spl6_4 ),
inference(forward_demodulation,[],[f420,f259]) ).
fof(f430,plain,
( sF2 = sdtasdt0(xl,sF5)
| ~ spl6_4 ),
inference(forward_demodulation,[],[f428,f338]) ).
fof(f432,plain,
( ~ doDivides0(xl,sF2)
| ~ aNaturalNumber0(sF5)
| sz00 = xl
| sdtsldt0(sF2,xl) = sF5
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl6_4 ),
inference(superposition,[],[f182,f430]) ).
fof(f710,plain,
( doDivides0(xl,sF2)
| ~ aNaturalNumber0(sF5)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl6_4 ),
inference(superposition,[],[f181,f430]) ).
fof(f725,plain,
( ~ aNaturalNumber0(sF5)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl6_4
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f710,f273]) ).
fof(f736,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl6_1
| ~ spl6_4
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f725,f202]) ).
fof(f745,plain,
( ~ aNaturalNumber0(sF2)
| ~ spl6_1
| ~ spl6_4
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f736,f169]) ).
fof(f760,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f745,f223]) ).
fof(f761,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| spl6_9 ),
inference(avatar_contradiction_clause,[],[f760]) ).
fof(f786,plain,
( ~ doDivides0(xl,sF2)
| sz00 = xl
| sdtsldt0(sF2,xl) = sF5
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f432,f202]) ).
fof(f804,plain,
( ~ doDivides0(xl,sF2)
| sdtsldt0(sF2,xl) = sF5
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF2)
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f786,f171]) ).
fof(f817,plain,
( ~ doDivides0(xl,sF2)
| sdtsldt0(sF2,xl) = sF5
| ~ aNaturalNumber0(sF2)
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f804,f169]) ).
fof(f829,plain,
( ~ doDivides0(xl,sF2)
| sdtsldt0(sF2,xl) = sF5
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6 ),
inference(forward_subsumption_resolution,[],[f817,f223]) ).
fof(f867,plain,
( sdtsldt0(sF2,xl) = sF5
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f829,f272]) ).
fof(f899,plain,
( sF3 = sF5
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(forward_demodulation,[],[f867,f188]) ).
fof(f901,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f899,f193]) ).
fof(f902,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f901]) ).
cnf(s3,plain,
spl6_6,
inference(sat_conversion,[],[f240]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_4 ),
inference(sat_conversion,[],[f241]) ).
cnf(s6,plain,
spl6_4,
inference(sat_conversion,[],[f281]) ).
cnf(s41,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| spl6_9 ),
inference(sat_conversion,[],[f761]) ).
cnf(s46,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(sat_conversion,[],[f902]) ).
cnf(s54,plain,
spl6_1,
inference(rat,[],[s4,s6]) ).
cnf(s61,plain,
~ spl6_9,
inference(rat,[],[s46,s54,s6,s3]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s41,s54,s6,s61,s3]) ).
fof(f903,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM480+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 20:06:07 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.56/1.52 % (3847134)Detected formulas, will run a generic FOF schedule.
% 4.56/1.52 % (3847139)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2301477716:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.56/1.52 % (3847143)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2330988433:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.56/1.52 % (3847140)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1274371659:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.56/1.52 % (3847142)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2443059947:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.56/1.52 % (3847141)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3276720619:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.56/1.52 % (3847145)dis-21_1_sil=8000:lcm=predicate:random_seed=3142070539:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.56/1.52 % (3847144)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2919806854:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.56/1.52 % (3847142)Refutation not found, incomplete strategy
% 4.56/1.52 % (3847142)------------------------------
% 4.56/1.52 % (3847142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.56/1.52 % (3847142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.56/1.52 % (3847142)CaDiCaL version: 2.1.3
% 4.56/1.52 % (3847142)Termination reason: Refutation not found, incomplete strategy
% 4.56/1.52 % (3847142)Time elapsed: 0.005 s
% 4.56/1.52 % (3847142)Peak memory usage: 88 MB
% 4.56/1.52 % (3847142)Instructions burned: 5 (million)
% 4.56/1.52 % (3847143)Instruction limit reached!
% 4.56/1.52 % (3847143)------------------------------
% 4.56/1.52 % (3847143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.56/1.52 % (3847143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.56/1.52 % (3847143)CaDiCaL version: 2.1.3
% 4.56/1.52 % (3847143)Termination reason: Instruction limit
% 4.56/1.52 % (3847143)Termination phase: Saturation
% 4.56/1.52 % (3847143)Time elapsed: 0.069 s
% 4.56/1.52 % (3847143)Peak memory usage: 88 MB
% 4.56/1.52 % (3847143)Instructions burned: 119 (million)
% 4.56/1.52 % (3847145)Instruction limit reached!
% 4.56/1.52 % (3847145)------------------------------
% 4.56/1.52 % (3847145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.56/1.52 % (3847145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.56/1.52 % (3847145)CaDiCaL version: 2.1.3
% 4.56/1.52 % (3847145)Termination reason: Instruction limit
% 4.56/1.52 % (3847145)Termination phase: Saturation
% 4.56/1.52 % (3847145)Time elapsed: 0.079 s
% 4.56/1.52 % (3847145)Peak memory usage: 90 MB
% 4.56/1.52 % (3847145)Instructions burned: 131 (million)
% 4.56/1.52 % (3847144)Instruction limit reached!
% 4.56/1.52 % (3847144)------------------------------
% 4.56/1.52 % (3847144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.56/1.52 % (3847144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.56/1.52 % (3847144)CaDiCaL version: 2.1.3
% 4.56/1.52 % (3847144)Termination reason: Instruction limit
% 4.56/1.52 % (3847144)Termination phase: Saturation
% 4.56/1.52 % (3847144)Time elapsed: 0.090 s
% 4.56/1.52 % (3847144)Peak memory usage: 90 MB
% 4.56/1.52 % (3847144)Instructions burned: 140 (million)
% 4.56/1.52 % (3847153)lrs+10_1_sil=8000:sp=occurrence:random_seed=3642850063:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.56/1.52 % (3847154)lrs+10_1_sil=32000:urr=on:br=off:random_seed=207629945:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.56/1.52 % (3847142)------------------------------
% 4.56/1.52 % (3847142)------------------------------
% 4.56/1.52 % (3847155)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2689333276:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.56/1.52 % (3847154)Instruction limit reached!
% 4.56/1.52 % (3847154)------------------------------
% 4.56/1.52 % (3847154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.56/1.52 % (3847154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.56/1.52 % (3847154)CaDiCaL version: 2.1.3
% 4.56/1.52 % (3847154)Termination reason: Instruction limit
% 4.56/1.52 % (3847154)Termination phase: Saturation
% 4.56/1.52 % (3847154)Time elapsed: 0.070 s
% 4.56/1.52 % (3847154)Peak memory usage: 90 MB
% 4.56/1.52 % (3847154)Instructions burned: 159 (million)
% 4.56/1.52 % (3847139)First to succeed.
% 4.56/1.52 % (3847139)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3847134"
% 4.56/1.52 % (3847153)Instruction limit reached!
% 4.56/1.52 % (3847153)------------------------------
% 4.56/1.52 % (3847153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.56/1.52 % (3847153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.56/1.52 % (3847153)CaDiCaL version: 2.1.3
% 4.56/1.52 % (3847153)Termination reason: Instruction limit
% 4.56/1.52 % (3847153)Termination phase: Saturation
% 4.56/1.52 % (3847153)Time elapsed: 0.160 s
% 4.56/1.52 % (3847153)Peak memory usage: 91 MB
% 4.56/1.52 % (3847153)Instructions burned: 285 (million)
% 4.56/1.52 % (3847159)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3083064029:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.56/1.53 % (3847155)Instruction limit reached!
% 4.56/1.53 % (3847155)------------------------------
% 4.56/1.53 % (3847155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.56/1.53 % (3847155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.56/1.53 % (3847155)CaDiCaL version: 2.1.3
% 4.56/1.53 % (3847155)Termination reason: Instruction limit
% 4.56/1.53 % (3847155)Termination phase: Saturation
% 4.56/1.53 % (3847155)Time elapsed: 0.192 s
% 4.56/1.53 % (3847155)Peak memory usage: 92 MB
% 4.56/1.53 % (3847155)Instructions burned: 327 (million)
% 4.56/1.53 % (3847160)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1636448571:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.56/1.53 % (3847139)Refutation found. Thanks to Tanya!
% 4.56/1.53 % SZS status Theorem for theBenchmark
% 4.56/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.34/1.62 % (3847139)------------------------------
% 5.34/1.62 % (3847139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.34/1.62 % (3847139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.34/1.62 % (3847139)CaDiCaL version: 2.1.3
% 5.34/1.62 % (3847139)Termination reason: Refutation
% 5.34/1.62 % (3847139)Time elapsed: 0.396 s
% 5.34/1.62 % (3847139)Peak memory usage: 130 MB
% 5.34/1.62 % (3847139)Instructions burned: 1011 (million)
% 5.34/1.62 % (3847139)------------------------------
% 5.34/1.62 % (3847139)------------------------------
% 5.34/1.62 % (3847134)Success in time 0.685 s
% 5.34/1.62 % Vampire exiting
%------------------------------------------------------------------------------