%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM529+3 : 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 02:25:51 PM UTC 2026
% Result : Theorem 17.84s 3.71s
% Output : CNFRefutation 17.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 137 ( 39 unt; 0 def)
% Number of atoms : 572 ( 215 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 719 ( 284 ~; 305 |; 104 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 176 ( 0 sgn 160 !; 16 ?; 46 :)
% 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(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
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(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(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& X0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
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(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
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(f40,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& X1 != sz00
& X0 != sz00
& aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X2,sdtasdt0(X1,X1)) = sdtasdt0(X0,X0)
=> ( iLess0(X0,xn)
=> ~ ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X3 = X2
| X3 = sz10 ) )
& X2 != sz10 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2963) ).
fof(f43,axiom,
( isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(f44,axiom,
( doDivides0(xp,xn)
& ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(f45,axiom,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(f46,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(f47,axiom,
( sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) )
& xm != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3124) ).
fof(f52,plain,
( doDivides0(xp,xn)
& ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f44]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f54]) ).
fof(f62,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f67,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f73,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(f74,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,[],[f73]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f79]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f84]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(flattening,[],[f92]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f98]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f110]) ).
fof(f120,plain,
! [X0,X1,X2] :
( sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ( ~ isPrime0(X2)
& ( ? [X3] :
( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3)
& X2 != X3
& sz10 != X3 )
| sz10 = X2 ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f121,plain,
! [X0,X1,X2] :
( sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ( ~ isPrime0(X2)
& ( ? [X3] :
( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3)
& X2 != X3
& sz10 != X3 )
| sz10 = X2 ) ) ),
inference(flattening,[],[f120]) ).
fof(f122,plain,
( isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10 ),
inference(ennf_transformation,[],[f43]) ).
fof(f123,plain,
( isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10 ),
inference(flattening,[],[f122]) ).
fof(f124,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,[],[f80]) ).
fof(f125,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,[],[f124]) ).
fof(f126,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))],[f125]) ).
fof(f139,plain,
! [X0,X1,X2] :
( sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ( ~ isPrime0(X2)
& ( ( doDivides0(sK4(X2),X2)
& sdtasdt0(sK4(X2),sK5(X2)) = X2
& aNaturalNumber0(sK5(X2))
& aNaturalNumber0(sK4(X2))
& sK4(X2) != X2
& sz10 != sK4(X2) )
| sz10 = X2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X3,sK4(X2)),skolemize(X4,sK5(X2))],[f121]) ).
fof(f140,plain,
( doDivides0(xp,xn)
& xn = sdtasdt0(xp,sK7)
& aNaturalNumber0(sK7)
& doDivides0(xp,sdtasdt0(xn,xn))
& sdtasdt0(xn,xn) = sdtasdt0(xp,sK6)
& aNaturalNumber0(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f52]) ).
fof(f141,plain,
( sdtlseqdt0(xm,xn)
& xn = sdtpldt0(xm,sK8)
& aNaturalNumber0(sK8)
& xm != xn ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f47]) ).
fof(f142,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f143,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f144,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f145,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f149,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f62]) ).
fof(f154,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f67]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f173,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f85]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f187,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f188,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f198,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f211,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f212,plain,
sz00 != xm,
inference(cnf_transformation,[],[f40]) ).
fof(f213,plain,
sz00 != xn,
inference(cnf_transformation,[],[f40]) ).
fof(f214,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f215,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f216,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f217,plain,
! [X2,X0,X1] :
( sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ~ isPrime0(X2) ),
inference(cnf_transformation,[],[f139]) ).
fof(f225,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f123]) ).
fof(f229,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f140]) ).
fof(f236,plain,
xn = sdtasdt0(xp,xq),
inference(cnf_transformation,[],[f45]) ).
fof(f237,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f45]) ).
fof(f238,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f46]) ).
fof(f239,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f141]) ).
fof(f242,plain,
xn != xm,
inference(cnf_transformation,[],[f141]) ).
fof(f243,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f168]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f142]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f144]) ).
tcf(c_51,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f143]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_68,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,[],[f162]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sz00 )
| ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X2,X1) ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_117,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f216]) ).
tcf(c_118,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f215]) ).
tcf(c_119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f214]) ).
tcf(c_120,plain,
sz00 != xn,
inference(cnf_transformation,[],[f213]) ).
tcf(c_121,plain,
sz00 != xm,
inference(cnf_transformation,[],[f212]) ).
tcf(c_122,plain,
sz00 != xp,
inference(cnf_transformation,[],[f211]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sz00 )
| ( X1 = sz00 )
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ iLess0(X2,xn)
| ( sdtasdt0(X0,sdtasdt0(X1,X1)) != sdtasdt0(X2,X2) ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_134,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f225]) ).
tcf(c_140,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f229]) ).
tcf(c_141,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f237]) ).
tcf(c_142,plain,
sdtasdt0(xp,xq) = xn,
inference(cnf_transformation,[],[f236]) ).
tcf(c_144,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xm,xm),
inference(cnf_transformation,[],[f238]) ).
tcf(c_145,plain,
xn != xm,
inference(cnf_transformation,[],[f242]) ).
tcf(c_148,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f239]) ).
tcf(c_296,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(superposition,[status(thm)],[c_50,c_57]) ).
tcf(c_592,plain,
( sdtlseqdt0(xp,xn)
| ( sz00 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_142,c_93]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_682,plain,
( sdtlseqdt0(xp,xn)
| ( sz00 = xn )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_140,c_104]) ).
tcf(c_701,plain,
( iLess0(xm,xn)
| ( xn = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_148,c_94]) ).
tcf(c_755,plain,
sdtasdt0(xp,sz10) = xp,
inference(superposition,[status(thm)],[c_119,c_60]) ).
tcf(c_1533,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != xn ) ),
inference(superposition,[status(thm)],[c_142,c_68]) ).
tcf(c_1631,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ( sz00 = xp )
| ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xq,X0) ),
inference(superposition,[status(thm)],[c_142,c_89]) ).
tcf(c_1825,plain,
! [X0: $i] :
( ( sz00 = xq )
| ( sz00 = xp )
| ( X0 = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,xn)
| ( sdtasdt0(X0,X0) != sdtasdt0(xm,xm) ) ),
inference(superposition,[status(thm)],[c_144,c_129]) ).
tcf(c_3104,plain,
( sdtlseqdt0(sz00,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_296,c_634]) ).
tcf(c_3404,plain,
! [X0: $i] :
( ( sz00 = xq )
| ( X0 = xp )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xq) != xn ) ),
inference(superposition,[status(thm)],[c_142,c_69]) ).
tcf(c_3477,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != xn ) ),
inference(superposition,[status(thm)],[c_142,c_68]) ).
tcf(c_3608,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ( sz00 = xp )
| ( X0 = xq )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xq,X0) ),
inference(superposition,[status(thm)],[c_142,c_89]) ).
tcf(c_6510,plain,
sdtlseqdt0(xp,xn),
inference(global_subsumption_just,[status(thm)],[c_592,c_119,c_117,c_120,c_682]) ).
tcf(c_6531,plain,
( ( xn = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xp) ),
inference(superposition,[status(thm)],[c_6510,c_80]) ).
tcf(c_17596,plain,
! [X0: $i] :
( ( sdtasdt0(xp,X0) != xn )
| ~ aNaturalNumber0(X0)
| ( X0 = xq ) ),
inference(global_subsumption_just,[status(thm)],[c_1533,c_141,c_119,c_122,c_1533]) ).
tcf(c_17597,plain,
! [X0: $i] :
( ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != xn ) ),
inference(renaming,[status(thm)],[c_17596]) ).
tcf(c_20189,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ~ sdtlseqdt0(xq,X0)
| ~ aNaturalNumber0(X0)
| ( X0 = xq ) ),
inference(global_subsumption_just,[status(thm)],[c_1631,c_141,c_119,c_122,c_1631]) ).
tcf(c_20190,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xq,X0) ),
inference(renaming,[status(thm)],[c_20189]) ).
tcf(c_23640,plain,
! [X0: $i] :
( ( sz00 = xq )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,xn)
| ( sdtasdt0(X0,X0) != sdtasdt0(xm,xm) )
| ( X0 = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_1825,c_141,c_134,c_119,c_122,c_1825]) ).
tcf(c_23641,plain,
! [X0: $i] :
( ( sz00 = xq )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ iLess0(X0,xn)
| ( sdtasdt0(X0,X0) != sdtasdt0(xm,xm) ) ),
inference(renaming,[status(thm)],[c_23640]) ).
tcf(c_23653,plain,
( ( sz00 = xq )
| ( sz00 = xm )
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn) ),
inference(equality_resolution,[status(thm)],[c_23641]) ).
tcf(c_33988,plain,
sz00 = xq,
inference(global_subsumption_just,[status(thm)],[c_3404,c_118,c_117,c_145,c_121,c_701,c_23653]) ).
tcf(c_34039,plain,
! [X0: $i] :
( ( sdtasdt0(xp,X0) != xn )
| ~ aNaturalNumber0(X0)
| ( X0 = xq ) ),
inference(global_subsumption_just,[status(thm)],[c_3477,c_17597]) ).
tcf(c_34040,plain,
! [X0: $i] :
( ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != xn ) ),
inference(renaming,[status(thm)],[c_34039]) ).
tcf(c_34044,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != xn ) ),
inference(light_normalisation,[status(thm)],[c_34040,c_33988]) ).
tcf(c_34057,plain,
( ( sz00 = sz10 )
| ~ aNaturalNumber0(sz10)
| ( xn != xp ) ),
inference(superposition,[status(thm)],[c_755,c_34044]) ).
tcf(c_36986,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ~ sdtlseqdt0(xq,X0)
| ~ aNaturalNumber0(X0)
| ( X0 = xq ) ),
inference(global_subsumption_just,[status(thm)],[c_3608,c_20190]) ).
tcf(c_36987,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ( X0 = xq )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xq,X0) ),
inference(renaming,[status(thm)],[c_36986]) ).
tcf(c_36992,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(light_normalisation,[status(thm)],[c_36987,c_33988]) ).
tcf(c_37007,plain,
( sdtlseqdt0(xn,xp)
| ( sz00 = sz10 )
| ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz00,sz10) ),
inference(superposition,[status(thm)],[c_755,c_36992]) ).
tcf(c_37051,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_37007,c_34057,c_6531,c_3104,c_51,c_49,c_50,c_117,c_119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM529+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 04:30:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 17.84/3.71 % SZS status Started for theBenchmark.p
% 17.84/3.71 % SZS status Theorem for theBenchmark.p
% 17.84/3.71
% 17.84/3.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.84/3.71
% 17.84/3.71 % ------ iProver source info
% 17.84/3.71
% 17.84/3.71 % git: date: 2026-07-19 20:42:38 +0200
% 17.84/3.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.84/3.71 % git: non_committed_changes: false
% 17.84/3.71
% 17.84/3.71 % ------ Parsing...
% 17.84/3.71 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.84/3.71 % ------ Proving...
% 17.84/3.71 % ------ Problem Properties
% 17.84/3.71
% 17.84/3.71 %
% 17.84/3.71 % clauses 101
% 17.84/3.71 % conjectures 1
% 17.84/3.71 % EPR 32
% 17.84/3.71 % Horn 65
% 17.84/3.71 % unary 26
% 17.84/3.71 % binary 11
% 17.84/3.71 % lits 396
% 17.84/3.71 % lits eq 135
% 17.84/3.71 % fd_pure 0
% 17.84/3.71 % fd_pseudo 0
% 17.84/3.71 % fd_cond 23
% 17.84/3.71 % fd_pseudo_cond 15
% 17.84/3.71 % AC symbols 0
% 17.84/3.71
% 17.84/3.71 % ------ Input Options Time Limit: Unbounded
% 17.84/3.71
% 17.84/3.71
% 17.84/3.71 % ------
% 17.84/3.71 % Current options:
% 17.84/3.71 % ------
% 17.84/3.71
% 17.84/3.71
% 17.84/3.71 %
% 17.84/3.71
% 17.84/3.71 % ------ Proving...
% 17.84/3.71 %
% 17.84/3.71
% 17.84/3.71 % ------ Proving...
% 17.84/3.71 %
% 17.84/3.71
% 17.84/3.71 % ------ Proving...
% 17.84/3.71 %
% 17.84/3.71
% 17.84/3.71 % SZS status Theorem for theBenchmark.p
% 17.84/3.71
% 17.84/3.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.84/3.71
%------------------------------------------------------------------------------