%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM465+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 : n009.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 12:15:18 PM UTC 2026
% Result : Theorem 1.02s 0.98s
% Output : Refutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 18
% Syntax : Number of formulae : 115 ( 19 unt; 6 def)
% Number of atoms : 357 ( 92 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 427 ( 185 ~; 178 |; 40 &)
% ( 12 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 78 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
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(f27,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(f28,axiom,
( xm != sz00
=> sdtlseqdt0(sz10,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1007) ).
fof(f29,conjecture,
( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f40,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f45,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f46,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f57,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f60,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f70,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(f71,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,[],[f70]) ).
fof(f74,plain,
( sdtlseqdt0(sz10,xm)
| sz00 = xm ),
inference(ennf_transformation,[],[f28]) ).
fof(f75,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& xm != sz00 ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f58]) ).
fof(f77,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f60]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f83,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f89,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f94,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f107,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f108,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f110,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f111,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| sz00 = X0
| X1 = X2
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f126,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f127,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f128,plain,
( sdtlseqdt0(sz10,xm)
| sz00 = xm ),
inference(cnf_transformation,[],[f74]) ).
fof(f129,plain,
sz00 != xm,
inference(cnf_transformation,[],[f75]) ).
fof(f130,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f75]) ).
fof(f131,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f107]) ).
fof(f132,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f110]) ).
fof(f134,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f108]) ).
fof(f139,definition,
( spl1_1
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f143,definition,
( spl1_2
<=> sdtlseqdt0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f145,plain,
( sdtlseqdt0(sz10,xm)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f128,f143,f139]) ).
fof(f147,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f129,f139]) ).
fof(f255,definition,
( spl1_8
<=> sz10 = xm ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f257,plain,
( sz10 = xm
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f297,definition,
( spl1_10
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f298,plain,
( sz00 = xn
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( sz00 != xn
| spl1_10 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f310,plain,
! [X0] :
( sdtpldt0(X0,sdtmndt0(X0,X0)) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f134,f111]) ).
fof(f314,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sdtmndt0(X0,X0)) = X0 ),
inference(duplicate_literal_removal,[],[f310]) ).
fof(f555,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2 ),
inference(forward_subsumption_resolution,[],[f132,f131]) ).
fof(f568,definition,
( spl1_17
<=> aNaturalNumber0(sdtpldt0(xn,sz00)) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f569,plain,
( aNaturalNumber0(sdtpldt0(xn,sz00))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f570,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,sz00))
| spl1_17 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f618,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| spl1_17 ),
inference(superposition,[],[f570,f89]) ).
fof(f619,plain,
( ~ aNaturalNumber0(xn)
| spl1_17 ),
inference(duplicate_literal_removal,[],[f618]) ).
fof(f620,plain,
( $false
| spl1_17 ),
inference(forward_subsumption_resolution,[],[f619,f126]) ).
fof(f621,plain,
spl1_17,
inference(avatar_contradiction_clause,[],[f620]) ).
fof(f650,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| sz00 = sdtmndt0(sdtpldt0(xn,sz00),xn)
| ~ spl1_17 ),
inference(resolution,[],[f569,f555]) ).
fof(f651,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xn,sdtpldt0(xn,sz00))
| ~ spl1_17 ),
inference(resolution,[],[f569,f131]) ).
fof(f666,plain,
( ~ aNaturalNumber0(xn)
| sdtlseqdt0(xn,sdtpldt0(xn,sz00))
| ~ spl1_17 ),
inference(forward_subsumption_resolution,[],[f651,f81]) ).
fof(f667,plain,
( ~ aNaturalNumber0(xn)
| sz00 = sdtmndt0(sdtpldt0(xn,sz00),xn)
| ~ spl1_17 ),
inference(forward_subsumption_resolution,[],[f650,f81]) ).
fof(f668,plain,
( sdtlseqdt0(xn,sdtpldt0(xn,sz00))
| ~ spl1_17 ),
inference(forward_subsumption_resolution,[],[f666,f126]) ).
fof(f669,plain,
( sz00 = sdtmndt0(sdtpldt0(xn,sz00),xn)
| ~ spl1_17 ),
inference(forward_subsumption_resolution,[],[f667,f126]) ).
fof(f687,plain,
( ! [X0] :
( sz00 = X0
| sz10 = xm
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) )
| ~ spl1_2 ),
inference(resolution,[],[f122,f145]) ).
fof(f700,plain,
( ! [X0] :
( sz00 = X0
| sz10 = xm
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) )
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f687,f83]) ).
fof(f707,plain,
( ! [X0] :
( sz00 = X0
| sz10 = xm
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0) )
| ~ spl1_2 ),
inference(forward_subsumption_resolution,[],[f700,f127]) ).
fof(f710,definition,
( spl1_28
<=> ! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl1_28])],[avatar_definition]) ).
fof(f711,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,sz10),sdtasdt0(X0,xm)) )
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f712,plain,
( spl1_8
| spl1_28
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f707,f143,f710,f255]) ).
fof(f766,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,sz10))
| ~ spl1_8 ),
inference(superposition,[],[f130,f257]) ).
fof(f808,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl1_8 ),
inference(superposition,[],[f766,f93]) ).
fof(f809,plain,
( ~ aNaturalNumber0(xn)
| ~ spl1_8 ),
inference(forward_subsumption_resolution,[],[f808,f111]) ).
fof(f812,plain,
( $false
| ~ spl1_8 ),
inference(forward_subsumption_resolution,[],[f809,f126]) ).
fof(f813,plain,
~ spl1_8,
inference(avatar_contradiction_clause,[],[f812]) ).
fof(f938,plain,
( sz00 = sdtmndt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl1_17 ),
inference(superposition,[],[f669,f89]) ).
fof(f940,plain,
( sz00 = sdtmndt0(xn,xn)
| ~ spl1_17 ),
inference(forward_subsumption_resolution,[],[f938,f126]) ).
fof(f1324,plain,
xn = sdtpldt0(xn,sdtmndt0(xn,xn)),
inference(resolution,[],[f314,f126]) ).
fof(f1327,plain,
( xn = sdtpldt0(xn,sz00)
| ~ spl1_17 ),
inference(forward_demodulation,[],[f1324,f940]) ).
fof(f1332,plain,
( sdtlseqdt0(xn,xn)
| ~ spl1_17 ),
inference(superposition,[],[f668,f1327]) ).
fof(f1442,plain,
( sz00 = xn
| sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))
| ~ spl1_28 ),
inference(resolution,[],[f711,f126]) ).
fof(f1450,plain,
( sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))
| spl1_10
| ~ spl1_28 ),
inference(forward_subsumption_resolution,[],[f1442,f299]) ).
fof(f3432,plain,
( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| spl1_10
| ~ spl1_28 ),
inference(superposition,[],[f1450,f93]) ).
fof(f3433,plain,
( ~ aNaturalNumber0(xn)
| spl1_10
| ~ spl1_28 ),
inference(forward_subsumption_resolution,[],[f3432,f130]) ).
fof(f3441,plain,
( $false
| spl1_10
| ~ spl1_28 ),
inference(forward_subsumption_resolution,[],[f3433,f126]) ).
fof(f3442,plain,
( spl1_10
| ~ spl1_28 ),
inference(avatar_contradiction_clause,[],[f3441]) ).
fof(f3567,plain,
( ~ sdtlseqdt0(sz00,sdtasdt0(sz00,xm))
| ~ spl1_10 ),
inference(superposition,[],[f130,f298]) ).
fof(f3608,plain,
( sdtlseqdt0(sz00,sz00)
| ~ spl1_10
| ~ spl1_17 ),
inference(superposition,[],[f1332,f298]) ).
fof(f4038,plain,
( ~ sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(xm)
| ~ spl1_10 ),
inference(superposition,[],[f3567,f94]) ).
fof(f4039,plain,
( ~ aNaturalNumber0(xm)
| ~ spl1_10
| ~ spl1_17 ),
inference(forward_subsumption_resolution,[],[f4038,f3608]) ).
fof(f4044,plain,
( $false
| ~ spl1_10
| ~ spl1_17 ),
inference(forward_subsumption_resolution,[],[f4039,f127]) ).
fof(f4045,plain,
( ~ spl1_10
| ~ spl1_17 ),
inference(avatar_contradiction_clause,[],[f4044]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f146]) ).
cnf(s2,plain,
~ spl1_1,
inference(sat_conversion,[],[f147]) ).
cnf(s22,plain,
spl1_17,
inference(sat_conversion,[],[f621]) ).
cnf(s26,plain,
( ~ spl1_2
| spl1_8
| spl1_28 ),
inference(sat_conversion,[],[f712]) ).
cnf(s28,plain,
~ spl1_8,
inference(sat_conversion,[],[f813]) ).
cnf(s146,plain,
( spl1_10
| ~ spl1_28 ),
inference(sat_conversion,[],[f3442]) ).
cnf(s179,plain,
( ~ spl1_10
| ~ spl1_17 ),
inference(sat_conversion,[],[f4045]) ).
cnf(s180,plain,
( ~ spl1_2
| spl1_28 ),
inference(rat,[],[s26,s28]) ).
cnf(s182,plain,
~ spl1_10,
inference(rat,[],[s179,s22]) ).
cnf(s186,plain,
~ spl1_28,
inference(rat,[],[s146,s182]) ).
cnf(s187,plain,
~ spl1_2,
inference(rat,[],[s180,s186]) ).
cnf(s219,plain,
$false,
inference(rat,[],[s1,s187,s2]) ).
fof(f4049,plain,
$false,
inference(avatar_sat_refutation,[],[s219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM465+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % 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 20:03:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 1.02/0.98 % (2362384)Detected formulas, will run a generic FOF schedule.
% 1.02/0.98 % (2362394)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3093185751:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.02/0.98 % (2362391)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=1121457200:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.02/0.98 % (2362393)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=517006408:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.02/0.98 % (2362389)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=3681302794:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.02/0.98 % (2362390)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=35853048:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.02/0.98 % (2362392)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3295708614:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.02/0.98 % (2362395)dis-21_1_sil=8000:lcm=predicate:random_seed=3243034944: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)
% 1.02/0.98 % (2362394)First to succeed.
% 1.02/0.98 % (2362394)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2362384"
% 1.02/0.98 % (2362392)Instruction limit reached!
% 1.02/0.98 % (2362392)------------------------------
% 1.02/0.98 % (2362392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.02/0.98 % (2362392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.98 % (2362392)CaDiCaL version: 2.1.3
% 1.02/0.98 % (2362392)Termination reason: Instruction limit
% 1.02/0.98 % (2362392)Termination phase: Saturation
% 1.02/0.98 % (2362392)Time elapsed: 0.065 s
% 1.02/0.98 % (2362392)Peak memory usage: 89 MB
% 1.02/0.98 % (2362392)Instructions burned: 110 (million)
% 1.02/0.98 % (2362393)Instruction limit reached!
% 1.02/0.98 % (2362393)------------------------------
% 1.02/0.98 % (2362393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.02/0.98 % (2362393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.98 % (2362393)CaDiCaL version: 2.1.3
% 1.02/0.98 % (2362393)Termination reason: Instruction limit
% 1.02/0.98 % (2362393)Termination phase: Saturation
% 1.02/0.98 % (2362393)Time elapsed: 0.070 s
% 1.02/0.98 % (2362393)Peak memory usage: 88 MB
% 1.02/0.98 % (2362393)Instructions burned: 120 (million)
% 1.02/0.98 % (2362395)Instruction limit reached!
% 1.02/0.98 % (2362395)------------------------------
% 1.02/0.98 % (2362395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.02/0.98 % (2362395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.98 % (2362395)CaDiCaL version: 2.1.3
% 1.02/0.98 % (2362395)Termination reason: Instruction limit
% 1.02/0.98 % (2362395)Termination phase: Saturation
% 1.02/0.98 % (2362395)Time elapsed: 0.079 s
% 1.02/0.98 % (2362395)Peak memory usage: 90 MB
% 1.02/0.98 % (2362395)Instructions burned: 129 (million)
% 1.02/0.98 % (2362394)Refutation found. Thanks to Tanya!
% 1.02/0.98 % SZS status Theorem for theBenchmark
% 1.02/0.98 % SZS output start Proof for theBenchmark
% See solution above
% 2.89/1.09 % (2362394)------------------------------
% 2.89/1.09 % (2362394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.89/1.09 % (2362394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.89/1.09 % (2362394)CaDiCaL version: 2.1.3
% 2.89/1.09 % (2362394)Termination reason: Refutation
% 2.89/1.09 % (2362394)Time elapsed: 0.046 s
% 2.89/1.09 % (2362394)Peak memory usage: 92 MB
% 2.89/1.09 % (2362394)Instructions burned: 139 (million)
% 2.89/1.09 % (2362394)------------------------------
% 2.89/1.09 % (2362394)------------------------------
% 2.89/1.09 % (2362384)Success in time 0.367 s
% 2.89/1.09 % Vampire exiting
%------------------------------------------------------------------------------