%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM461+2 : 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 : n010.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 12:15:17 PM UTC 2026
% Result : Theorem 2.51s 1.29s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 120 ( 31 unt; 12 def)
% Number of atoms : 340 ( 72 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 407 ( 187 ~; 174 |; 32 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 66 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtpldt0(X0,X1) = sdtpldt0(X0,X2)
| sdtpldt0(X1,X0) = sdtpldt0(X2,X0) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f24,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__840) ).
fof(f25,axiom,
( xl != xn
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xl,X0) = xn )
& sdtlseqdt0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__840_03) ).
fof(f26,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__873) ).
fof(f27,conjecture,
( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn) )
| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtpldt0(xl,xm),X0) = sdtpldt0(xn,xm) )
| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn) )
| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtpldt0(xl,xm),X0) = sdtpldt0(xn,xm) )
| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
~ ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn) )
| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,xm) = sdtpldt0(sdtpldt0(xl,xm),X1) )
| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
inference(rectify,[],[f28]) ).
fof(f31,plain,
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(sdtpldt0(xm,xl),X0) )
& ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtpldt0(xn,xm) != sdtpldt0(sdtpldt0(xl,xm),X1) )
& ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f44,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
( xl != xn
& aNaturalNumber0(sK0)
& xn = sdtpldt0(xl,sK0)
& sdtlseqdt0(xl,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f25]) ).
fof(f53,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f24]) ).
fof(f54,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f24]) ).
fof(f56,plain,
xn = sdtpldt0(xl,sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f57,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f49]) ).
fof(f58,plain,
xl != xn,
inference(cnf_transformation,[],[f49]) ).
fof(f59,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f26]) ).
fof(f63,plain,
! [X0,X1] :
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(sdtpldt0(xm,xl),X0)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| sdtpldt0(xn,xm) != sdtpldt0(sdtpldt0(xl,xm),X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f73,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f74,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f75,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f76,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f77,definition,
~ sP2(xl),
introduced(definition,[new_symbols(definition,[sP2])],[inequality_splitting_name_introduction]) ).
fof(f78,plain,
sP2(xn),
inference(inequality_splitting,[],[f58,f77]) ).
fof(f79,definition,
~ sP3(sdtpldt0(xm,xn)),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f80,definition,
~ sP4(sdtpldt0(xn,xm)),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f81,plain,
! [X0,X1] :
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0)
| sP3(sdtpldt0(sdtpldt0(xm,xl),X0))
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| sP4(sdtpldt0(sdtpldt0(xl,xm),X1)) ),
inference(inequality_splitting,[],[f63,f80,f79]) ).
fof(f88,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sP3(sdtpldt0(sdtpldt0(xm,xl),X0))
| sP7 ),
inference(cnf_transformation,[],[f88_D]) ).
fof(f88_D,definition,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sP3(sdtpldt0(sdtpldt0(xm,xl),X0)) )
<=> ~ sP7 ),
introduced(definition,[new_symbols(definition,[sP7])],[general_splitting_component_introduction]) ).
fof(f89,plain,
! [X1] :
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| sP4(sdtpldt0(sdtpldt0(xl,xm),X1))
| ~ sP7 ),
inference(general_splitting,[],[f81,f88_D]) ).
fof(f116,plain,
sP2(sdtpldt0(xl,sK0)),
inference(forward_demodulation,[],[f78,f56]) ).
fof(f117,plain,
aNaturalNumber0(sdtpldt0(xl,sK0)),
inference(forward_demodulation,[],[f53,f56]) ).
fof(f119,definition,
( spl8_7
<=> sP7 ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
fof(f123,definition,
( spl8_8
<=> ! [X0] :
( ~ aNaturalNumber0(X0)
| sP3(sdtpldt0(sdtpldt0(xm,xl),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
fof(f124,plain,
( ! [X0] :
( sP3(sdtpldt0(sdtpldt0(xm,xl),X0))
| ~ aNaturalNumber0(X0) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f125,plain,
( spl8_7
| spl8_8 ),
inference(avatar_split_clause,[],[f88,f123,f119]) ).
fof(f126,plain,
! [X1] :
( sdtpldt0(xm,xl) = sdtpldt0(xm,sdtpldt0(xl,sK0))
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| sP4(sdtpldt0(sdtpldt0(xl,xm),X1))
| ~ sP7 ),
inference(forward_demodulation,[],[f89,f56]) ).
fof(f127,plain,
! [X1] :
( sdtpldt0(xl,xm) = sdtpldt0(sdtpldt0(xl,sK0),xm)
| sdtpldt0(xm,xl) = sdtpldt0(xm,sdtpldt0(xl,sK0))
| ~ aNaturalNumber0(X1)
| sP4(sdtpldt0(sdtpldt0(xl,xm),X1))
| ~ sP7 ),
inference(forward_demodulation,[],[f126,f56]) ).
fof(f129,definition,
( spl8_9
<=> ! [X1] :
( ~ aNaturalNumber0(X1)
| sP4(sdtpldt0(sdtpldt0(xl,xm),X1)) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f130,plain,
( ! [X1] :
( sP4(sdtpldt0(sdtpldt0(xl,xm),X1))
| ~ aNaturalNumber0(X1) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,definition,
( spl8_10
<=> sdtpldt0(xm,xl) = sdtpldt0(xm,sdtpldt0(xl,sK0)) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f133,plain,
( sdtpldt0(xm,xl) != sdtpldt0(xm,sdtpldt0(xl,sK0))
| spl8_10 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f134,plain,
( sdtpldt0(xm,xl) = sdtpldt0(xm,sdtpldt0(xl,sK0))
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f136,definition,
( spl8_11
<=> sdtpldt0(xl,xm) = sdtpldt0(sdtpldt0(xl,sK0),xm) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
fof(f138,plain,
( sdtpldt0(xl,xm) = sdtpldt0(sdtpldt0(xl,sK0),xm)
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( ~ spl8_7
| spl8_9
| spl8_10
| spl8_11 ),
inference(avatar_split_clause,[],[f127,f136,f132,f129,f119]) ).
fof(f162,plain,
( ! [X0] :
( sP3(sdtpldt0(xm,sdtpldt0(xl,X0)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) )
| ~ spl8_8 ),
inference(superposition,[],[f124,f74]) ).
fof(f168,plain,
( ! [X0] :
( sP3(sdtpldt0(xm,sdtpldt0(xl,X0)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) )
| ~ spl8_8 ),
inference(duplicate_literal_removal,[],[f162]) ).
fof(f179,plain,
( ! [X0] :
( sP3(sdtpldt0(xm,sdtpldt0(xl,X0)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) )
| ~ spl8_8 ),
inference(forward_subsumption_resolution,[],[f168,f59]) ).
fof(f184,plain,
( ! [X0] :
( sP3(sdtpldt0(xm,sdtpldt0(xl,X0)))
| ~ aNaturalNumber0(X0) )
| ~ spl8_8 ),
inference(forward_subsumption_resolution,[],[f179,f54]) ).
fof(f193,plain,
( ! [X0] :
( sP4(sdtpldt0(X0,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) )
| ~ spl8_9 ),
inference(superposition,[],[f130,f75]) ).
fof(f196,plain,
( ! [X0] :
( sP4(sdtpldt0(X0,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,xm)) )
| ~ spl8_9 ),
inference(duplicate_literal_removal,[],[f193]) ).
fof(f199,definition,
( spl8_15
<=> aNaturalNumber0(sdtpldt0(xl,xm)) ),
introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition]) ).
fof(f201,plain,
( ~ aNaturalNumber0(sdtpldt0(xl,xm))
| spl8_15 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f203,definition,
( spl8_16
<=> ! [X0] :
( sP4(sdtpldt0(X0,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl8_16])],[avatar_definition]) ).
fof(f204,plain,
( ! [X0] :
( sP4(sdtpldt0(X0,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(X0) )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f206,plain,
( ~ spl8_15
| spl8_16
| ~ spl8_9 ),
inference(avatar_split_clause,[],[f196,f129,f203,f199]) ).
fof(f219,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xl))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| spl8_15 ),
inference(superposition,[],[f201,f75]) ).
fof(f222,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f219,f76]) ).
fof(f225,plain,
( ~ aNaturalNumber0(xl)
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f222,f59]) ).
fof(f230,plain,
( $false
| spl8_15 ),
inference(forward_subsumption_resolution,[],[f225,f54]) ).
fof(f231,plain,
spl8_15,
inference(avatar_contradiction_clause,[],[f230]) ).
fof(f361,plain,
( sdtpldt0(xl,xm) = sdtpldt0(xm,sdtpldt0(xl,sK0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xl,sK0))
| ~ spl8_11 ),
inference(superposition,[],[f75,f138]) ).
fof(f365,plain,
( sdtpldt0(xl,xm) = sdtpldt0(xm,sdtpldt0(xl,sK0))
| ~ aNaturalNumber0(sdtpldt0(xl,sK0))
| ~ spl8_11 ),
inference(forward_subsumption_resolution,[],[f361,f59]) ).
fof(f379,plain,
( sdtpldt0(xl,xm) = sdtpldt0(xm,sdtpldt0(xl,sK0))
| ~ spl8_11 ),
inference(forward_subsumption_resolution,[],[f365,f117]) ).
fof(f538,definition,
( spl8_25
<=> xl = sdtpldt0(xl,sK0) ),
introduced(definition,[new_symbols(definition,[spl8_25])],[avatar_definition]) ).
fof(f540,plain,
( xl = sdtpldt0(xl,sK0)
| ~ spl8_25 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f561,plain,
~ sP4(sdtpldt0(sdtpldt0(xl,sK0),xm)),
inference(superposition,[],[f80,f56]) ).
fof(f562,plain,
~ sP3(sdtpldt0(xm,sdtpldt0(xl,sK0))),
inference(superposition,[],[f79,f56]) ).
fof(f578,plain,
( ~ sP4(sdtpldt0(sdtpldt0(sK0,xl),xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK0) ),
inference(superposition,[],[f561,f75]) ).
fof(f583,plain,
( ~ sP4(sdtpldt0(sdtpldt0(sK0,xl),xm))
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f578,f54]) ).
fof(f586,plain,
~ sP4(sdtpldt0(sdtpldt0(sK0,xl),xm)),
inference(forward_subsumption_resolution,[],[f583,f57]) ).
fof(f879,plain,
( ~ aNaturalNumber0(sK0)
| ~ spl8_8 ),
inference(resolution,[],[f184,f562]) ).
fof(f891,plain,
( $false
| ~ spl8_8 ),
inference(forward_subsumption_resolution,[],[f879,f57]) ).
fof(f892,plain,
~ spl8_8,
inference(avatar_contradiction_clause,[],[f891]) ).
fof(f924,plain,
( ~ sP4(sdtpldt0(sK0,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f586,f74]) ).
fof(f927,plain,
( ~ sP4(sdtpldt0(sK0,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f924,f57]) ).
fof(f928,plain,
( ~ sP4(sdtpldt0(sK0,sdtpldt0(xl,xm)))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f927,f54]) ).
fof(f929,plain,
~ sP4(sdtpldt0(sK0,sdtpldt0(xl,xm))),
inference(forward_subsumption_resolution,[],[f928,f59]) ).
fof(f1053,plain,
( ! [X0] :
( sdtpldt0(xm,xl) != sdtpldt0(xm,X0)
| sdtpldt0(xl,sK0) = X0
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,sK0)) )
| ~ spl8_10 ),
inference(superposition,[],[f73,f134]) ).
fof(f1058,plain,
( ! [X0] :
( sdtpldt0(xm,xl) != sdtpldt0(xm,X0)
| sdtpldt0(xl,sK0) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xl,sK0)) )
| ~ spl8_10 ),
inference(forward_subsumption_resolution,[],[f1053,f59]) ).
fof(f1063,plain,
( ! [X0] :
( sdtpldt0(xm,xl) != sdtpldt0(xm,X0)
| sdtpldt0(xl,sK0) = X0
| ~ aNaturalNumber0(X0) )
| ~ spl8_10 ),
inference(forward_subsumption_resolution,[],[f1058,f117]) ).
fof(f1176,plain,
( sdtpldt0(xm,xl) = sdtpldt0(xm,sdtpldt0(xl,sK0))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ spl8_11 ),
inference(superposition,[],[f379,f75]) ).
fof(f1719,plain,
( xl = sdtpldt0(xl,sK0)
| ~ aNaturalNumber0(xl)
| ~ spl8_10 ),
inference(equality_resolution,[],[f1063]) ).
fof(f1723,plain,
( xl = sdtpldt0(xl,sK0)
| ~ spl8_10 ),
inference(forward_subsumption_resolution,[],[f1719,f54]) ).
fof(f1726,plain,
( spl8_25
| ~ spl8_10 ),
inference(avatar_split_clause,[],[f1723,f132,f538]) ).
fof(f1741,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| spl8_10
| ~ spl8_11 ),
inference(forward_subsumption_resolution,[],[f1176,f133]) ).
fof(f1800,plain,
( ~ aNaturalNumber0(xl)
| spl8_10
| ~ spl8_11 ),
inference(forward_subsumption_resolution,[],[f1741,f59]) ).
fof(f1833,plain,
( $false
| spl8_10
| ~ spl8_11 ),
inference(forward_subsumption_resolution,[],[f1800,f54]) ).
fof(f1834,plain,
( spl8_10
| ~ spl8_11 ),
inference(avatar_contradiction_clause,[],[f1833]) ).
fof(f2034,plain,
( ~ aNaturalNumber0(sK0)
| ~ spl8_16 ),
inference(resolution,[],[f204,f929]) ).
fof(f2045,plain,
( $false
| ~ spl8_16 ),
inference(forward_subsumption_resolution,[],[f2034,f57]) ).
fof(f2046,plain,
~ spl8_16,
inference(avatar_contradiction_clause,[],[f2045]) ).
fof(f2385,plain,
( sP2(xl)
| ~ spl8_25 ),
inference(superposition,[],[f116,f540]) ).
fof(f2425,plain,
( $false
| ~ spl8_25 ),
inference(forward_subsumption_resolution,[],[f2385,f77]) ).
fof(f2426,plain,
~ spl8_25,
inference(avatar_contradiction_clause,[],[f2425]) ).
cnf(s4,plain,
( spl8_7
| spl8_8 ),
inference(sat_conversion,[],[f125]) ).
cnf(s5,plain,
( ~ spl8_7
| spl8_9
| spl8_10
| spl8_11 ),
inference(sat_conversion,[],[f139]) ).
cnf(s11,plain,
( ~ spl8_9
| ~ spl8_15
| spl8_16 ),
inference(sat_conversion,[],[f206]) ).
cnf(s15,plain,
spl8_15,
inference(sat_conversion,[],[f231]) ).
cnf(s37,plain,
~ spl8_8,
inference(sat_conversion,[],[f892]) ).
cnf(s54,plain,
( ~ spl8_10
| spl8_25 ),
inference(sat_conversion,[],[f1726]) ).
cnf(s59,plain,
( spl8_10
| ~ spl8_11 ),
inference(sat_conversion,[],[f1834]) ).
cnf(s86,plain,
~ spl8_16,
inference(sat_conversion,[],[f2046]) ).
cnf(s102,plain,
~ spl8_25,
inference(sat_conversion,[],[f2426]) ).
cnf(s108,plain,
~ spl8_10,
inference(rat,[],[s54,s102]) ).
cnf(s109,plain,
~ spl8_11,
inference(rat,[],[s59,s108]) ).
cnf(s119,plain,
~ spl8_9,
inference(rat,[],[s11,s86,s15]) ).
cnf(s122,plain,
~ spl8_7,
inference(rat,[],[s5,s109,s108,s119]) ).
cnf(s123,plain,
$false,
inference(rat,[],[s4,s37,s122]) ).
fof(f2439,plain,
$false,
inference(avatar_sat_refutation,[],[s123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM461+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:01:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.51/1.29 % (1271689)Detected formulas, will run a generic FOF schedule.
% 2.51/1.29 % (1271695)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=1253376643:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.51/1.29 % (1271697)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2081304538:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.51/1.29 % (1271694)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=2406906669:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.51/1.29 % (1271698)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1140594579:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.51/1.29 % (1271700)dis-21_1_sil=8000:lcm=predicate:random_seed=1486141172: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)
% 2.51/1.29 % (1271696)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=1383789547:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.51/1.29 % (1271699)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=571125858:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.51/1.29 % (1271697)First to succeed.
% 2.51/1.29 % (1271697)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1271689"
% 2.51/1.29 % (1271698)Instruction limit reached!
% 2.51/1.29 % (1271698)------------------------------
% 2.51/1.29 % (1271698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.29 % (1271698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.29 % (1271698)CaDiCaL version: 2.1.3
% 2.51/1.29 % (1271698)Termination reason: Instruction limit
% 2.51/1.29 % (1271698)Termination phase: Saturation
% 2.51/1.29 % (1271698)Time elapsed: 0.067 s
% 2.51/1.29 % (1271698)Peak memory usage: 88 MB
% 2.51/1.29 % (1271698)Instructions burned: 120 (million)
% 2.51/1.29 % (1271700)Instruction limit reached!
% 2.51/1.29 % (1271700)------------------------------
% 2.51/1.29 % (1271700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.29 % (1271700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.29 % (1271700)CaDiCaL version: 2.1.3
% 2.51/1.29 % (1271700)Termination reason: Instruction limit
% 2.51/1.29 % (1271700)Termination phase: Saturation
% 2.51/1.29 % (1271700)Time elapsed: 0.081 s
% 2.51/1.29 % (1271700)Peak memory usage: 90 MB
% 2.51/1.29 % (1271700)Instructions burned: 130 (million)
% 2.51/1.29 % (1271699)Instruction limit reached!
% 2.51/1.29 % (1271699)------------------------------
% 2.51/1.29 % (1271699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.29 % (1271699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.29 % (1271699)CaDiCaL version: 2.1.3
% 2.51/1.29 % (1271699)Termination reason: Instruction limit
% 2.51/1.29 % (1271699)Termination phase: Saturation
% 2.51/1.29 % (1271699)Time elapsed: 0.088 s
% 2.51/1.29 % (1271699)Peak memory usage: 90 MB
% 2.51/1.29 % (1271699)Instructions burned: 139 (million)
% 2.51/1.29 % (1271708)lrs+10_1_sil=8000:sp=occurrence:random_seed=3190786235:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.51/1.29 % (1271710)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1544852789:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.51/1.29 % (1271709)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1017054590:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.51/1.29 % (1271709)Also succeeded, but the first one will report.
% 2.51/1.29 % (1271697)Refutation found. Thanks to Tanya!
% 2.51/1.29 % SZS status Theorem for theBenchmark
% 2.51/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.38 % (1271697)------------------------------
% 3.54/1.38 % (1271697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.38 % (1271697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.38 % (1271697)CaDiCaL version: 2.1.3
% 3.54/1.38 % (1271697)Termination reason: Refutation
% 3.54/1.38 % (1271697)Time elapsed: 0.039 s
% 3.54/1.38 % (1271697)Peak memory usage: 90 MB
% 3.54/1.38 % (1271697)Instructions burned: 60 (million)
% 3.54/1.38 % (1271697)------------------------------
% 3.54/1.38 % (1271697)------------------------------
% 3.54/1.38 % (1271689)Success in time 0.435 s
% 3.54/1.38 % Vampire exiting
%------------------------------------------------------------------------------