%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM459+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 : n007.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 12:15:16 PM UTC 2026
% Result : Theorem 9.46s 2.29s
% Output : Refutation 10.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 150 ( 46 unt; 3 def)
% Number of atoms : 391 ( 131 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 434 ( 193 ~; 186 |; 35 &)
% ( 9 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 117 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X0 = sz00
& X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
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(f21,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__745) ).
fof(f22,conjecture,
( ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) )
=> xm = xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f23,negated_conjecture,
~ ( ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) )
=> xm = xn ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f29]) ).
fof(f31,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(f32,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f46,plain,
! [X0,X1] :
( ( X0 = sz00
& X1 = sz00 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f47,plain,
! [X0,X1] :
( ( X0 = sz00
& X1 = sz00 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f50]) ).
fof(f52,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(f53,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f52]) ).
fof(f55,plain,
( xm != xn
& sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) ),
inference(ennf_transformation,[],[f23]) ).
fof(f56,plain,
( xm != xn
& sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) ),
inference(flattening,[],[f55]) ).
fof(f57,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,[],[f51]) ).
fof(f58,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,[],[f57]) ).
fof(f59,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))],[f58]) ).
fof(f60,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,[],[f53]) ).
fof(f61,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,[],[f60]) ).
fof(f62,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f70,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f33]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f88,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f89,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f90,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f91,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f93,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f21]) ).
fof(f94,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f21]) ).
fof(f95,plain,
sdtlseqdt0(xn,xm),
inference(cnf_transformation,[],[f56]) ).
fof(f96,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f56]) ).
fof(f97,plain,
xm != xn,
inference(cnf_transformation,[],[f56]) ).
fof(f98,plain,
! [X2,X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f88]) ).
fof(f99,plain,
! [X2,X0] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f91]) ).
fof(f100,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f90]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f89]) ).
fof(f102,plain,
xm = sdtpldt0(xm,sz00),
inference(resolution,[],[f94,f70]) ).
fof(f103,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| xm = sdtpldt0(X0,sK0(X0,xm)) ),
inference(resolution,[],[f94,f86]) ).
fof(f104,plain,
xn = sdtpldt0(xn,sz00),
inference(resolution,[],[f93,f70]) ).
fof(f105,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| xn = sdtpldt0(X0,sK0(X0,xn)) ),
inference(resolution,[],[f93,f86]) ).
fof(f106,plain,
( ~ aNaturalNumber0(xm)
| xn = sdtpldt0(xm,sK0(xm,xn)) ),
inference(resolution,[],[f105,f96]) ).
fof(f107,plain,
xn = sdtpldt0(xm,sK0(xm,xn)),
inference(forward_subsumption_resolution,[],[f106,f94]) ).
fof(f108,plain,
( ~ aNaturalNumber0(xn)
| xm = sdtpldt0(xn,sK0(xn,xm)) ),
inference(resolution,[],[f103,f95]) ).
fof(f109,plain,
xm = sdtpldt0(xn,sK0(xn,xm)),
inference(forward_subsumption_resolution,[],[f108,f93]) ).
fof(f110,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| xm = sdtpldt0(X0,sdtmndt0(xm,X0)) ),
inference(resolution,[],[f101,f94]) ).
fof(f112,plain,
( ~ aNaturalNumber0(xn)
| xm = sdtpldt0(xn,sdtmndt0(xm,xn)) ),
inference(resolution,[],[f110,f95]) ).
fof(f113,plain,
xm = sdtpldt0(xn,sdtmndt0(xm,xn)),
inference(forward_subsumption_resolution,[],[f112,f93]) ).
fof(f116,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK0(X0,xm)) ),
inference(resolution,[],[f87,f94]) ).
fof(f117,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK0(X0,xn)) ),
inference(resolution,[],[f87,f93]) ).
fof(f118,plain,
( ~ aNaturalNumber0(xn)
| aNaturalNumber0(sK0(xn,xm)) ),
inference(resolution,[],[f116,f95]) ).
fof(f119,plain,
aNaturalNumber0(sK0(xn,xm)),
inference(forward_subsumption_resolution,[],[f118,f93]) ).
fof(f124,plain,
( ~ aNaturalNumber0(xm)
| aNaturalNumber0(sK0(xm,xn)) ),
inference(resolution,[],[f117,f96]) ).
fof(f125,plain,
aNaturalNumber0(sK0(xm,xn)),
inference(forward_subsumption_resolution,[],[f124,f94]) ).
fof(f132,plain,
sz00 = sdtpldt0(sz00,sz00),
inference(resolution,[],[f62,f70]) ).
fof(f146,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(X0,xm) ),
inference(resolution,[],[f67,f94]) ).
fof(f147,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,X0) = sdtpldt0(X0,xn) ),
inference(resolution,[],[f67,f93]) ).
fof(f149,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sK0(xm,xn)) = sdtpldt0(sK0(xm,xn),X0) ),
inference(resolution,[],[f67,f125]) ).
fof(f172,plain,
( aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f100,f96]) ).
fof(f173,plain,
( aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f100,f95]) ).
fof(f174,plain,
( aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f173,f93]) ).
fof(f175,plain,
( aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f172,f94]) ).
fof(f176,plain,
aNaturalNumber0(sdtmndt0(xm,xn)),
inference(forward_subsumption_resolution,[],[f174,f94]) ).
fof(f177,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(forward_subsumption_resolution,[],[f175,f93]) ).
fof(f185,plain,
sdtpldt0(xm,sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),xm),
inference(resolution,[],[f176,f146]) ).
fof(f186,plain,
sdtpldt0(xn,sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),xn),
inference(resolution,[],[f176,f147]) ).
fof(f187,plain,
xm = sdtpldt0(sdtmndt0(xm,xn),xn),
inference(forward_demodulation,[],[f186,f113]) ).
fof(f200,plain,
sdtpldt0(sdtmndt0(xm,xn),sK0(xm,xn)) = sdtpldt0(sK0(xm,xn),sdtmndt0(xm,xn)),
inference(resolution,[],[f149,f176]) ).
fof(f204,plain,
sdtpldt0(sK0(xn,xm),sK0(xm,xn)) = sdtpldt0(sK0(xm,xn),sK0(xn,xm)),
inference(resolution,[],[f149,f119]) ).
fof(f252,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),sK0(xn,xm)) = sdtpldt0(X0,sdtpldt0(X1,sK0(xn,xm))) ),
inference(resolution,[],[f68,f119]) ).
fof(f253,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),sK0(xm,xn)) = sdtpldt0(X0,sdtpldt0(X1,sK0(xm,xn))) ),
inference(resolution,[],[f68,f125]) ).
fof(f260,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,sK0(xn,xm)),sK0(xm,xn)) = sdtpldt0(X0,sdtpldt0(sK0(xn,xm),sK0(xm,xn))) ),
inference(resolution,[],[f253,f119]) ).
fof(f262,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,sK0(xn,xm)),sK0(xm,xn)) = sdtpldt0(X0,sdtpldt0(sK0(xm,xn),sK0(xn,xm))) ),
inference(forward_demodulation,[],[f260,f204]) ).
fof(f270,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,xn),sK0(xn,xm)) = sdtpldt0(X0,sdtpldt0(xn,sK0(xn,xm))) ),
inference(resolution,[],[f252,f93]) ).
fof(f271,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,sK0(xn,xm)),sK0(xn,xm)) = sdtpldt0(X0,sdtpldt0(sK0(xn,xm),sK0(xn,xm))) ),
inference(resolution,[],[f252,f119]) ).
fof(f273,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,xm) = sdtpldt0(sdtpldt0(X0,xn),sK0(xn,xm)) ),
inference(forward_demodulation,[],[f270,f109]) ).
fof(f280,plain,
sdtpldt0(sdtpldt0(xn,sK0(xn,xm)),sK0(xm,xn)) = sdtpldt0(xn,sdtpldt0(sK0(xm,xn),sK0(xn,xm))),
inference(resolution,[],[f262,f93]) ).
fof(f283,plain,
sdtpldt0(xm,sK0(xm,xn)) = sdtpldt0(xn,sdtpldt0(sK0(xm,xn),sK0(xn,xm))),
inference(forward_demodulation,[],[f280,f109]) ).
fof(f285,plain,
xn = sdtpldt0(xn,sdtpldt0(sK0(xm,xn),sK0(xn,xm))),
inference(forward_demodulation,[],[f283,f107]) ).
fof(f307,plain,
sdtpldt0(sdtmndt0(xm,xn),xm) = sdtpldt0(sdtpldt0(sdtmndt0(xm,xn),xn),sK0(xn,xm)),
inference(resolution,[],[f273,f176]) ).
fof(f317,plain,
sdtpldt0(xm,sK0(xn,xm)) = sdtpldt0(sdtmndt0(xm,xn),xm),
inference(forward_demodulation,[],[f307,f187]) ).
fof(f321,plain,
sdtpldt0(xm,sK0(xn,xm)) = sdtpldt0(xm,sdtmndt0(xm,xn)),
inference(forward_demodulation,[],[f317,f185]) ).
fof(f336,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(xm,X0))
| sdtlseqdt0(xm,sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f98,f94]) ).
fof(f337,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(xn,X0))
| sdtlseqdt0(xn,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f98,f93]) ).
fof(f387,plain,
sdtpldt0(sdtpldt0(xn,sK0(xn,xm)),sK0(xn,xm)) = sdtpldt0(xn,sdtpldt0(sK0(xn,xm),sK0(xn,xm))),
inference(resolution,[],[f271,f93]) ).
fof(f390,plain,
sdtpldt0(xm,sK0(xn,xm)) = sdtpldt0(xn,sdtpldt0(sK0(xn,xm),sK0(xn,xm))),
inference(forward_demodulation,[],[f387,f109]) ).
fof(f393,plain,
sdtpldt0(xm,sdtmndt0(xm,xn)) = sdtpldt0(xn,sdtpldt0(sK0(xn,xm),sK0(xn,xm))),
inference(forward_demodulation,[],[f390,f321]) ).
fof(f421,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xm,sdtpldt0(xm,X0))
| sdtmndt0(sdtpldt0(xm,X0),xm) = X0
| ~ aNaturalNumber0(sdtpldt0(xm,X0)) ),
inference(resolution,[],[f99,f94]) ).
fof(f422,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,sdtpldt0(xn,X0))
| sdtmndt0(sdtpldt0(xn,X0),xn) = X0
| ~ aNaturalNumber0(sdtpldt0(xn,X0)) ),
inference(resolution,[],[f99,f93]) ).
fof(f427,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(xn,X0))
| sdtmndt0(sdtpldt0(xn,X0),xn) = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f422,f337]) ).
fof(f428,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(xm,X0))
| sdtmndt0(sdtpldt0(xm,X0),xm) = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f421,f336]) ).
fof(f435,plain,
( ~ aNaturalNumber0(xn)
| sK0(xm,xn) = sdtmndt0(xn,xm)
| ~ aNaturalNumber0(sK0(xm,xn)) ),
inference(superposition,[],[f428,f107]) ).
fof(f436,plain,
( sK0(xm,xn) = sdtmndt0(xn,xm)
| ~ aNaturalNumber0(sK0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f435,f93]) ).
fof(f438,plain,
sK0(xm,xn) = sdtmndt0(xn,xm),
inference(forward_subsumption_resolution,[],[f436,f125]) ).
fof(f450,plain,
( ~ aNaturalNumber0(xn)
| sz00 = sdtmndt0(xn,xn)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[],[f427,f104]) ).
fof(f454,plain,
( ~ aNaturalNumber0(xm)
| sK0(xn,xm) = sdtmndt0(xm,xn)
| ~ aNaturalNumber0(sK0(xn,xm)) ),
inference(superposition,[],[f427,f109]) ).
fof(f455,plain,
( sK0(xn,xm) = sdtmndt0(xm,xn)
| ~ aNaturalNumber0(sK0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f454,f94]) ).
fof(f462,plain,
( sz00 = sdtmndt0(xn,xn)
| ~ aNaturalNumber0(sz00) ),
inference(forward_subsumption_resolution,[],[f450,f93]) ).
fof(f463,plain,
sK0(xn,xm) = sdtmndt0(xm,xn),
inference(forward_subsumption_resolution,[],[f455,f119]) ).
fof(f472,plain,
sz00 = sdtmndt0(xn,xn),
inference(forward_subsumption_resolution,[],[f462,f62]) ).
fof(f482,definition,
( spl1_11
<=> aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f483,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)))
| spl1_11 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f491,plain,
xn = sdtpldt0(xn,sdtpldt0(sK0(xm,xn),sdtmndt0(xm,xn))),
inference(superposition,[],[f285,f463]) ).
fof(f493,plain,
sdtpldt0(xm,sdtmndt0(xm,xn)) = sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xm,xn))),
inference(superposition,[],[f393,f463]) ).
fof(f496,plain,
xn = sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sK0(xm,xn))),
inference(forward_demodulation,[],[f491,f200]) ).
fof(f497,plain,
xn = sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))),
inference(forward_demodulation,[],[f496,f438]) ).
fof(f498,plain,
( ~ aNaturalNumber0(xn)
| sdtmndt0(xn,xn) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ),
inference(superposition,[],[f427,f497]) ).
fof(f514,plain,
( $false
| spl1_11 ),
inference(unit_resulting_resolution,[],[f65,f177,f176,f483]) ).
fof(f515,plain,
spl1_11,
inference(avatar_contradiction_clause,[],[f514]) ).
fof(f516,plain,
( sdtmndt0(xn,xn) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ),
inference(forward_subsumption_resolution,[],[f498,f93]) ).
fof(f517,plain,
( sz00 = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ),
inference(forward_demodulation,[],[f516,f472]) ).
fof(f519,definition,
( spl1_13
<=> sz00 = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f520,plain,
( sz00 = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f521,plain,
( ~ spl1_11
| spl1_13 ),
inference(avatar_split_clause,[],[f517,f519,f482]) ).
fof(f4373,plain,
! [X0] :
( sz00 != sdtpldt0(X0,sdtmndt0(xn,xm))
| ~ aNaturalNumber0(X0)
| sz00 = X0 ),
inference(resolution,[],[f84,f177]) ).
fof(f5850,definition,
( spl1_104
<=> sz00 = sdtmndt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl1_104])],[avatar_definition]) ).
fof(f5851,plain,
( sz00 = sdtmndt0(xm,xn)
| ~ spl1_104 ),
inference(avatar_component_clause,[],[f5850]) ).
fof(f7043,plain,
( sdtpldt0(xm,sz00) = sdtpldt0(xn,sdtpldt0(sz00,sz00))
| ~ spl1_104 ),
inference(superposition,[],[f493,f5851]) ).
fof(f7054,plain,
( sdtpldt0(xm,sz00) = sdtpldt0(xn,sz00)
| ~ spl1_104 ),
inference(forward_demodulation,[],[f7043,f132]) ).
fof(f7063,plain,
( xn = sdtpldt0(xm,sz00)
| ~ spl1_104 ),
inference(forward_demodulation,[],[f7054,f104]) ).
fof(f7067,plain,
( xm = xn
| ~ spl1_104 ),
inference(forward_demodulation,[],[f7063,f102]) ).
fof(f7068,plain,
( $false
| ~ spl1_104 ),
inference(forward_subsumption_resolution,[],[f7067,f97]) ).
fof(f7069,plain,
~ spl1_104,
inference(avatar_contradiction_clause,[],[f7068]) ).
fof(f7635,plain,
( sz00 != sz00
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| sz00 = sdtmndt0(xm,xn)
| ~ spl1_13 ),
inference(superposition,[],[f4373,f520]) ).
fof(f7637,plain,
( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| sz00 = sdtmndt0(xm,xn)
| ~ spl1_13 ),
inference(trivial_inequality_removal,[],[f7635]) ).
fof(f7638,plain,
( sz00 = sdtmndt0(xm,xn)
| ~ spl1_13 ),
inference(forward_subsumption_resolution,[],[f7637,f176]) ).
fof(f7639,plain,
( spl1_104
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f7638,f519,f5850]) ).
cnf(s12,plain,
spl1_11,
inference(sat_conversion,[],[f515]) ).
cnf(s13,plain,
( ~ spl1_11
| spl1_13 ),
inference(sat_conversion,[],[f521]) ).
cnf(s219,plain,
~ spl1_104,
inference(sat_conversion,[],[f7069]) ).
cnf(s245,plain,
( ~ spl1_13
| spl1_104 ),
inference(sat_conversion,[],[f7639]) ).
cnf(s248,plain,
~ spl1_13,
inference(rat,[],[s245,s219]) ).
cnf(s289,plain,
~ spl1_11,
inference(rat,[],[s13,s248]) ).
cnf(s290,plain,
$false,
inference(rat,[],[s12,s289]) ).
fof(f7640,plain,
$false,
inference(avatar_sat_refutation,[],[s290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM459+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n007.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 19:58:26 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 9.46/2.29 % (1743913)Detected formulas, will run a generic FOF schedule.
% 9.46/2.29 % (1743922)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=281667531:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.46/2.29 % (1743922)Instruction limit reached!
% 9.46/2.29 % (1743922)------------------------------
% 9.46/2.29 % (1743922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743922)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743922)Termination reason: Instruction limit
% 9.46/2.29 % (1743922)Termination phase: Saturation
% 9.46/2.29 % (1743922)Time elapsed: 0.034 s
% 9.46/2.29 % (1743922)Peak memory usage: 89 MB
% 9.46/2.29 % (1743922)Instructions burned: 119 (million)
% 9.46/2.29 % (1743920)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=3226265915:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.46/2.29 % (1743918)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=2179948948:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.46/2.29 % (1743919)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=3286612468:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.46/2.29 % (1743921)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2455716867:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.46/2.29 % (1743921)Refutation not found, incomplete strategy
% 9.46/2.29 % (1743921)------------------------------
% 9.46/2.29 % (1743921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743921)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743921)Termination reason: Refutation not found, incomplete strategy
% 9.46/2.29 % (1743921)Time elapsed: 0.001 s
% 9.46/2.29 % (1743921)Peak memory usage: 88 MB
% 9.46/2.29 % (1743923)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3855276536:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.46/2.29 % (1743924)dis-21_1_sil=8000:lcm=predicate:random_seed=1140727103: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)
% 9.46/2.29 % (1743924)Instruction limit reached!
% 9.46/2.29 % (1743924)------------------------------
% 9.46/2.29 % (1743924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743923)Instruction limit reached!
% 9.46/2.29 % (1743923)------------------------------
% 9.46/2.29 % (1743923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743923)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743923)Termination reason: Instruction limit
% 9.46/2.29 % (1743923)Termination phase: Saturation
% 9.46/2.29 % (1743924)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743923)Time elapsed: 0.082 s
% 9.46/2.29 % (1743923)Peak memory usage: 90 MB
% 9.46/2.29 % (1743924)Termination reason: Instruction limit
% 9.46/2.29 % (1743924)Termination phase: Saturation
% 9.46/2.29 % (1743924)Time elapsed: 0.077 s
% 9.46/2.29 % (1743923)Instructions burned: 140 (million)
% 9.46/2.29 % (1743924)Peak memory usage: 90 MB
% 9.46/2.29 % (1743924)Instructions burned: 131 (million)
% 9.46/2.29 % (1743930)lrs+10_1_sil=8000:sp=occurrence:random_seed=2062565834:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.46/2.29 % (1743930)Instruction limit reached!
% 9.46/2.29 % (1743930)------------------------------
% 9.46/2.29 % (1743930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743930)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743930)Termination reason: Instruction limit
% 9.46/2.29 % (1743930)Termination phase: Saturation
% 9.46/2.29 % (1743930)Time elapsed: 0.086 s
% 9.46/2.29 % (1743930)Peak memory usage: 92 MB
% 9.46/2.29 % (1743930)Instructions burned: 288 (million)
% 9.46/2.29 % (1743934)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2033694031:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.46/2.29 % (1743933)lrs+10_1_sil=32000:urr=on:br=off:random_seed=969629123:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.46/2.29 % (1743921)------------------------------
% 9.46/2.29 % (1743921)------------------------------
% 9.46/2.29 % (1743936)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=2974204188:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 9.46/2.29 % (1743933)Instruction limit reached!
% 9.46/2.29 % (1743933)------------------------------
% 9.46/2.29 % (1743933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743933)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743933)Termination reason: Instruction limit
% 9.46/2.29 % (1743933)Termination phase: Saturation
% 9.46/2.29 % (1743933)Time elapsed: 0.083 s
% 9.46/2.29 % (1743933)Peak memory usage: 90 MB
% 9.46/2.29 % (1743933)Instructions burned: 158 (million)
% 9.46/2.29 % (1743936)Instruction limit reached!
% 9.46/2.29 % (1743936)------------------------------
% 9.46/2.29 % (1743936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743936)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743936)Termination reason: Instruction limit
% 9.46/2.29 % (1743936)Termination phase: Saturation
% 9.46/2.29 % (1743936)Time elapsed: 0.063 s
% 9.46/2.29 % (1743936)Peak memory usage: 93 MB
% 9.46/2.29 % (1743936)Instructions burned: 250 (million)
% 9.46/2.29 % (1743939)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3514991041:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 9.46/2.29 % (1743939)Refutation not found, incomplete strategy
% 9.46/2.29 % (1743939)------------------------------
% 9.46/2.29 % (1743939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743939)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743939)Termination reason: Refutation not found, incomplete strategy
% 9.46/2.29 % (1743939)Time elapsed: 0.002 s
% 9.46/2.29 % (1743939)Peak memory usage: 88 MB
% 9.46/2.29 % (1743939)Instructions burned: 1 (million)
% 9.46/2.29 % (1743934)Instruction limit reached!
% 9.46/2.29 % (1743934)------------------------------
% 9.46/2.29 % (1743934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743934)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743934)Termination reason: Instruction limit
% 9.46/2.29 % (1743934)Termination phase: Saturation
% 9.46/2.29 % (1743934)Time elapsed: 0.190 s
% 9.46/2.29 % (1743934)Peak memory usage: 93 MB
% 9.46/2.29 % (1743934)Instructions burned: 325 (million)
% 9.46/2.29 % (1743942)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3297547885:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 9.46/2.29 % (1743941)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4210736056:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 9.46/2.29 % (1743942)Instruction limit reached!
% 9.46/2.29 % (1743942)------------------------------
% 9.46/2.29 % (1743942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743942)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743942)Termination reason: Instruction limit
% 9.46/2.29 % (1743942)Termination phase: Saturation
% 9.46/2.29 % (1743942)Time elapsed: 0.040 s
% 9.46/2.29 % (1743942)Peak memory usage: 90 MB
% 9.46/2.29 % (1743942)Instructions burned: 115 (million)
% 9.46/2.29 % (1743944)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3095589365:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 9.46/2.29 % (1743947)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3119052299:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 9.46/2.29 % (1743947)Instruction limit reached!
% 9.46/2.29 % (1743947)------------------------------
% 9.46/2.29 % (1743947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743947)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743947)Termination reason: Instruction limit
% 9.46/2.29 % (1743947)Termination phase: Saturation
% 9.46/2.29 % (1743947)Time elapsed: 0.037 s
% 9.46/2.29 % (1743947)Peak memory usage: 89 MB
% 9.46/2.29 % (1743947)Instructions burned: 116 (million)
% 9.46/2.29 % (1743944)Instruction limit reached!
% 9.46/2.29 % (1743944)------------------------------
% 9.46/2.29 % (1743944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743944)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743944)Termination reason: Instruction limit
% 9.46/2.29 % (1743944)Termination phase: Saturation
% 9.46/2.29 % (1743944)Time elapsed: 0.062 s
% 9.46/2.29 % (1743944)Peak memory usage: 89 MB
% 9.46/2.29 % (1743944)Instructions burned: 128 (million)
% 9.46/2.29 % (1743939)------------------------------
% 9.46/2.29 % (1743939)------------------------------
% 9.46/2.29 % (1743950)lrs+10_1_sil=8000:sp=occurrence:random_seed=2873570285:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.46/2.29 % (1743951)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3143294696:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 9.46/2.29 % (1743951)Refutation not found, incomplete strategy
% 9.46/2.29 % (1743951)------------------------------
% 9.46/2.29 % (1743951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743951)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743951)Termination reason: Refutation not found, incomplete strategy
% 9.46/2.29 % (1743951)Time elapsed: 0.002 s
% 9.46/2.29 % (1743951)Peak memory usage: 88 MB
% 9.46/2.29 % (1743951)Instructions burned: 2 (million)
% 9.46/2.29 % (1743952)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2076166730:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 9.46/2.29 % (1743950)Instruction limit reached!
% 9.46/2.29 % (1743950)------------------------------
% 9.46/2.29 % (1743950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743950)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743950)Termination reason: Instruction limit
% 9.46/2.29 % (1743950)Termination phase: Saturation
% 9.46/2.29 % (1743950)Time elapsed: 0.271 s
% 9.46/2.29 % (1743950)Peak memory usage: 102 MB
% 9.46/2.29 % (1743950)Instructions burned: 907 (million)
% 9.46/2.29 % (1743951)------------------------------
% 9.46/2.29 % (1743951)------------------------------
% 9.46/2.29 % (1743919)First to succeed.
% 9.46/2.29 % (1743919)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1743913"
% 9.46/2.29 % (1743956)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3709756178:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 9.46/2.29 % (1743956)Instruction limit reached!
% 9.46/2.29 % (1743956)------------------------------
% 9.46/2.29 % (1743956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.46/2.29 % (1743956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.46/2.29 % (1743956)CaDiCaL version: 2.1.3
% 9.46/2.29 % (1743956)Termination reason: Instruction limit
% 9.46/2.29 % (1743956)Termination phase: Saturation
% 9.46/2.29 % (1743956)Time elapsed: 0.034 s
% 9.46/2.29 % (1743956)Peak memory usage: 91 MB
% 9.46/2.29 % (1743956)Instructions burned: 140 (million)
% 9.46/2.29 % (1743957)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3290787797:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 9.46/2.29 % (1743918)Also succeeded, but the first one will report.
% 9.46/2.29 % (1743959)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2398285107:st=3:i=13193:sd=3:ss=axioms_2987 on theBenchmark for (2987ds/13193Mi)
% 9.46/2.29 % (1743919)Refutation found. Thanks to Tanya!
% 9.46/2.29 % SZS status Theorem for theBenchmark
% 9.46/2.29 % SZS output start Proof for theBenchmark
% See solution above
% 10.53/2.49 % (1743919)------------------------------
% 10.53/2.49 % (1743919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.53/2.49 % (1743919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.53/2.49 % (1743919)CaDiCaL version: 2.1.3
% 10.53/2.49 % (1743919)Termination reason: Refutation
% 10.53/2.49 % (1743919)Time elapsed: 1.003 s
% 10.53/2.49 % (1743919)Peak memory usage: 134 MB
% 10.53/2.49 % (1743919)Instructions burned: 1537 (million)
% 10.53/2.49 % (1743919)------------------------------
% 10.53/2.49 % (1743919)------------------------------
% 10.53/2.49 % (1743913)Success in time 1.415 s
% 10.53/2.49 % Vampire exiting
%------------------------------------------------------------------------------