%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM473+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 : 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 12:15:20 PM UTC 2026
% Result : Theorem 4.99s 2.21s
% Output : Refutation 10.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 122 ( 29 unt; 6 def)
% Number of atoms : 387 ( 86 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 467 ( 202 ~; 216 |; 32 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X0 != sz00
& X1 != X2
& sdtlseqdt0(X1,X2) )
=> ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
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,axiom,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
fof(f39,axiom,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
fof(f40,conjecture,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f41,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f44,plain,
~ sdtlseqdt0(xp,xq),
inference(flattening,[],[f41]) ).
fof(f46,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f46]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f77,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f76]) ).
fof(f80,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f81,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f80]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f84]) ).
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(f106,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(f107,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,[],[f106]) ).
fof(f111,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f139,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f141,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f149,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f157,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f158,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f162,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f163,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f164,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f165,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f166,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f167,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f168,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f169,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f170,plain,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f39]) ).
fof(f171,plain,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f44]) ).
fof(f180,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f158]) ).
fof(f181,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f157]) ).
fof(f185,plain,
( aNaturalNumber0(xp)
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f180,f168]) ).
fof(f186,plain,
( aNaturalNumber0(xq)
| sz00 = xl
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[],[f180,f169]) ).
fof(f187,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f186,f167]) ).
fof(f188,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f185,f167]) ).
fof(f189,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f187,f165]) ).
fof(f190,plain,
( aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f188,f166]) ).
fof(f191,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f189,f164]) ).
fof(f192,plain,
( aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f190,f164]) ).
fof(f194,definition,
( spl2_1
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f195,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f196,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| spl2_1 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f198,definition,
( spl2_2
<=> aNaturalNumber0(xq) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f200,plain,
( aNaturalNumber0(xq)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f191,f198,f194]) ).
fof(f202,plain,
aNaturalNumber0(xp),
inference(forward_subsumption_resolution,[],[f192,f163]) ).
fof(f203,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl2_1 ),
inference(resolution,[],[f196,f111]) ).
fof(f204,plain,
( ~ aNaturalNumber0(xn)
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f203,f163]) ).
fof(f205,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f204,f162]) ).
fof(f206,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f205]) ).
fof(f241,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| xm = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f139,f170]) ).
fof(f255,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| xm = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(xm)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f241,f195]) ).
fof(f258,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| xm = sdtpldt0(xm,xn)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f255,f163]) ).
fof(f262,definition,
( spl2_3
<=> xm = sdtpldt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f264,plain,
( xm = sdtpldt0(xm,xn)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f266,definition,
( spl2_4
<=> sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f268,plain,
( ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| spl2_4 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,plain,
( spl2_3
| ~ spl2_4
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f258,f194,f266,f262]) ).
fof(f529,plain,
( sz00 = xl
| sdtpldt0(xm,xn) = sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[],[f181,f165]) ).
fof(f530,plain,
( sz00 = xl
| xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f181,f166]) ).
fof(f531,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f530,f167]) ).
fof(f532,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f529,f167]) ).
fof(f533,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f531,f164]) ).
fof(f534,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f532,f164]) ).
fof(f535,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f533,f163]) ).
fof(f536,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f534,f195]) ).
fof(f537,plain,
xm = sdtasdt0(xl,xp),
inference(forward_demodulation,[],[f535,f168]) ).
fof(f538,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f536,f169]) ).
fof(f898,plain,
( ! [X0] :
( sdtlseqdt0(sdtpldt0(xm,xn),sdtasdt0(xl,X0))
| sz00 = xl
| xq = X0
| ~ sdtlseqdt0(xq,X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0) )
| ~ spl2_1 ),
inference(superposition,[],[f149,f538]) ).
fof(f915,plain,
( ! [X0] :
( sdtlseqdt0(sdtpldt0(xm,xn),sdtasdt0(xl,X0))
| xq = X0
| ~ sdtlseqdt0(xq,X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0) )
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f898,f167]) ).
fof(f927,plain,
( ! [X0] :
( sdtlseqdt0(sdtpldt0(xm,xn),sdtasdt0(xl,X0))
| xq = X0
| ~ sdtlseqdt0(xq,X0)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(X0) )
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f915,f164]) ).
fof(f945,plain,
( ! [X0] :
( sdtlseqdt0(sdtpldt0(xm,xn),sdtasdt0(xl,X0))
| xq = X0
| ~ sdtlseqdt0(xq,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl2_1
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f927,f200]) ).
fof(f1018,plain,
( sdtlseqdt0(sdtpldt0(xm,xn),xm)
| xp = xq
| ~ sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xp)
| ~ spl2_1
| ~ spl2_2 ),
inference(superposition,[],[f945,f537]) ).
fof(f1019,plain,
( xp = xq
| ~ sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xp)
| ~ spl2_1
| ~ spl2_2
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f1018,f268]) ).
fof(f1023,plain,
( xp = xq
| ~ sdtlseqdt0(xq,xp)
| ~ spl2_1
| ~ spl2_2
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f1019,f202]) ).
fof(f1027,definition,
( spl2_30
<=> sdtlseqdt0(xq,xp) ),
introduced(definition,[new_symbols(definition,[spl2_30])],[avatar_definition]) ).
fof(f1028,plain,
( sdtlseqdt0(xq,xp)
| ~ spl2_30 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1029,plain,
( ~ sdtlseqdt0(xq,xp)
| spl2_30 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1031,definition,
( spl2_31
<=> xp = xq ),
introduced(definition,[new_symbols(definition,[spl2_31])],[avatar_definition]) ).
fof(f1032,plain,
( xp != xq
| spl2_31 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1033,plain,
( xp = xq
| ~ spl2_31 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1034,plain,
( ~ spl2_30
| spl2_31
| ~ spl2_1
| ~ spl2_2
| spl2_4 ),
inference(avatar_split_clause,[],[f1023,f266,f198,f194,f1031,f1027]) ).
fof(f1039,plain,
( sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| spl2_30 ),
inference(resolution,[],[f1029,f141]) ).
fof(f1042,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| spl2_30 ),
inference(forward_subsumption_resolution,[],[f1039,f171]) ).
fof(f1044,plain,
( ~ aNaturalNumber0(xp)
| ~ spl2_2
| spl2_30 ),
inference(forward_subsumption_resolution,[],[f1042,f200]) ).
fof(f1047,plain,
( $false
| ~ spl2_2
| spl2_30 ),
inference(forward_subsumption_resolution,[],[f1044,f202]) ).
fof(f1048,plain,
( ~ spl2_2
| spl2_30 ),
inference(avatar_contradiction_clause,[],[f1047]) ).
fof(f1049,plain,
( ~ sdtlseqdt0(xp,xp)
| ~ spl2_31 ),
inference(superposition,[],[f171,f1033]) ).
fof(f1067,plain,
( sdtlseqdt0(xp,xp)
| ~ spl2_30
| ~ spl2_31 ),
inference(superposition,[],[f1028,f1033]) ).
fof(f1068,plain,
( $false
| ~ spl2_30
| ~ spl2_31 ),
inference(forward_subsumption_resolution,[],[f1067,f1049]) ).
fof(f1069,plain,
( ~ spl2_30
| ~ spl2_31 ),
inference(avatar_contradiction_clause,[],[f1068]) ).
fof(f1155,plain,
( sdtsldt0(xm,xl) = xq
| ~ spl2_3 ),
inference(superposition,[],[f169,f264]) ).
fof(f1181,plain,
( xp = xq
| ~ spl2_3 ),
inference(forward_demodulation,[],[f1155,f168]) ).
fof(f1189,plain,
( $false
| ~ spl2_3
| spl2_31 ),
inference(forward_subsumption_resolution,[],[f1181,f1032]) ).
fof(f1190,plain,
( ~ spl2_3
| spl2_31 ),
inference(avatar_contradiction_clause,[],[f1189]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f201]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f206]) ).
cnf(s3,plain,
( ~ spl2_1
| spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f269]) ).
cnf(s23,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_4
| ~ spl2_30
| spl2_31 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s25,plain,
( ~ spl2_2
| spl2_30 ),
inference(sat_conversion,[],[f1048]) ).
cnf(s26,plain,
( ~ spl2_30
| ~ spl2_31 ),
inference(sat_conversion,[],[f1069]) ).
cnf(s29,plain,
( ~ spl2_3
| spl2_31 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s33,plain,
spl2_2,
inference(rat,[],[s1,s2]) ).
cnf(s34,plain,
spl2_30,
inference(rat,[],[s25,s33]) ).
cnf(s37,plain,
~ spl2_31,
inference(rat,[],[s26,s34]) ).
cnf(s41,plain,
~ spl2_3,
inference(rat,[],[s29,s37]) ).
cnf(s42,plain,
spl2_4,
inference(rat,[],[s23,s33,s34,s2,s37]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s3,s2,s42,s41]) ).
fof(f1191,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM473+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 20:04:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 4.99/2.21 % (3844491)Detected formulas, will run a generic FOF schedule.
% 4.99/2.21 % (3844601)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=202980332:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.99/2.21 % (3844597)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=13591689:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.99/2.21 % (3844598)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=3297039428:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.99/2.21 % (3844602)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3804697236:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.99/2.21 % (3844599)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=1623027269:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.99/2.21 % (3844603)dis-21_1_sil=8000:lcm=predicate:random_seed=3020406895: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)
% 4.99/2.21 % (3844601)Instruction limit reached!
% 4.99/2.21 % (3844601)------------------------------
% 4.99/2.21 % (3844601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844601)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844601)Termination reason: Instruction limit
% 4.99/2.21 % (3844601)Termination phase: Saturation
% 4.99/2.21 % (3844601)Time elapsed: 0.038 s
% 4.99/2.21 % (3844601)Peak memory usage: 89 MB
% 4.99/2.21 % (3844601)Instructions burned: 122 (million)
% 4.99/2.21 % (3844600)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3034272646:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.99/2.21 % (3844602)Instruction limit reached!
% 4.99/2.21 % (3844602)------------------------------
% 4.99/2.21 % (3844602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844602)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844602)Termination reason: Instruction limit
% 4.99/2.21 % (3844602)Termination phase: Saturation
% 4.99/2.21 % (3844602)Time elapsed: 0.089 s
% 4.99/2.21 % (3844602)Peak memory usage: 89 MB
% 4.99/2.21 % (3844602)Instructions burned: 141 (million)
% 4.99/2.21 % (3844603)Instruction limit reached!
% 4.99/2.21 % (3844603)------------------------------
% 4.99/2.21 % (3844603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844603)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844603)Termination reason: Instruction limit
% 4.99/2.21 % (3844603)Termination phase: Saturation
% 4.99/2.21 % (3844603)Time elapsed: 0.093 s
% 4.99/2.21 % (3844603)Peak memory usage: 91 MB
% 4.99/2.21 % (3844603)Instructions burned: 130 (million)
% 4.99/2.21 % (3844600)Instruction limit reached!
% 4.99/2.21 % (3844600)------------------------------
% 4.99/2.21 % (3844600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844600)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844600)Termination reason: Instruction limit
% 4.99/2.21 % (3844600)Termination phase: Saturation
% 4.99/2.21 % (3844600)Time elapsed: 0.068 s
% 4.99/2.21 % (3844600)Peak memory usage: 89 MB
% 4.99/2.21 % (3844600)Instructions burned: 110 (million)
% 4.99/2.21 % (3844610)lrs+10_1_sil=8000:sp=occurrence:random_seed=2480084398:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.99/2.21 % (3844610)Instruction limit reached!
% 4.99/2.21 % (3844610)------------------------------
% 4.99/2.21 % (3844610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844610)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844610)Termination reason: Instruction limit
% 4.99/2.21 % (3844610)Termination phase: Saturation
% 4.99/2.21 % (3844610)Time elapsed: 0.089 s
% 4.99/2.21 % (3844610)Peak memory usage: 92 MB
% 4.99/2.21 % (3844610)Instructions burned: 288 (million)
% 4.99/2.21 % (3844626)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1065614228:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.99/2.21 % (3844627)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=2331477799:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.99/2.21 % (3844629)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2744171045:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.99/2.21 % (3844625)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2289969902:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.99/2.21 % (3844625)Refutation not found, incomplete strategy
% 4.99/2.21 % (3844625)------------------------------
% 4.99/2.21 % (3844625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844625)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844625)Termination reason: Refutation not found, incomplete strategy
% 4.99/2.21 % (3844625)Time elapsed: 0.003 s
% 4.99/2.21 % (3844625)Peak memory usage: 89 MB
% 4.99/2.21 % (3844625)Instructions burned: 2 (million)
% 4.99/2.21 % (3844627)Instruction limit reached!
% 4.99/2.21 % (3844627)------------------------------
% 4.99/2.21 % (3844627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844627)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844627)Termination reason: Instruction limit
% 4.99/2.21 % (3844627)Termination phase: Saturation
% 4.99/2.21 % (3844627)Time elapsed: 0.115 s
% 4.99/2.21 % (3844627)Peak memory usage: 94 MB
% 4.99/2.21 % (3844627)Instructions burned: 249 (million)
% 4.99/2.21 % (3844629)Instruction limit reached!
% 4.99/2.21 % (3844629)------------------------------
% 4.99/2.21 % (3844629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844629)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844629)Termination reason: Instruction limit
% 4.99/2.21 % (3844629)Termination phase: Saturation
% 4.99/2.21 % (3844629)Time elapsed: 0.090 s
% 4.99/2.21 % (3844629)Peak memory usage: 89 MB
% 4.99/2.21 % (3844629)Instructions burned: 295 (million)
% 4.99/2.21 % (3844626)Instruction limit reached!
% 4.99/2.21 % (3844626)------------------------------
% 4.99/2.21 % (3844626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844626)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844626)Termination reason: Instruction limit
% 4.99/2.21 % (3844626)Termination phase: Saturation
% 4.99/2.21 % (3844626)Time elapsed: 0.193 s
% 4.99/2.21 % (3844626)Peak memory usage: 92 MB
% 4.99/2.21 % (3844626)Instructions burned: 326 (million)
% 4.99/2.21 % (3844634)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3849380418:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.99/2.21 % (3844635)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=996805271:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.99/2.21 % (3844635)Instruction limit reached!
% 4.99/2.21 % (3844635)------------------------------
% 4.99/2.21 % (3844635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844635)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844635)Termination reason: Instruction limit
% 4.99/2.21 % (3844635)Termination phase: Saturation
% 4.99/2.21 % (3844635)Time elapsed: 0.037 s
% 4.99/2.21 % (3844635)Peak memory usage: 90 MB
% 4.99/2.21 % (3844635)Instructions burned: 113 (million)
% 4.99/2.21 % (3844625)------------------------------
% 4.99/2.21 % (3844625)------------------------------
% 4.99/2.21 % (3844636)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=795155277:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.99/2.21 % (3844636)Instruction limit reached!
% 4.99/2.21 % (3844636)------------------------------
% 4.99/2.21 % (3844636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844636)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844636)Termination reason: Instruction limit
% 4.99/2.21 % (3844636)Termination phase: Saturation
% 4.99/2.21 % (3844636)Time elapsed: 0.066 s
% 4.99/2.21 % (3844636)Peak memory usage: 89 MB
% 4.99/2.21 % (3844636)Instructions burned: 128 (million)
% 4.99/2.21 % (3844639)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=188074616:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 4.99/2.21 % (3844597)First to succeed.
% 4.99/2.21 % (3844597)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3844491"
% 4.99/2.21 % (3844640)lrs+10_1_sil=8000:sp=occurrence:random_seed=901089293:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 4.99/2.21 % (3844639)Instruction limit reached!
% 4.99/2.21 % (3844639)------------------------------
% 4.99/2.21 % (3844639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/2.21 % (3844639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/2.21 % (3844639)CaDiCaL version: 2.1.3
% 4.99/2.21 % (3844639)Termination reason: Instruction limit
% 4.99/2.21 % (3844639)Termination phase: Saturation
% 4.99/2.21 % (3844639)Time elapsed: 0.047 s
% 4.99/2.21 % (3844639)Peak memory usage: 89 MB
% 4.99/2.21 % (3844639)Instructions burned: 115 (million)
% 4.99/2.21 % (3844650)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=433984009:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 4.99/2.21 % (3844653)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3053528249:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 4.99/2.21 % (3844650)Also succeeded, but the first one will report.
% 4.99/2.21 % (3844597)Refutation found. Thanks to Tanya!
% 4.99/2.21 % SZS status Theorem for theBenchmark
% 4.99/2.21 % SZS output start Proof for theBenchmark
% See solution above
% 10.11/2.35 % (3844597)------------------------------
% 10.11/2.35 % (3844597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.11/2.35 % (3844597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.11/2.35 % (3844597)CaDiCaL version: 2.1.3
% 10.11/2.35 % (3844597)Termination reason: Refutation
% 10.11/2.35 % (3844597)Time elapsed: 0.764 s
% 10.11/2.35 % (3844597)Peak memory usage: 129 MB
% 10.11/2.35 % (3844597)Instructions burned: 1094 (million)
% 10.11/2.35 % (3844597)------------------------------
% 10.11/2.35 % (3844597)------------------------------
% 10.11/2.35 % (3844491)Success in time 1.348 s
% 10.11/2.35 % Vampire exiting
%------------------------------------------------------------------------------