%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM496+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:25:20 PM UTC 2026
% Result : Theorem 7.61s 1.78s
% Output : CNFRefutation 7.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of formulae : 123 ( 24 unt; 1 def)
% Number of atoms : 512 ( 208 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 635 ( 246 ~; 247 |; 126 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn 119 !; 26 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f38,axiom,
! [X0] :
( ( X0 != sz10
& X0 != sz00
& aNaturalNumber0(X0) )
=> ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(f46,axiom,
( ( doDivides0(xp,xm)
& ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) )
| ( doDivides0(xp,xr)
& ? [X0] :
( xr = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2027) ).
fof(f47,conjecture,
( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ( doDivides0(xp,xm)
| ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
| doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f52,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
inference(rectify,[],[f41]) ).
fof(f53,plain,
( ( doDivides0(xp,xm)
& ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
| ( doDivides0(xp,xr)
& ? [X0] :
( xr = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
inference(rectify,[],[f46]) ).
fof(f54,plain,
~ ( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f48]) ).
fof(f63,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f68,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f76]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(flattening,[],[f107]) ).
fof(f115,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(f116,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f118,plain,
! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
inference(flattening,[],[f117]) ).
fof(f121,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(ennf_transformation,[],[f52]) ).
fof(f122,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
( ~ doDivides0(xp,xm)
& ! [X1] :
( xm != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) )
& ~ doDivides0(xp,xn)
& ! [X0] :
( xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f54]) ).
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(nnf_transformation,[],[f116]) ).
fof(f140,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,[],[f139]) ).
fof(f141,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,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ( doDivides0(sK5(X0),X0)
& aNaturalNumber0(sK5(X0))
& sK5(X0) != X0
& sz10 != sK5(X0) )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f141]) ).
fof(f143,plain,
! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ( isPrime0(sK6(X0))
& doDivides0(sK6(X0),X0)
& aNaturalNumber0(sK6(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f118]) ).
fof(f152,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK11)
& aNaturalNumber0(sK11)
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11)],[f122]) ).
fof(f159,plain,
( sP2
| ( doDivides0(xp,xr)
& xr = sdtasdt0(xp,sK16)
& aNaturalNumber0(sK16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f128]) ).
fof(f160,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f162,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f167,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f63]) ).
fof(f172,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f181,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f219,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz10 != X0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f225,plain,
! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| isPrime0(sK6(X0)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f226,plain,
! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| doDivides0(sK6(X0),X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f227,plain,
! [X0] :
( sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK6(X0)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f228,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f251,plain,
! [X0] :
( ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0)
| xp = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f152]) ).
fof(f252,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| xp = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f152]) ).
fof(f253,plain,
sz10 != xp,
inference(cnf_transformation,[],[f152]) ).
fof(f254,plain,
sz00 != xp,
inference(cnf_transformation,[],[f152]) ).
fof(f259,plain,
xn = sdtpldt0(xp,xr),
inference(cnf_transformation,[],[f43]) ).
fof(f260,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f43]) ).
fof(f271,plain,
( sP2
| doDivides0(xp,xr) ),
inference(cnf_transformation,[],[f159]) ).
fof(f274,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f123]) ).
fof(f276,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f123]) ).
fof(f289,plain,
( ~ aNaturalNumber0(sz10)
| ~ isPrime0(sz10) ),
inference(equality_resolution,[],[f219]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f160]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f162]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_101,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,[],[f213]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_111,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_113,plain,
! [X0: $i] :
( aNaturalNumber0(sK6(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_114,plain,
! [X0: $i] :
( doDivides0(sK6(X0),X0)
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_115,plain,
! [X0: $i] :
( isPrime0(sK6(X0))
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f228]) ).
tcf(c_135,plain,
sz00 != xp,
inference(cnf_transformation,[],[f254]) ).
tcf(c_136,plain,
sz10 != xp,
inference(cnf_transformation,[],[f253]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( ( X0 = xp )
| ( X0 = sz10 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != xp ) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_138,plain,
! [X0: $i] :
( ( X0 = xp )
| ( X0 = sz10 )
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_146,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f260]) ).
tcf(c_147,plain,
sdtpldt0(xp,xr) = xn,
inference(cnf_transformation,[],[f259]) ).
tcf(c_161,plain,
( sP2
| doDivides0(xp,xr) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_163,negated_conjecture,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f276]) ).
tcf(c_165,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f274]) ).
tcf(c_173,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_200,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_237,plain,
~ isPrime0(sz10),
inference(global_subsumption_just,[status(thm)],[c_111,c_50,c_111]) ).
tcf(c_7497,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_7499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_7506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_7508,plain,
! [X0: $i,X1: $i] :
( isPrime0(X0)
| ~ isPrime0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9221,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ( sz10 != X0 ) ),
inference(resolution,[status(thm)],[c_7508,c_237]) ).
tcf(c_9248,plain,
! [X0: $i] :
( ( xp != X0 )
| ( sz00 != X0 ) ),
inference(resolution,[status(thm)],[c_7499,c_135]) ).
tcf(c_9249,plain,
( ( xp != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_9248]) ).
tcf(c_9250,plain,
! [X0: $i] :
( ( xp != X0 )
| ( sz10 != X0 ) ),
inference(resolution,[status(thm)],[c_7499,c_136]) ).
tcf(c_9259,plain,
! [X0: $i,X1: $i] :
( ~ isPrime0(X0)
| ( sz10 != X1 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_7499,c_9221]) ).
tcf(c_9271,plain,
! [X0: $i,X1: $i] :
( ( xp != X1 )
| ( sz10 != X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_9250,c_7499]) ).
tcf(c_9389,plain,
( ( xp = xp )
| ( xp = sz10 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ( sdtasdt0(xp,sz10) != xp ) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_9390,plain,
( ( sdtasdt0(xp,sz10) = xp )
| ~ aNaturalNumber0(xp) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_9660,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ( X0 != sz10 ) ),
inference(resolution,[status(thm)],[c_9259,c_7497]) ).
tcf(c_9695,plain,
! [X0: $i] :
( doDivides0(X0,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,xr)
| ~ doDivides0(X0,xp) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_10364,plain,
( ( xp != sz10 )
| ( sz10 != sz10 ) ),
inference(factoring,[status(thm)],[c_9271]) ).
tcf(c_10365,plain,
xp != sz10,
inference(equality_resolution_simp,[status(thm)],[c_10364]) ).
tcf(c_10366,plain,
! [X0: $i] :
( ( sz10 != X0 )
| ( X0 != xp ) ),
inference(resolution,[status(thm)],[c_9271,c_7497]) ).
tcf(c_10663,plain,
( isPrime0(sK6(xp))
| ( xp = sz10 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_10664,plain,
( aNaturalNumber0(sK6(xp))
| ( xp = sz10 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_10683,plain,
! [X0: $i,X1: $i] :
( ( xp = X0 )
| ( xp != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_7499]) ).
tcf(c_12288,plain,
! [X0: $i,X1: $i] :
( doDivides0(xp,xn)
| ~ doDivides0(X1,X0)
| ( xp != X1 )
| ( xn != X0 ) ),
inference(instantiation,[status(thm)],[c_7506]) ).
tcf(c_12501,plain,
! [X0: $i] :
( doDivides0(xp,xn)
| ~ doDivides0(X0,xn)
| ( xp != X0 )
| ( xn != xn ) ),
inference(instantiation,[status(thm)],[c_12288]) ).
tcf(c_12502,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_7497]) ).
tcf(c_18793,plain,
! [X0: $i] :
( ( xp = X0 )
| ( xp != xp )
| ( X0 != xp ) ),
inference(instantiation,[status(thm)],[c_10683]) ).
tcf(c_21056,plain,
! [X0: $i] :
( ( X0 = xp )
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp) ),
inference(resolution,[status(thm)],[c_138,c_9660]) ).
tcf(c_21685,plain,
! [X0: $i] :
( doDivides0(X0,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xr)
| ~ doDivides0(X0,xp) ),
inference(superposition,[status(thm)],[c_147,c_102]) ).
tcf(c_23732,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp)
| ( sz10 != X0 ) ),
inference(resolution,[status(thm)],[c_21056,c_10366]) ).
fof(f127,definition,
( ~ sP2
| ( doDivides0(xp,xm)
& ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f128,plain,
( sP2
| ( doDivides0(xp,xr)
& ? [X0] :
( xr = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
inference(definition_folding,[],[f53,f127]) ).
fof(f156,plain,
( ~ sP2
| ( doDivides0(xp,xm)
& ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) ) ),
inference(nnf_transformation,[],[f127]) ).
fof(f157,plain,
( ~ sP2
| ( doDivides0(xp,xm)
& ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
inference(rectify,[],[f156]) ).
fof(f158,plain,
( ~ sP2
| ( doDivides0(xp,xm)
& xm = sdtasdt0(xp,sK15)
& aNaturalNumber0(sK15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f157]) ).
fof(f268,plain,
( ~ sP2
| doDivides0(xp,xm) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_158,plain,
( doDivides0(xp,xm)
| ~ sP2 ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_23734,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp) ),
inference(global_subsumption_just,[status(thm)],[c_23732,c_146,c_118,c_50,c_165,c_163,c_161,c_158,c_9389,c_9390,c_9695,c_10365,c_12501,c_12502,c_18793,c_21056,c_21685]) ).
tcf(c_23739,plain,
( ( xp = sz10 )
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ isPrime0(sK6(xp))
| ~ aNaturalNumber0(sK6(xp)) ),
inference(resolution,[status(thm)],[c_23734,c_114]) ).
tcf(c_23740,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_23739,c_10663,c_10664,c_10365,c_9249,c_200,c_173,c_49,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM496+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:17:14 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 7.61/1.78 % SZS status Started for theBenchmark.p
% 7.61/1.78 % SZS status Theorem for theBenchmark.p
% 7.61/1.78
% 7.61/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.61/1.78
% 7.61/1.78 % ------ iProver source info
% 7.61/1.78
% 7.61/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 7.61/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.61/1.78 % git: non_committed_changes: false
% 7.61/1.78
% 7.61/1.78 % ------ Parsing...
% 7.61/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.61/1.78
% 7.61/1.78 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.61/1.78
% 7.61/1.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.61/1.78
% 7.61/1.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.61/1.78 % ------ Proving...
% 7.61/1.78 % ------ Problem Properties
% 7.61/1.78
% 7.61/1.78 %
% 7.61/1.78 % clauses 109
% 7.61/1.78 % conjectures 4
% 7.61/1.78 % EPR 35
% 7.61/1.78 % Horn 71
% 7.61/1.78 % unary 32
% 7.61/1.78 % binary 13
% 7.61/1.78 % lits 373
% 7.61/1.78 % lits eq 109
% 7.61/1.78 % fd_pure 0
% 7.61/1.78 % fd_pseudo 0
% 7.61/1.78 % fd_cond 22
% 7.61/1.78 % fd_pseudo_cond 11
% 7.61/1.78 % AC symbols 0
% 7.61/1.78
% 7.61/1.78 % ------ Input Options Time Limit: Unbounded
% 7.61/1.78
% 7.61/1.78
% 7.61/1.78 % ------
% 7.61/1.78 % Current options:
% 7.61/1.78 % ------
% 7.61/1.78
% 7.61/1.78
% 7.61/1.78 %
% 7.61/1.78
% 7.61/1.78 % ------ Proving...
% 7.61/1.78 %
% 7.61/1.78
% 7.61/1.78 % SZS status Theorem for theBenchmark.p
% 7.61/1.78
% 7.61/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.61/1.78
% 7.61/1.78
%------------------------------------------------------------------------------