%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM518+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 : n012.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 02:25:48 PM UTC 2026
% Result : Theorem 31.25s 11.74s
% Output : CNFRefutation 31.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 128 ( 36 unt; 0 def)
% Number of atoms : 471 ( 152 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 591 ( 248 ~; 252 |; 69 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 133 !; 8 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
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(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(f44,axiom,
( sdtlseqdt0(xm,xp)
& xm != xp
& sdtlseqdt0(xn,xp)
& xn != xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f53,axiom,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& sdtsldt0(xn,xr) != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(f55,axiom,
( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2645) ).
fof(f56,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f62]) ).
fof(f74,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)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f92]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f106]) ).
fof(f108,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(f109,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,[],[f108]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f117,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f116]) ).
fof(f120,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(f121,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f120]) ).
fof(f127,plain,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,xn) ),
inference(ennf_transformation,[],[f57]) ).
fof(f133,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,[],[f107]) ).
fof(f134,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,[],[f133]) ).
fof(f135,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))],[f134]) ).
fof(f136,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,[],[f109]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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,[],[f121]) ).
fof(f139,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,[],[f138]) ).
fof(f140,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,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ( doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0))
& sK2(X0) != X0
& sz10 != sK2(X0) )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f140]) ).
fof(f143,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f147,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f157,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f74]) ).
fof(f174,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f137]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f137]) ).
fof(f199,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f203,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f141]) ).
fof(f211,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f213,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f221,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f228,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f230,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f236,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f237,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f53]) ).
fof(f238,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f53]) ).
fof(f240,plain,
( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f241,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f127]) ).
fof(f242,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f127]) ).
fof(f249,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f192]) ).
fof(f251,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f194]) ).
fof(f252,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f193]) ).
fof(f253,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f203]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f143]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_110,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f213]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f211]) ).
tcf(c_125,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f221]) ).
tcf(c_133,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f230]) ).
tcf(c_135,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f228]) ).
tcf(c_141,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f236]) ).
tcf(c_142,plain,
sdtsldt0(xn,xr) != xn,
inference(cnf_transformation,[],[f238]) ).
tcf(c_143,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f237]) ).
tcf(c_145,plain,
( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_146,negated_conjecture,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f242]) ).
tcf(c_147,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f241]) ).
tcf(c_191,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(prop_impl_just,[status(thm)],[c_49,c_110]) ).
tcf(c_560,plain,
( ~ aNaturalNumber0(sz00)
| ( sz00 != xr ) ),
inference(resolution_lifted,[status(thm)],[c_191,c_135]) ).
tcf(c_1596,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1598,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i] :
( doDivides0(xp,xn)
| ~ doDivides0(X1,X0)
| ( xp != X1 )
| ( xn != X0 ) ),
inference(instantiation,[status(thm)],[c_1605]) ).
tcf(c_1767,plain,
doDivides0(xp,sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_145,c_147,c_145]) ).
tcf(c_1794,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_62]) ).
tcf(c_1831,plain,
doDivides0(xp,sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_145,c_147,c_145]) ).
tcf(c_2001,plain,
sdtasdt0(xr,sz00) = sz00,
inference(superposition,[status(thm)],[c_133,c_62]) ).
tcf(c_2528,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
tcf(c_2592,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_1767,c_104]) ).
tcf(c_2597,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(global_subsumption_just,[status(thm)],[c_2592,c_118,c_2592]) ).
tcf(c_2671,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_1596]) ).
tcf(c_2925,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_1596]) ).
tcf(c_3134,plain,
( ( sdtsldt0(xn,xr) = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_143,c_80]) ).
tcf(c_3145,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(global_subsumption_just,[status(thm)],[c_3134,c_116,c_142,c_3134]) ).
tcf(c_3403,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_1831,c_104]) ).
tcf(c_3408,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(global_subsumption_just,[status(thm)],[c_3403,c_118,c_2592]) ).
tcf(c_3659,plain,
! [X0: $i] :
( sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xp,X0) ),
inference(superposition,[status(thm)],[c_125,c_81]) ).
tcf(c_3677,plain,
! [X0: $i] :
( sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xp,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3659,c_118,c_116,c_3659]) ).
tcf(c_4463,plain,
( ( sz00 = xr )
| ( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_141,c_100]) ).
tcf(c_4800,plain,
! [X0: $i,X1: $i] :
( ( xn = X0 )
| ( xn != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1598]) ).
tcf(c_6004,plain,
( ( sz00 = xr )
| ( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_141,c_100]) ).
tcf(c_6007,plain,
sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
inference(global_subsumption_just,[status(thm)],[c_6004,c_133,c_116,c_49,c_560,c_4463]) ).
tcf(c_6716,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_1794,c_2528]) ).
tcf(c_10287,plain,
! [X0: $i] :
( doDivides0(xp,xn)
| ~ doDivides0(xp,X0)
| ( xp != xp )
| ( xn != X0 ) ),
inference(instantiation,[status(thm)],[c_1705]) ).
tcf(c_10288,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,sz00)
| ( xp != xp )
| ( xn != sz00 ) ),
inference(instantiation,[status(thm)],[c_10287]) ).
tcf(c_11878,plain,
! [X0: $i] :
( ( xn = X0 )
| ( xn != xn )
| ( X0 != xn ) ),
inference(instantiation,[status(thm)],[c_4800]) ).
tcf(c_11879,plain,
( ( xn = sz00 )
| ( xn != xn )
| ( sz00 != xn ) ),
inference(instantiation,[status(thm)],[c_11878]) ).
tcf(c_32536,plain,
( sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_2597,c_3677]) ).
tcf(c_32543,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtsldt0(xn,xr) = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_32536,c_3145,c_32536]) ).
tcf(c_32544,plain,
( ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(renaming,[status(thm)],[c_32543]) ).
tcf(c_33225,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ( sdtsldt0(xn,xr) = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_3408,c_32544]) ).
tcf(c_33226,plain,
( ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(renaming,[status(thm)],[c_33225]) ).
tcf(c_33229,plain,
( ( sz00 = xr )
| ( sdtsldt0(xn,xr) = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn) ),
inference(superposition,[status(thm)],[c_99,c_33226]) ).
tcf(c_33230,plain,
sdtsldt0(xn,xr) = sz00,
inference(global_subsumption_just,[status(thm)],[c_33229,c_133,c_116,c_49,c_141,c_560,c_33229]) ).
tcf(c_33271,plain,
sdtasdt0(xr,sz00) = xn,
inference(demodulation,[status(thm)],[c_6007,c_33230]) ).
tcf(c_33320,plain,
sz00 = xn,
inference(demodulation,[status(thm)],[c_2001,c_33271]) ).
tcf(c_33321,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_33320,c_11879,c_10288,c_6716,c_2925,c_2671,c_146,c_49,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM518+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.34 % Computer : n012.cluster.edu
% 0.08/5.34 % Model : x86_64 x86_64
% 0.08/5.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.34 % Memory : 8046.5625MB
% 0.08/5.34 % OS : Linux 6.8.0-71-generic
% 0.08/5.34 % CPULimit : 300
% 0.08/5.34 % WCLimit : 300
% 0.08/5.34 % DateTime : Thu Sep 24 04:24:22 UTC 2026
% 0.08/5.35 % CPUTime :
% 0.08/5.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.38 Running first-order theorem proving
% 0.08/5.38 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
% 0.08/5.39
% 0.08/5.39 % ======== iProver multi-core TPTP/SMT =========
% 0.08/5.39
% 0.08/5.39 % Detected problem language: tptp
% 0.11/5.40 % Proving...
% 31.25/11.74 % SZS status Started for theBenchmark.p
% 31.25/11.74 % SZS status Theorem for theBenchmark.p
% 31.25/11.74
% 31.25/11.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.25/11.74
% 31.25/11.74 % ------ iProver source info
% 31.25/11.74
% 31.25/11.74 % git: date: 2026-07-19 20:42:38 +0200
% 31.25/11.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.25/11.74 % git: non_committed_changes: false
% 31.25/11.74
% 31.25/11.74 % ------ Parsing...
% 31.25/11.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.25/11.74
% 31.25/11.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e sf_s rm: 1 0s sf_e pe_s pe_e %
% 31.25/11.74
% 31.25/11.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 31.25/11.74
% 31.25/11.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.25/11.74 % ------ Proving...
% 31.25/11.74 % ------ Problem Properties
% 31.25/11.74
% 31.25/11.74 %
% 31.25/11.74 % clauses 95
% 31.25/11.74 % conjectures 2
% 31.25/11.74 % EPR 35
% 31.25/11.74 % Horn 67
% 31.25/11.74 % unary 30
% 31.25/11.74 % binary 10
% 31.25/11.74 % lits 321
% 31.25/11.74 % lits eq 88
% 31.25/11.74 % fd_pure 0
% 31.25/11.74 % fd_pseudo 0
% 31.25/11.74 % fd_cond 15
% 31.25/11.74 % fd_pseudo_cond 15
% 31.25/11.74 % AC symbols 0
% 31.25/11.74
% 31.25/11.74 % ------ Input Options Time Limit: Unbounded
% 31.25/11.74
% 31.25/11.74
% 31.25/11.74 % ------
% 31.25/11.74 % Current options:
% 31.25/11.74 % ------
% 31.25/11.74
% 31.25/11.74
% 31.25/11.74 %
% 31.25/11.74
% 31.25/11.74 % ------ Proving...
% 31.25/11.74 %
% 31.25/11.74
% 31.25/11.74 % SZS status Theorem for theBenchmark.p
% 31.25/11.74
% 31.25/11.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.25/11.74
% 31.25/11.74
%------------------------------------------------------------------------------