%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM498+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 : Fri Sep 25 02:25:20 PM UTC 2026
% Result : Theorem 207.26s 32.80s
% Output : CNFRefutation 207.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 219 ( 60 unt; 0 def)
% Number of atoms : 788 ( 280 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 978 ( 409 ~; 431 |; 96 &)
% ( 12 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 244 ( 0 sgn 231 !; 13 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( X1 != sz00
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f42,axiom,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f46,conjecture,
( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( xk = sz10
| xk = sz00 )
=> ( doDivides0(xp,xm)
| doDivides0(xp,xn) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f52,plain,
( ( xk = sz10
| xk = sz00 )
& ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn) ),
inference(ennf_transformation,[],[f47]) ).
fof(f53,plain,
( ( xk = sz10
| xk = sz00 )
& ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn) ),
inference(flattening,[],[f52]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f62]) ).
fof(f68,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(flattening,[],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f86,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f96]) ).
fof(f100,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f101,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f100]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f106]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f111]) ).
fof(f115,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f117,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(rectify,[],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f120]) ).
fof(f123,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f124,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ( doDivides0(sK3(X0),X0)
& aNaturalNumber0(sK3(X0))
& sK3(X0) != X0
& sz10 != sK3(X0) )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f112]) ).
fof(f128,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f130,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f131,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f133,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f134,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f135,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f138,plain,
xm != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f141,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f142,plain,
( sz10 = xk
| sz00 = xk ),
inference(cnf_transformation,[],[f53]) ).
fof(f143,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f53]) ).
fof(f144,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f53]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f154,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f63]) ).
fof(f160,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f164,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f169,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f174,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f84]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f178,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f87]) ).
fof(f180,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f181,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f187,plain,
! [X2,X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 ),
inference(cnf_transformation,[],[f126]) ).
fof(f189,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f197,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f203,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f207,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f115]) ).
fof(f208,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f209,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f210,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f153]) ).
fof(f211,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f168]) ).
fof(f212,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f189]) ).
fof(f217,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f200]) ).
tcf(c_49,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f131]) ).
tcf(c_50,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f130]) ).
tcf(c_51,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f129]) ).
tcf(c_53,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f134]) ).
tcf(c_54,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f133]) ).
tcf(c_55,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f135]) ).
tcf(c_59,plain,
xm != xp,
inference(cnf_transformation,[],[f138]) ).
tcf(c_61,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f141]) ).
tcf(c_62,negated_conjecture,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f144]) ).
tcf(c_63,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f143]) ).
tcf(c_64,negated_conjecture,
( ( xk = sz10 )
| ( xk = sz00 ) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_81,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_97,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_111,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f212]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz10 )
| ( X0 = X1 )
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_123,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f203]) ).
tcf(c_125,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_127,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f209]) ).
tcf(c_128,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f208]) ).
tcf(c_133,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_150,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_170,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_111,c_123,c_111]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_86,c_101,c_86]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_84,c_71]) ).
tcf(c_1578,plain,
xp != sz00,
inference(resolution_lifted,[status(thm)],[c_53,c_170]) ).
tcf(c_3296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4506,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_50,c_81]) ).
tcf(c_4516,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_51,c_97]) ).
tcf(c_4517,plain,
sdtasdt0(sz00,sz00) = sz00,
inference(superposition,[status(thm)],[c_123,c_97]) ).
tcf(c_4642,plain,
( doDivides0(sz00,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_4517,c_172]) ).
tcf(c_4645,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_4516,c_172]) ).
tcf(c_4649,plain,
doDivides0(sz00,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_4642,c_123]) ).
tcf(c_4650,plain,
doDivides0(xp,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_4645,c_123,c_51]) ).
tcf(c_4680,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_4506,c_175]) ).
tcf(c_4686,plain,
sdtlseqdt0(sz00,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_4680,c_123,c_50]) ).
tcf(c_4861,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_100]) ).
tcf(c_5028,plain,
! [X0: $i] :
( doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,X0)
| ~ doDivides0(X0,xn) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_5029,plain,
( doDivides0(xp,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(sz00,xn)
| ~ doDivides0(xp,sz00) ),
inference(instantiation,[status(thm)],[c_5028]) ).
tcf(c_5030,plain,
! [X0: $i] :
( doDivides0(xp,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,X0)
| ~ doDivides0(X0,xm) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_5031,plain,
( doDivides0(xp,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ doDivides0(sz00,xm)
| ~ doDivides0(xp,sz00) ),
inference(instantiation,[status(thm)],[c_5030]) ).
tcf(c_5096,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,xn)
| ~ doDivides0(X1,X2)
| ( xn != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3296]) ).
tcf(c_5097,plain,
( doDivides0(sz00,xn)
| ~ doDivides0(sz00,sz00)
| ( sz00 != sz00 )
| ( xn != sz00 ) ),
inference(instantiation,[status(thm)],[c_5096]) ).
tcf(c_5121,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,xm)
| ~ doDivides0(X1,X2)
| ( xm != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3296]) ).
tcf(c_5122,plain,
( doDivides0(sz00,xm)
| ~ doDivides0(sz00,sz00)
| ( sz00 != sz00 )
| ( xm != sz00 ) ),
inference(instantiation,[status(thm)],[c_5121]) ).
tcf(c_5279,plain,
! [X0: $i] :
( ( xn = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xn,X0) != sz00 ) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_5501,plain,
! [X0: $i] :
( ( xm = X0 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xm,X0)
| ~ sdtlseqdt0(X0,xm) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_5505,plain,
( ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sz00,xm)
| ~ sdtlseqdt0(xm,sz00) ),
inference(instantiation,[status(thm)],[c_5501]) ).
tcf(c_5548,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ( sdtasdt0(xn,xm) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_54,c_102]) ).
tcf(c_5570,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ( sdtasdt0(xn,xm) = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5548,c_51]) ).
tcf(c_8723,plain,
( ( xp = sz00 )
| ( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_54,c_122]) ).
tcf(c_8772,plain,
( ( xp = sz00 )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(light_normalisation,[status(thm)],[c_8723,c_61]) ).
tcf(c_8773,plain,
( ( xp = sz00 )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8772,c_51]) ).
tcf(c_9137,plain,
( ( xm = sz00 )
| ( xn = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xn,xm) != sz00 ) ),
inference(instantiation,[status(thm)],[c_5279]) ).
tcf(c_18692,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_50,c_4861]) ).
tcf(c_18820,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_18692,c_101]) ).
tcf(c_18827,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_18820,c_50,c_49]) ).
tcf(c_325989,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_50,c_81]) ).
tcf(c_326657,plain,
sdtasdt0(xn,sz00) = sz00,
inference(superposition,[status(thm)],[c_49,c_97]) ).
tcf(c_326659,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_51,c_97]) ).
tcf(c_326753,plain,
! [X0: $i] :
( ( xn = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xn,X0) != sz00 ) ),
inference(superposition,[status(thm)],[c_326657,c_95]) ).
tcf(c_326756,plain,
! [X0: $i] :
( ( xn = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xn,X0) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_326753,c_123,c_49]) ).
tcf(c_326865,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_100]) ).
tcf(c_327030,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ( sdtasdt0(xn,xm) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_54,c_102]) ).
tcf(c_327032,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ( sdtasdt0(xn,xm) = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_327030,c_51]) ).
tcf(c_328125,plain,
( ( xp = sz00 )
| ( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_54,c_122]) ).
tcf(c_328129,plain,
( ( xp = sz00 )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(light_normalisation,[status(thm)],[c_328125,c_61]) ).
tcf(c_328130,plain,
( ( xp = sz00 )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_328129,c_51]) ).
tcf(c_328193,plain,
sdtasdt0(xn,sz10) = xn,
inference(superposition,[status(thm)],[c_49,c_125]) ).
tcf(c_328195,plain,
sdtasdt0(xp,sz10) = xp,
inference(superposition,[status(thm)],[c_51,c_125]) ).
tcf(c_328553,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_325989,c_175]) ).
tcf(c_328564,plain,
sdtlseqdt0(sz00,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_328553,c_123,c_50]) ).
tcf(c_329429,plain,
( ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,sz00) ),
inference(superposition,[status(thm)],[c_328564,c_117]) ).
tcf(c_329436,plain,
( ( xm = sz00 )
| ~ sdtlseqdt0(xm,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_329429,c_123,c_50]) ).
tcf(c_336983,plain,
~ sdtlseqdt0(xm,sz00),
inference(global_subsumption_just,[status(thm)],[c_329436,c_123,c_51,c_50,c_63,c_133,c_150,c_4650,c_4649,c_4686,c_5031,c_5122,c_5505]) ).
tcf(c_351952,plain,
! [X0: $i] :
( ( sdtasdt0(xn,X0) != sz00 )
| ~ aNaturalNumber0(X0)
| ( X0 = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_326756,c_123,c_51,c_49,c_62,c_133,c_150,c_4650,c_4649,c_5029,c_5097,c_5279]) ).
tcf(c_351953,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xn,X0) != sz00 ) ),
inference(renaming,[status(thm)],[c_351952]) ).
tcf(c_351961,plain,
( ( sz00 = sz10 )
| ~ aNaturalNumber0(sz10)
| ( xn != sz00 ) ),
inference(superposition,[status(thm)],[c_328193,c_351953]) ).
tcf(c_351966,plain,
xn != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_351961,c_128,c_127]) ).
tcf(c_354503,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_50,c_326865]) ).
tcf(c_359255,plain,
sdtlseqdt0(xp,sdtasdt0(xn,xm)),
inference(global_subsumption_just,[status(thm)],[c_327032,c_123,c_51,c_50,c_49,c_63,c_62,c_133,c_150,c_4650,c_4649,c_5029,c_5031,c_5097,c_5122,c_5570,c_9137,c_18827]) ).
tcf(c_384405,plain,
( doDivides0(xm,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_354503,c_172]) ).
tcf(c_384410,plain,
( sdtlseqdt0(xm,sdtasdt0(xn,xm))
| ( xn = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_354503,c_89]) ).
tcf(c_384426,plain,
doDivides0(xm,sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_384405,c_50,c_49]) ).
tcf(c_384429,plain,
sdtlseqdt0(xm,sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_384410,c_351966,c_50,c_49]) ).
tcf(c_392612,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(global_subsumption_just,[status(thm)],[c_328130,c_1578,c_8773,c_18827]) ).
tcf(c_392615,plain,
sdtlseqdt0(xm,sdtasdt0(xp,xk)),
inference(demodulation,[status(thm)],[c_384429,c_392612]) ).
tcf(c_392618,plain,
doDivides0(xm,sdtasdt0(xp,xk)),
inference(demodulation,[status(thm)],[c_384426,c_392612]) ).
tcf(c_392623,plain,
sdtlseqdt0(xp,sdtasdt0(xp,xk)),
inference(demodulation,[status(thm)],[c_359255,c_392612]) ).
tcf(c_396175,plain,
( doDivides0(xm,sdtasdt0(xp,sz10))
| ( xk = sz00 ) ),
inference(superposition,[status(thm)],[c_64,c_392618]) ).
tcf(c_396208,plain,
( doDivides0(xm,xp)
| ( xk = sz00 ) ),
inference(light_normalisation,[status(thm)],[c_396175,c_328195]) ).
tcf(c_399145,plain,
( ( xk = sz00 )
| ( xm = sz10 )
| ( xm = xp )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_396208,c_113]) ).
tcf(c_399173,plain,
( ( xk = sz00 )
| ( xm = sz10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_399145,c_59,c_53,c_51,c_50]) ).
tcf(c_452925,plain,
( sdtlseqdt0(xm,sdtasdt0(xp,sz00))
| ( xm = sz10 ) ),
inference(superposition,[status(thm)],[c_399173,c_392615]) ).
tcf(c_452948,plain,
( sdtlseqdt0(xm,sz00)
| ( xm = sz10 ) ),
inference(light_normalisation,[status(thm)],[c_452925,c_326659]) ).
tcf(c_452949,plain,
xm = sz10,
inference(forward_subsumption_resolution,[status(thm)],[c_452948,c_336983]) ).
tcf(c_452997,plain,
sdtasdt0(xn,sz10) = sdtasdt0(xp,xk),
inference(demodulation,[status(thm)],[c_392612,c_452949]) ).
tcf(c_453107,plain,
sdtasdt0(xp,xk) = xn,
inference(light_normalisation,[status(thm)],[c_452997,c_328193]) ).
tcf(c_453119,plain,
sdtlseqdt0(xp,xn),
inference(demodulation,[status(thm)],[c_392623,c_453107]) ).
tcf(c_453122,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_453119,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM498+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n018.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Thu Sep 24 04:20:05 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.63
% 0.15/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.63
% 0.15/0.64 % Detected problem language: tptp
% 0.15/0.65 % Proving...
% 207.26/32.80 % SZS status Started for theBenchmark.p
% 207.26/32.80 % SZS status Theorem for theBenchmark.p
% 207.26/32.80
% 207.26/32.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 207.26/32.80
% 207.26/32.80 % ------ iProver source info
% 207.26/32.80
% 207.26/32.80 % git: date: 2026-07-19 20:42:38 +0200
% 207.26/32.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 207.26/32.80 % git: non_committed_changes: false
% 207.26/32.80
% 207.26/32.80 % ------ Parsing...
% 207.26/32.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 207.26/32.80
% 207.26/32.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 207.26/32.80
% 207.26/32.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 207.26/32.80
% 207.26/32.80 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 207.26/32.80 % ------ Proving...
% 207.26/32.80 % ------ Problem Properties
% 207.26/32.80
% 207.26/32.80 %
% 207.26/32.80 % clauses 75
% 207.26/32.80 % conjectures 3
% 207.26/32.80 % EPR 27
% 207.26/32.80 % Horn 49
% 207.26/32.80 % unary 19
% 207.26/32.80 % binary 8
% 207.26/32.80 % lits 263
% 207.26/32.80 % lits eq 74
% 207.26/32.80 % fd_pure 0
% 207.26/32.80 % fd_pseudo 0
% 207.26/32.80 % fd_cond 15
% 207.26/32.80 % fd_pseudo_cond 11
% 207.26/32.80 % AC symbols 0
% 207.26/32.80
% 207.26/32.80 % ------ Schedule dynamic 5 is on
% 207.26/32.80
% 207.26/32.80 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 207.26/32.80
% 207.26/32.80
% 207.26/32.80 % ------
% 207.26/32.80 % Current options:
% 207.26/32.80 % ------
% 207.26/32.80
% 207.26/32.80
% 207.26/32.80 %
% 207.26/32.80
% 207.26/32.80 % ------ Proving...
% 207.26/32.80 % Proof_search_loop: time out after: 3050 full_loop iterations
% 207.26/32.80
% 207.26/32.80 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 207.26/32.80
% 207.26/32.80
% 207.26/32.80 % ------
% 207.26/32.80 % Current options:
% 207.26/32.80 % ------
% 207.26/32.80
% 207.26/32.80
% 207.26/32.80 %
% 207.26/32.80
% 207.26/32.80 % ------ Proving...
% 207.26/32.80 % Proof_search_loop: time out after: 4611 full_loop iterations
% 207.26/32.80
% 207.26/32.80 % ------ Option_1: Negative Selections Time Limit: 35.
% 207.26/32.80
% 207.26/32.80
% 207.26/32.80 % ------
% 207.26/32.80 % Current options:
% 207.26/32.80 % ------
% 207.26/32.80
% 207.26/32.80
% 207.26/32.80 %
% 207.26/32.80
% 207.26/32.80 % ------ Proving...
% 207.26/32.80 %
% 207.26/32.80
% 207.26/32.80 % SZS status Theorem for theBenchmark.p
% 207.26/32.80
% 207.26/32.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 207.26/32.80
% 207.26/32.80
%------------------------------------------------------------------------------