%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM462+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 2.58s 1.29s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 11
% Syntax : Number of formulae : 87 ( 10 unt; 0 def)
% Number of atoms : 420 ( 104 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 614 ( 281 ~; 267 |; 51 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 134 ( 122 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f25,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__897) ).
fof(f26,axiom,
( xm != sz00
& xl != xn
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xl,X0) = xn )
& sdtlseqdt0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__897_03) ).
fof(f27,conjecture,
( sdtasdt0(xm,xl) != sdtasdt0(xm,xn)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn) )
| sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xl,xm),X0) = sdtasdt0(xn,xm) )
| sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f28,negated_conjecture,
~ ( sdtasdt0(xm,xl) != sdtasdt0(xm,xn)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn) )
| sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xl,xm),X0) = sdtasdt0(xn,xm) )
| sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
~ ( sdtasdt0(xm,xl) != sdtasdt0(xm,xn)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn) )
| sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xl,xm),X1) )
| sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ) ),
inference(rectify,[],[f28]) ).
fof(f31,plain,
( sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X0) )
& ~ sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn)) )
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(xn,xm) != sdtpldt0(sdtasdt0(xl,xm),X1) )
& ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f36,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f37,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f36]) ).
fof(f44,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f44]) ).
fof(f48,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f50,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f49]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f59]) ).
fof(f63,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f66,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
( xm != sz00
& xl != xn
& aNaturalNumber0(sK0)
& xn = sdtpldt0(xl,sK0)
& sdtlseqdt0(xl,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f26]) ).
fof(f68,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,[],[f50]) ).
fof(f69,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,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtpldt0(X0,sK1(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f69]) ).
fof(f71,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f25]) ).
fof(f72,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f25]) ).
fof(f73,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f25]) ).
fof(f75,plain,
xn = sdtpldt0(xl,sK0),
inference(cnf_transformation,[],[f67]) ).
fof(f76,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f67]) ).
fof(f77,plain,
xl != xn,
inference(cnf_transformation,[],[f67]) ).
fof(f78,plain,
sz00 != xm,
inference(cnf_transformation,[],[f67]) ).
fof(f81,plain,
! [X0] :
( sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xm,xl),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f86,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f99,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f101,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f102,plain,
! [X0,X1] :
( sdtpldt0(X0,sK1(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f103,plain,
! [X0,X1] :
( aNaturalNumber0(sK1(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f104,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f109,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f110,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f113,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f114,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f116,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f104]) ).
fof(f194,plain,
! [X0] :
( sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f81,f113]) ).
fof(f205,plain,
! [X0] :
( sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f194,f72]) ).
fof(f209,plain,
! [X0] :
( sdtasdt0(xm,xn) != sdtpldt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f205,f73]) ).
fof(f262,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f116,f109]) ).
fof(f282,plain,
! [X0] :
( sdtasdt0(xm,xn) != X0
| ~ aNaturalNumber0(sK1(sdtasdt0(xl,xm),X0))
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f209,f102]) ).
fof(f293,plain,
! [X0] :
( sdtasdt0(xm,xn) != X0
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f282,f103]) ).
fof(f317,plain,
! [X0] :
( sdtasdt0(xn,xm) != X0
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f293,f113]) ).
fof(f319,plain,
! [X0] :
( sdtasdt0(xn,xm) != X0
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f317]) ).
fof(f321,plain,
! [X0] :
( sdtasdt0(xn,xm) != X0
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f319,f73]) ).
fof(f323,plain,
! [X0] :
( sdtasdt0(xn,xm) != X0
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f321,f71]) ).
fof(f359,plain,
( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(equality_resolution,[],[f323]) ).
fof(f360,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(duplicate_literal_removal,[],[f359]) ).
fof(f361,plain,
! [X0] :
( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f360,f99]) ).
fof(f364,plain,
! [X0] :
( sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f361]) ).
fof(f529,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(superposition,[],[f86,f364]) ).
fof(f540,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f529,f71]) ).
fof(f544,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f540,f78]) ).
fof(f546,plain,
! [X0,X1] :
( sdtasdt0(xl,xm) != sdtasdt0(X0,xm)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X1)
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f544,f73]) ).
fof(f551,plain,
! [X0] :
( xl = xn
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f546]) ).
fof(f554,plain,
! [X0] :
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f551,f77]) ).
fof(f558,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xl,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f554,f72]) ).
fof(f563,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xm)) ),
inference(resolution,[],[f558,f262]) ).
fof(f564,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtasdt0(xl,xm),X0))
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f563]) ).
fof(f568,plain,
! [X0] :
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xl,xm),X0),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f564,f109]) ).
fof(f758,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xl,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f568,f110]) ).
fof(f817,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f758,f114]) ).
fof(f851,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f817,f114]) ).
fof(f859,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f851,f73]) ).
fof(f863,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xl,X0),xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f859,f72]) ).
fof(f867,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK0) ),
inference(superposition,[],[f863,f75]) ).
fof(f886,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f867,f101]) ).
fof(f888,plain,
~ aNaturalNumber0(sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[],[f886,f76]) ).
fof(f889,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f888,f114]) ).
fof(f892,plain,
~ aNaturalNumber0(xm),
inference(forward_subsumption_resolution,[],[f889,f71]) ).
fof(f893,plain,
$false,
inference(forward_subsumption_resolution,[],[f892,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM462+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:01:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.58/1.29 % (1271266)Detected formulas, will run a generic FOF schedule.
% 2.58/1.29 % (1271277)dis-21_1_sil=8000:lcm=predicate:random_seed=3001158065: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)
% 2.58/1.29 % (1271271)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=2061665871:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.29 % (1271275)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=901216329:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.29 % (1271272)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=2009555521:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.29 % (1271274)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1077655371:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.29 % (1271273)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=2490839761:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.29 % (1271276)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2702836464:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.29 % (1271277)Instruction limit reached!
% 2.58/1.29 % (1271277)------------------------------
% 2.58/1.29 % (1271277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (1271277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (1271277)CaDiCaL version: 2.1.3
% 2.58/1.29 % (1271277)Termination reason: Instruction limit
% 2.58/1.29 % (1271277)Termination phase: Saturation
% 2.58/1.29 % (1271277)Time elapsed: 0.044 s
% 2.58/1.29 % (1271277)Peak memory usage: 91 MB
% 2.58/1.29 % (1271277)Instructions burned: 130 (million)
% 2.58/1.29 % (1271275)First to succeed.
% 2.58/1.29 % (1271275)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1271266"
% 2.58/1.29 % (1271274)Instruction limit reached!
% 2.58/1.29 % (1271274)------------------------------
% 2.58/1.29 % (1271274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (1271274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (1271274)CaDiCaL version: 2.1.3
% 2.58/1.29 % (1271274)Termination reason: Instruction limit
% 2.58/1.29 % (1271274)Termination phase: Saturation
% 2.58/1.29 % (1271274)Time elapsed: 0.063 s
% 2.58/1.29 % (1271274)Peak memory usage: 89 MB
% 2.58/1.29 % (1271274)Instructions burned: 110 (million)
% 2.58/1.29 % (1271285)lrs+10_1_sil=8000:sp=occurrence:random_seed=2890933988:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.58/1.29 % (1271276)Instruction limit reached!
% 2.58/1.29 % (1271276)------------------------------
% 2.58/1.29 % (1271276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (1271276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (1271276)CaDiCaL version: 2.1.3
% 2.58/1.29 % (1271276)Termination reason: Instruction limit
% 2.58/1.29 % (1271276)Termination phase: Saturation
% 2.58/1.29 % (1271276)Time elapsed: 0.088 s
% 2.58/1.29 % (1271276)Peak memory usage: 90 MB
% 2.58/1.29 % (1271276)Instructions burned: 139 (million)
% 2.58/1.29 % (1271285)Instruction limit reached!
% 2.58/1.29 % (1271285)------------------------------
% 2.58/1.29 % (1271285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (1271285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (1271285)CaDiCaL version: 2.1.3
% 2.58/1.29 % (1271285)Termination reason: Instruction limit
% 2.58/1.29 % (1271285)Termination phase: Saturation
% 2.58/1.29 % (1271285)Time elapsed: 0.089 s
% 2.58/1.29 % (1271285)Peak memory usage: 92 MB
% 2.58/1.29 % (1271285)Instructions burned: 287 (million)
% 2.58/1.29 % (1271286)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2320628013:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.58/1.29 % (1271288)lrs+1011_1_sil=32000:sp=occurrence:random_seed=433379464:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.58/1.29 % (1271289)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=585380269:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 2.58/1.29 % (1271286)Instruction limit reached!
% 2.58/1.29 % (1271286)------------------------------
% 2.58/1.29 % (1271286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (1271286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (1271286)CaDiCaL version: 2.1.3
% 2.58/1.29 % (1271286)Termination reason: Instruction limit
% 2.58/1.29 % (1271286)Termination phase: Saturation
% 2.58/1.29 % (1271286)Time elapsed: 0.072 s
% 2.58/1.29 % (1271286)Peak memory usage: 91 MB
% 2.58/1.29 % (1271286)Instructions burned: 159 (million)
% 2.58/1.29 % (1271275)Refutation found. Thanks to Tanya!
% 2.58/1.29 % SZS status Theorem for theBenchmark
% 2.58/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.49 % (1271275)------------------------------
% 3.58/1.49 % (1271275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.49 % (1271275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.49 % (1271275)CaDiCaL version: 2.1.3
% 3.58/1.49 % (1271275)Termination reason: Refutation
% 3.58/1.49 % (1271275)Time elapsed: 0.019 s
% 3.58/1.49 % (1271275)Peak memory usage: 88 MB
% 3.58/1.49 % (1271275)Instructions burned: 31 (million)
% 3.58/1.49 % (1271275)------------------------------
% 3.58/1.49 % (1271275)------------------------------
% 3.58/1.49 % (1271266)Success in time 0.422 s
% 3.58/1.49 % Vampire exiting
%------------------------------------------------------------------------------