%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM478+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 4.32s 1.52s
% Output : Refutation 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 118 ( 32 unt; 8 def)
% Number of atoms : 377 ( 94 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 469 ( 210 ~; 218 |; 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/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/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/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(f36,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).
fof(f37,axiom,
( xl != sz00
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524_04) ).
fof(f38,axiom,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).
fof(f39,conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f43,plain,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(flattening,[],[f40]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f47]) ).
fof(f54,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f55,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f54]) ).
fof(f56,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(f57,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f56]) ).
fof(f89,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f90,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f89]) ).
fof(f91,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(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(flattening,[],[f91]) ).
fof(f106,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,[],[f90]) ).
fof(f107,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,[],[f106]) ).
fof(f108,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))],[f107]) ).
fof(f109,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,[],[f92]) ).
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(flattening,[],[f109]) ).
fof(f115,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f120,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f159,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f160,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f161,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f162,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,[],[f110]) ).
fof(f167,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f36]) ).
fof(f168,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f36]) ).
fof(f169,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f37]) ).
fof(f170,plain,
sz00 != xl,
inference(cnf_transformation,[],[f37]) ).
fof(f171,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f38]) ).
fof(f172,plain,
sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl),
inference(cnf_transformation,[],[f43]) ).
fof(f179,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f159]) ).
fof(f180,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,[],[f162]) ).
fof(f181,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f161]) ).
fof(f182,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f160]) ).
fof(f183,definition,
sF2 = sdtsldt0(xm,xl),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f184,plain,
sdtsldt0(xm,xl) = sF2,
inference(reorient_equations,[],[f183]) ).
fof(f185,definition,
sF3 = sdtasdt0(xn,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f186,plain,
sdtasdt0(xn,sF2) = sF3,
inference(reorient_equations,[],[f185]) ).
fof(f187,definition,
sF4 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f188,plain,
sdtasdt0(xn,xm) = sF4,
inference(reorient_equations,[],[f187]) ).
fof(f189,definition,
sF5 = sdtsldt0(sF4,xl),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f190,plain,
sdtsldt0(sF4,xl) = sF5,
inference(reorient_equations,[],[f189]) ).
fof(f191,plain,
sF3 != sF5,
inference(definition_folding,[],[f172,f190,f188,f186,f184]) ).
fof(f199,definition,
( spl6_1
<=> aNaturalNumber0(sF3) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f200,plain,
( aNaturalNumber0(sF3)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f201,plain,
( ~ aNaturalNumber0(sF3)
| spl6_1 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f211,definition,
( spl6_4
<=> aNaturalNumber0(sF2) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f212,plain,
( aNaturalNumber0(sF2)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( ~ aNaturalNumber0(sF2)
| spl6_4 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f220,definition,
( spl6_6
<=> aNaturalNumber0(sF4) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f221,plain,
( aNaturalNumber0(sF4)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f232,plain,
( aNaturalNumber0(sF3)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sF2) ),
inference(superposition,[],[f115,f186]) ).
fof(f233,plain,
( aNaturalNumber0(sF4)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f115,f188]) ).
fof(f234,plain,
( aNaturalNumber0(sF4)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f233,f171]) ).
fof(f235,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sF2)
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f232,f201]) ).
fof(f236,plain,
aNaturalNumber0(sF4),
inference(forward_subsumption_resolution,[],[f234,f167]) ).
fof(f237,plain,
( ~ aNaturalNumber0(sF2)
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f235,f171]) ).
fof(f238,plain,
spl6_6,
inference(avatar_split_clause,[],[f236,f220]) ).
fof(f239,plain,
( ~ spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f237,f199,f211]) ).
fof(f240,plain,
( sz00 = xl
| xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f182,f169]) ).
fof(f241,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f240,f170]) ).
fof(f242,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f241,f168]) ).
fof(f243,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f242,f167]) ).
fof(f244,plain,
xm = sdtasdt0(xl,sF2),
inference(forward_demodulation,[],[f243,f184]) ).
fof(f247,plain,
( aNaturalNumber0(sF2)
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f181,f184]) ).
fof(f250,plain,
( sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f247,f213]) ).
fof(f252,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f250,f170]) ).
fof(f254,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f252,f169]) ).
fof(f256,definition,
( spl6_9
<=> doDivides0(xl,sF4) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f257,plain,
( doDivides0(xl,sF4)
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( ~ doDivides0(xl,sF4)
| spl6_9 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f264,plain,
( ~ aNaturalNumber0(xm)
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f254,f168]) ).
fof(f265,plain,
( $false
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f264,f167]) ).
fof(f266,plain,
spl6_4,
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f271,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xn) = sdtasdt0(xn,X0) ),
inference(resolution,[],[f120,f171]) ).
fof(f278,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[],[f271,f167]) ).
fof(f280,plain,
( sdtasdt0(xn,sF2) = sdtasdt0(sF2,xn)
| ~ spl6_4 ),
inference(resolution,[],[f271,f212]) ).
fof(f283,plain,
( sF3 = sdtasdt0(sF2,xn)
| ~ spl6_4 ),
inference(forward_demodulation,[],[f280,f186]) ).
fof(f284,plain,
sF4 = sdtasdt0(xm,xn),
inference(forward_demodulation,[],[f278,f188]) ).
fof(f357,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),xn) = sdtasdt0(X0,sdtasdt0(X1,xn)) ),
inference(resolution,[],[f121,f171]) ).
fof(f366,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,sF2),xn) = sdtasdt0(X0,sdtasdt0(sF2,xn)) )
| ~ spl6_4 ),
inference(resolution,[],[f357,f212]) ).
fof(f370,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sF3) = sdtasdt0(sdtasdt0(X0,sF2),xn) )
| ~ spl6_4 ),
inference(forward_demodulation,[],[f366,f283]) ).
fof(f374,plain,
( sdtasdt0(xl,sF3) = sdtasdt0(sdtasdt0(xl,sF2),xn)
| ~ spl6_4 ),
inference(resolution,[],[f370,f168]) ).
fof(f382,plain,
( sdtasdt0(xm,xn) = sdtasdt0(xl,sF3)
| ~ spl6_4 ),
inference(forward_demodulation,[],[f374,f244]) ).
fof(f383,plain,
( sF4 = sdtasdt0(xl,sF3)
| ~ spl6_4 ),
inference(forward_demodulation,[],[f382,f284]) ).
fof(f385,plain,
( ~ doDivides0(xl,sF4)
| ~ aNaturalNumber0(sF3)
| sz00 = xl
| sF3 = sdtsldt0(sF4,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_4 ),
inference(superposition,[],[f180,f383]) ).
fof(f466,plain,
( doDivides0(xl,sF4)
| ~ aNaturalNumber0(sF3)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_4 ),
inference(superposition,[],[f179,f383]) ).
fof(f479,plain,
( ~ aNaturalNumber0(sF3)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_4
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f466,f258]) ).
fof(f487,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_1
| ~ spl6_4
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f479,f200]) ).
fof(f493,plain,
( ~ aNaturalNumber0(sF4)
| ~ spl6_1
| ~ spl6_4
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f487,f168]) ).
fof(f504,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f493,f221]) ).
fof(f505,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| spl6_9 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f513,plain,
( ~ aNaturalNumber0(sF3)
| sz00 = xl
| sF3 = sdtsldt0(sF4,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_4
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f385,f257]) ).
fof(f518,plain,
( sz00 = xl
| sF3 = sdtsldt0(sF4,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_1
| ~ spl6_4
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f513,f200]) ).
fof(f523,plain,
( sF3 = sdtsldt0(sF4,xl)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_1
| ~ spl6_4
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f518,f170]) ).
fof(f528,plain,
( sF3 = sdtsldt0(sF4,xl)
| ~ aNaturalNumber0(sF4)
| ~ spl6_1
| ~ spl6_4
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f523,f168]) ).
fof(f531,plain,
( sF3 = sdtsldt0(sF4,xl)
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f528,f221]) ).
fof(f532,plain,
( sF3 = sF5
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(forward_demodulation,[],[f531,f190]) ).
fof(f533,plain,
( $false
| ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(forward_subsumption_resolution,[],[f532,f191]) ).
fof(f534,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f533]) ).
cnf(s3,plain,
spl6_6,
inference(sat_conversion,[],[f238]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_4 ),
inference(sat_conversion,[],[f239]) ).
cnf(s6,plain,
spl6_4,
inference(sat_conversion,[],[f266]) ).
cnf(s15,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| spl6_9 ),
inference(sat_conversion,[],[f505]) ).
cnf(s16,plain,
( ~ spl6_1
| ~ spl6_4
| ~ spl6_6
| ~ spl6_9 ),
inference(sat_conversion,[],[f534]) ).
cnf(s18,plain,
spl6_1,
inference(rat,[],[s4,s6]) ).
cnf(s23,plain,
~ spl6_9,
inference(rat,[],[s16,s18,s6,s3]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s15,s18,s6,s23,s3]) ).
fof(f535,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM478+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n015.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
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:09:16 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.32/1.52 % (1981118)Detected formulas, will run a generic FOF schedule.
% 4.32/1.52 % (1981123)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=1030671700:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.32/1.52 % (1981126)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=364045261:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.32/1.52 % (1981127)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=78056147:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.32/1.52 % (1981129)dis-21_1_sil=8000:lcm=predicate:random_seed=4073351529: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)
% 4.32/1.52 % (1981128)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1061623577:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.32/1.52 % (1981125)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=911280068:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.32/1.52 % (1981124)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=2488386124:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.32/1.52 % (1981126)Refutation not found, incomplete strategy
% 4.32/1.52 % (1981126)------------------------------
% 4.32/1.52 % (1981126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.52 % (1981126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.52 % (1981126)CaDiCaL version: 2.1.3
% 4.32/1.52 % (1981126)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.52 % (1981126)Time elapsed: 0.003 s
% 4.32/1.52 % (1981126)Peak memory usage: 88 MB
% 4.32/1.52 % (1981126)Instructions burned: 2 (million)
% 4.32/1.52 % (1981127)Instruction limit reached!
% 4.32/1.52 % (1981127)------------------------------
% 4.32/1.52 % (1981127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.52 % (1981127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.52 % (1981127)CaDiCaL version: 2.1.3
% 4.32/1.52 % (1981127)Termination reason: Instruction limit
% 4.32/1.52 % (1981127)Termination phase: Saturation
% 4.32/1.52 % (1981127)Time elapsed: 0.070 s
% 4.32/1.52 % (1981127)Peak memory usage: 88 MB
% 4.32/1.52 % (1981127)Instructions burned: 119 (million)
% 4.32/1.52 % (1981129)Instruction limit reached!
% 4.32/1.52 % (1981129)------------------------------
% 4.32/1.52 % (1981129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.52 % (1981129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.52 % (1981129)CaDiCaL version: 2.1.3
% 4.32/1.52 % (1981129)Termination reason: Instruction limit
% 4.32/1.52 % (1981129)Termination phase: Saturation
% 4.32/1.52 % (1981129)Time elapsed: 0.081 s
% 4.32/1.52 % (1981129)Peak memory usage: 90 MB
% 4.32/1.52 % (1981129)Instructions burned: 129 (million)
% 4.32/1.52 % (1981128)Instruction limit reached!
% 4.32/1.52 % (1981128)------------------------------
% 4.32/1.52 % (1981128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.52 % (1981128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.52 % (1981128)CaDiCaL version: 2.1.3
% 4.32/1.52 % (1981128)Termination reason: Instruction limit
% 4.32/1.52 % (1981128)Termination phase: Saturation
% 4.32/1.52 % (1981128)Time elapsed: 0.087 s
% 4.32/1.52 % (1981128)Peak memory usage: 90 MB
% 4.32/1.52 % (1981128)Instructions burned: 139 (million)
% 4.32/1.52 % (1981137)lrs+10_1_sil=8000:sp=occurrence:random_seed=144730086:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.32/1.52 % (1981139)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2008433177:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.32/1.52 % (1981138)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1041093208:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.32/1.52 % (1981126)------------------------------
% 4.32/1.52 % (1981126)------------------------------
% 4.32/1.52 % (1981138)Instruction limit reached!
% 4.32/1.52 % (1981138)------------------------------
% 4.32/1.52 % (1981138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.52 % (1981138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.52 % (1981138)CaDiCaL version: 2.1.3
% 4.32/1.52 % (1981138)Termination reason: Instruction limit
% 4.32/1.52 % (1981138)Termination phase: Saturation
% 4.32/1.52 % (1981138)Time elapsed: 0.070 s
% 4.32/1.52 % (1981138)Peak memory usage: 90 MB
% 4.32/1.52 % (1981138)Instructions burned: 159 (million)
% 4.32/1.52 % (1981123)First to succeed.
% 4.32/1.52 % (1981123)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1981118"
% 4.32/1.52 % (1981137)Instruction limit reached!
% 4.32/1.52 % (1981137)------------------------------
% 4.32/1.52 % (1981137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.52 % (1981137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.52 % (1981137)CaDiCaL version: 2.1.3
% 4.32/1.52 % (1981137)Termination reason: Instruction limit
% 4.32/1.52 % (1981137)Termination phase: Saturation
% 4.32/1.52 % (1981137)Time elapsed: 0.166 s
% 4.32/1.52 % (1981137)Peak memory usage: 92 MB
% 4.32/1.52 % (1981137)Instructions burned: 286 (million)
% 4.32/1.52 % (1981143)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=3833548044:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.32/1.52 % (1981139)Instruction limit reached!
% 4.32/1.52 % (1981139)------------------------------
% 4.32/1.52 % (1981139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.52 % (1981139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.52 % (1981139)CaDiCaL version: 2.1.3
% 4.32/1.52 % (1981139)Termination reason: Instruction limit
% 4.32/1.52 % (1981139)Termination phase: Saturation
% 4.32/1.52 % (1981139)Time elapsed: 0.190 s
% 4.32/1.52 % (1981139)Peak memory usage: 91 MB
% 4.32/1.52 % (1981139)Instructions burned: 325 (million)
% 4.32/1.52 % (1981144)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2823016946:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.32/1.52 % (1981123)Refutation found. Thanks to Tanya!
% 4.32/1.52 % SZS status Theorem for theBenchmark
% 4.32/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.20/1.61 % (1981123)------------------------------
% 5.20/1.61 % (1981123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.61 % (1981123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.61 % (1981123)CaDiCaL version: 2.1.3
% 5.20/1.61 % (1981123)Termination reason: Refutation
% 5.20/1.61 % (1981123)Time elapsed: 0.376 s
% 5.20/1.61 % (1981123)Peak memory usage: 130 MB
% 5.20/1.61 % (1981123)Instructions burned: 984 (million)
% 5.20/1.61 % (1981123)------------------------------
% 5.20/1.61 % (1981123)------------------------------
% 5.20/1.61 % (1981118)Success in time 0.656 s
% 5.20/1.61 % Vampire exiting
%------------------------------------------------------------------------------