%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM518+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 : n003.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 54.69s 18.43s
% Output : CNFRefutation 54.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 185 ( 61 unt; 1 def)
% Number of atoms : 682 ( 225 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 735 ( 266 ~; 271 |; 172 &)
% ( 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 : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-2 aty)
% Number of variables : 174 ( 0 sgn 140 !; 34 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f44,axiom,
( sdtlseqdt0(xm,xp)
& ? [X0] :
( sdtpldt0(xm,X0) = xp
& aNaturalNumber0(X0) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( sdtpldt0(xn,X0) = xp
& aNaturalNumber0(X0) )
& xn != xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( xr = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xr
| X0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
( doDivides0(xr,xn)
& ? [X0] :
( xn = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(f53,axiom,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2504) ).
fof(f54,axiom,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& ? [X0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2529) ).
fof(f55,axiom,
( ( doDivides0(xp,xm)
& ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) )
| ( doDivides0(xp,sdtsldt0(xn,xr))
& ? [X0] :
( sdtsldt0(xn,xr) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2645) ).
fof(f56,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(f57,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)],[f56]) ).
fof(f62,plain,
( sdtlseqdt0(xm,xp)
& ? [X1] :
( xp = sdtpldt0(xm,X1)
& aNaturalNumber0(X1) )
& xm != xp
& sdtlseqdt0(xn,xp)
& ? [X0] :
( sdtpldt0(xn,X0) = xp
& aNaturalNumber0(X0) )
& xn != xp ),
inference(rectify,[],[f44]) ).
fof(f63,plain,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( sdtasdt0(X1,X2) = xr
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xr = X1
| sz10 = X1 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f66,plain,
( ( doDivides0(xp,xm)
& ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
| ( doDivides0(xp,sdtsldt0(xn,xr))
& ? [X0] :
( sdtsldt0(xn,xr) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(rectify,[],[f55]) ).
fof(f67,plain,
~ ( doDivides0(xp,xm)
| ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
| doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f57]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f68]) ).
fof(f76,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f82,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f87,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(f88,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,[],[f87]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f93]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f100]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f113,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f112]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f125,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f124]) ).
fof(f139,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f63]) ).
fof(f140,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn != sdtsldt0(xn,xr) ),
inference(ennf_transformation,[],[f53]) ).
fof(f142,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn != sdtsldt0(xn,xr) ),
inference(flattening,[],[f141]) ).
fof(f143,plain,
( ~ doDivides0(xp,xm)
& ! [X1] :
( xm != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) )
& ~ doDivides0(xp,xn)
& ! [X0] :
( xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f151,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,[],[f94]) ).
fof(f152,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,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1))],[f152]) ).
fof(f175,plain,
( sdtlseqdt0(xm,xp)
& xp = sdtpldt0(xm,sK14)
& aNaturalNumber0(sK14)
& xm != xp
& sdtlseqdt0(xn,xp)
& xp = sdtpldt0(xn,sK13)
& aNaturalNumber0(sK13)
& xn != xp ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f62]) ).
fof(f176,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK15)
& aNaturalNumber0(sK15)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f140]) ).
fof(f183,plain,
( doDivides0(xr,xn)
& xn = sdtasdt0(xr,sK21)
& aNaturalNumber0(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f52]) ).
fof(f184,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& xn = sdtpldt0(sdtsldt0(xn,xr),sK22)
& aNaturalNumber0(sK22)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn != sdtsldt0(xn,xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f142]) ).
fof(f185,plain,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK23)
& aNaturalNumber0(sK23)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X0,sK23)],[f54]) ).
fof(f188,plain,
( ( doDivides0(xp,xm)
& ? [X0] :
( xm = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) )
| sP3 ),
inference(rectify,[],[f150]) ).
fof(f189,plain,
( ( doDivides0(xp,xm)
& xm = sdtasdt0(xp,sK25)
& aNaturalNumber0(sK25) )
| sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(X0,sK25)],[f188]) ).
fof(f190,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f193,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f197,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f76]) ).
fof(f204,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f82]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f88]) ).
fof(f213,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f92]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f221,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f235,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f111]) ).
fof(f236,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f246,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f258,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f259,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f260,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f293,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f175]) ).
fof(f308,plain,
sz00 != xr,
inference(cnf_transformation,[],[f176]) ).
fof(f312,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f176]) ).
fof(f328,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f183]) ).
fof(f329,plain,
xn = sdtasdt0(xr,sK21),
inference(cnf_transformation,[],[f183]) ).
fof(f330,plain,
aNaturalNumber0(sK21),
inference(cnf_transformation,[],[f183]) ).
fof(f331,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f184]) ).
fof(f338,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f184]) ).
fof(f340,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK23),
inference(cnf_transformation,[],[f185]) ).
fof(f342,plain,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f185]) ).
fof(f343,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f185]) ).
fof(f349,plain,
( doDivides0(xp,xm)
| sP3 ),
inference(cnf_transformation,[],[f189]) ).
fof(f352,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f143]) ).
fof(f353,plain,
! [X1] :
( xm != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f355,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f356,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f216]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f190]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f204]) ).
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,[],[f210]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
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,[],[f222]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f260]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f259]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f258]) ).
tcf(c_150,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f293]) ).
tcf(c_162,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f312]) ).
tcf(c_166,plain,
sz00 != xr,
inference(cnf_transformation,[],[f308]) ).
tcf(c_186,plain,
aNaturalNumber0(sK21),
inference(cnf_transformation,[],[f330]) ).
tcf(c_187,plain,
sdtasdt0(xr,sK21) = xn,
inference(cnf_transformation,[],[f329]) ).
tcf(c_188,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f328]) ).
tcf(c_189,plain,
sdtsldt0(xn,xr) != xn,
inference(cnf_transformation,[],[f338]) ).
tcf(c_196,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f331]) ).
tcf(c_197,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f343]) ).
tcf(c_198,plain,
sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
inference(cnf_transformation,[],[f342]) ).
tcf(c_200,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK23),
inference(cnf_transformation,[],[f340]) ).
tcf(c_209,plain,
( sP3
| doDivides0(xp,xm) ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_210,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != xn ) ),
inference(cnf_transformation,[],[f355]) ).
tcf(c_212,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(xp,X0) != xm ) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_213,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f352]) ).
tcf(c_306,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_11325,plain,
! [X0: $i] :
( ( sdtasdt0(xp,X0) = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xp,X0))
| ~ sdtlseqdt0(xn,sdtasdt0(xp,X0))
| ~ sdtlseqdt0(sdtasdt0(xp,X0),xn) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_11784,plain,
( ( sdtasdt0(xp,sK24) = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xp,sK24))
| ~ sdtlseqdt0(xn,sdtasdt0(xp,sK24))
| ~ sdtlseqdt0(sdtasdt0(xp,sK24),xn) ),
inference(instantiation,[status(thm)],[c_11325]) ).
tcf(c_14856,plain,
( sdtlseqdt0(xr,xn)
| ( sz00 = xn )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_188,c_104]) ).
tcf(c_14872,plain,
( sdtlseqdt0(xr,xn)
| ( sz00 = xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14856,c_162,c_116]) ).
tcf(c_15500,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_62]) ).
tcf(c_15981,plain,
( ~ aNaturalNumber0(sz00)
| ( sz00 != xn ) ),
inference(superposition,[status(thm)],[c_15500,c_210]) ).
tcf(c_15982,plain,
sz00 != xn,
inference(forward_subsumption_resolution,[status(thm)],[c_15981,c_49]) ).
tcf(c_16809,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtasdt0(xp,sK24))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(sdtasdt0(xp,sK24))
| ~ sdtlseqdt0(X0,sdtasdt0(xp,sK24)) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_21772,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_118,c_62]) ).
tcf(c_26051,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( X0 = sK21 )
| ~ aNaturalNumber0(sK21)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xr,X0) != xn ) ),
inference(superposition,[status(thm)],[c_187,c_68]) ).
tcf(c_26132,plain,
! [X0: $i] :
( ( X0 = sK21 )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xr,X0) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26051,c_166,c_186,c_162]) ).
tcf(c_26141,plain,
( ( sz00 = sK21 )
| ~ aNaturalNumber0(sz00)
| ( sdtasdt0(xr,sz00) != xn ) ),
inference(instantiation,[status(thm)],[c_26132]) ).
tcf(c_28355,plain,
( sdtlseqdt0(xn,sdtasdt0(xp,sK24))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sK24))
| ~ sdtlseqdt0(xp,sdtasdt0(xp,sK24)) ),
inference(instantiation,[status(thm)],[c_16809]) ).
tcf(c_29444,plain,
( ~ aNaturalNumber0(sz00)
| ( sz00 != xm ) ),
inference(superposition,[status(thm)],[c_21772,c_212]) ).
tcf(c_29447,plain,
sz00 != xm,
inference(forward_subsumption_resolution,[status(thm)],[c_29444,c_49]) ).
tcf(c_38884,plain,
sdtpldt0(sz00,xr) = xr,
inference(superposition,[status(thm)],[c_162,c_57]) ).
tcf(c_38891,plain,
sdtpldt0(sz00,sK21) = sK21,
inference(superposition,[status(thm)],[c_186,c_57]) ).
tcf(c_38956,plain,
sdtasdt0(xr,sz00) = sz00,
inference(superposition,[status(thm)],[c_162,c_62]) ).
tcf(c_39369,plain,
( sdtlseqdt0(xr,xn)
| ( sz00 = sK21 )
| ~ aNaturalNumber0(sK21)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm)],[c_187,c_93]) ).
tcf(c_39393,plain,
( sdtlseqdt0(xr,xn)
| ( sz00 = sK21 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39369,c_186,c_162]) ).
tcf(c_39419,plain,
sdtlseqdt0(xr,xn),
inference(global_subsumption_just,[status(thm)],[c_39393,c_14872,c_15982]) ).
tcf(c_39549,plain,
( sdtlseqdt0(sz00,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_38884,c_306]) ).
tcf(c_39551,plain,
sdtlseqdt0(sz00,xr),
inference(forward_subsumption_resolution,[status(thm)],[c_39549,c_162,c_49]) ).
tcf(c_39869,plain,
( ( sz00 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xr,sz00) ),
inference(superposition,[status(thm)],[c_39551,c_80]) ).
tcf(c_39908,plain,
~ sdtlseqdt0(xr,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_39869,c_166,c_162,c_49]) ).
tcf(c_40009,plain,
( sdtlseqdt0(sz00,sK21)
| ~ aNaturalNumber0(sK21)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_38891,c_306]) ).
tcf(c_40011,plain,
sdtlseqdt0(sz00,sK21),
inference(forward_subsumption_resolution,[status(thm)],[c_40009,c_186,c_49]) ).
tcf(c_40015,plain,
( iLess0(sz00,sK21)
| ( sz00 = sK21 )
| ~ aNaturalNumber0(sK21)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_40011,c_94]) ).
tcf(c_40016,plain,
( iLess0(sz00,sK21)
| ( sz00 = sK21 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40015,c_186,c_49]) ).
fof(f149,definition,
( ~ sP3
| ( doDivides0(xp,sdtsldt0(xn,xr))
& ? [X0] :
( sdtsldt0(xn,xr) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f150,plain,
( ( doDivides0(xp,xm)
& ? [X1] :
( xm = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
| sP3 ),
inference(definition_folding,[],[f66,f149]) ).
fof(f186,plain,
( ~ sP3
| ( doDivides0(xp,sdtsldt0(xn,xr))
& ? [X0] :
( sdtsldt0(xn,xr) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(nnf_transformation,[],[f149]) ).
fof(f187,plain,
( ~ sP3
| ( doDivides0(xp,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) = sdtasdt0(xp,sK24)
& aNaturalNumber0(sK24)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(X0,sK24)],[f186]) ).
fof(f344,plain,
( ~ sP3
| doDivides0(xp,sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f345,plain,
( ~ sP3
| sdtsldt0(xn,xr) = sdtasdt0(xp,sK24) ),
inference(cnf_transformation,[],[f187]) ).
fof(f347,plain,
( ~ sP3
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f348,plain,
( ~ sP3
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_202,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sP3 ),
inference(cnf_transformation,[],[f348]) ).
tcf(c_203,plain,
( ( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn )
| ~ sP3 ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_205,plain,
( ( sdtasdt0(xp,sK24) = sdtsldt0(xn,xr) )
| ~ sP3 ),
inference(cnf_transformation,[],[f345]) ).
tcf(c_206,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| ~ sP3 ),
inference(cnf_transformation,[],[f344]) ).
tcf(c_289,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_202,c_197]) ).
tcf(c_297,plain,
doDivides0(xp,sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_206,c_213,c_209,c_206]) ).
tcf(c_299,plain,
sdtasdt0(xp,sK24) = sdtsldt0(xn,xr),
inference(global_subsumption_just,[status(thm)],[c_205,c_213,c_209,c_205]) ).
tcf(c_301,plain,
sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
inference(global_subsumption_just,[status(thm)],[c_203,c_198]) ).
tcf(c_1203,plain,
sdtasdt0(xp,sK24) != xn,
inference(demodulation,[status(thm)],[c_189,c_299]) ).
tcf(c_1205,plain,
sdtlseqdt0(sdtasdt0(xp,sK24),xn),
inference(demodulation,[status(thm)],[c_196,c_299]) ).
tcf(c_1206,plain,
doDivides0(xp,sdtasdt0(xp,sK24)),
inference(demodulation,[status(thm)],[c_297,c_299]) ).
tcf(c_1207,plain,
aNaturalNumber0(sdtasdt0(xp,sK24)),
inference(demodulation,[status(thm)],[c_289,c_299]) ).
tcf(c_1209,plain,
sdtasdt0(xr,sdtasdt0(xp,sK24)) = xn,
inference(light_normalisation,[status(thm)],[c_301,c_299]) ).
tcf(c_1250,plain,
sdtasdt0(sdtasdt0(xp,sK24),xm) = sdtasdt0(xp,sK23),
inference(light_normalisation,[status(thm)],[c_200,c_299]) ).
tcf(c_14858,plain,
( sdtlseqdt0(xp,sdtasdt0(xp,sK24))
| ( sdtasdt0(xp,sK24) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sK24)) ),
inference(superposition,[status(thm)],[c_1206,c_104]) ).
tcf(c_14875,plain,
( sdtlseqdt0(xp,sdtasdt0(xp,sK24))
| ( sdtasdt0(xp,sK24) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14858,c_118,c_1207]) ).
tcf(c_23194,plain,
( ( sz00 = xm )
| ( sdtasdt0(xp,sK24) = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xp,sK24))
| ( sdtasdt0(xp,sK23) != sz00 ) ),
inference(superposition,[status(thm)],[c_1250,c_72]) ).
tcf(c_23223,plain,
( ( sz00 = xm )
| ( sdtasdt0(xp,sK24) = sz00 )
| ( sdtasdt0(xp,sK23) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23194,c_117,c_1207]) ).
tcf(c_29481,plain,
( ( sdtasdt0(xp,sK24) = sz00 )
| ( sdtasdt0(xp,sK23) != sz00 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_23223,c_29447]) ).
tcf(c_37701,plain,
sdtasdt0(xp,sK24) = sz00,
inference(global_subsumption_just,[status(thm)],[c_29481,c_118,c_116,c_150,c_1203,c_1205,c_1207,c_11784,c_14875,c_28355]) ).
tcf(c_37708,plain,
sdtasdt0(xr,sz00) = xn,
inference(demodulation,[status(thm)],[c_1209,c_37701]) ).
tcf(c_40675,plain,
sz00 = sK21,
inference(global_subsumption_just,[status(thm)],[c_40016,c_49,c_26141,c_37708]) ).
tcf(c_40683,plain,
sdtasdt0(xr,sz00) = xn,
inference(demodulation,[status(thm)],[c_187,c_40675]) ).
tcf(c_40685,plain,
sz00 = xn,
inference(demodulation,[status(thm)],[c_40683,c_38956]) ).
tcf(c_40695,plain,
sdtlseqdt0(xr,sz00),
inference(demodulation,[status(thm)],[c_39419,c_40685]) ).
tcf(c_40727,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_40695,c_39908]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM518+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.41 % Computer : n003.cluster.edu
% 0.14/10.41 % Model : x86_64 x86_64
% 0.14/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.41 % Memory : 8046.5625MB
% 0.14/10.41 % OS : Linux 6.8.0-71-generic
% 0.14/10.41 % CPULimit : 300
% 0.14/10.41 % WCLimit : 300
% 0.14/10.41 % DateTime : Thu Sep 24 04:26:19 UTC 2026
% 0.14/10.42 % CPUTime :
% 0.14/10.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.45 Running first-order theorem proving
% 0.14/10.45 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
% 0.14/10.47
% 0.14/10.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.47
% 0.14/10.47 % Detected problem language: tptp
% 0.14/10.48 % Proving...
% 54.69/18.43 % SZS status Started for theBenchmark.p
% 54.69/18.43 % SZS status Theorem for theBenchmark.p
% 54.69/18.43
% 54.69/18.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 54.69/18.43
% 54.69/18.43 % ------ iProver source info
% 54.69/18.43
% 54.69/18.43 % git: date: 2026-07-19 20:42:38 +0200
% 54.69/18.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 54.69/18.43 % git: non_committed_changes: false
% 54.69/18.43
% 54.69/18.43 % ------ Parsing...
% 54.69/18.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 54.69/18.43
% 54.69/18.43 % ------ Preprocessing... sup_sim: 9 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 %
% 54.69/18.43
% 54.69/18.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 54.69/18.43
% 54.69/18.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 54.69/18.43 % ------ Proving...
% 54.69/18.43 % ------ Problem Properties
% 54.69/18.43
% 54.69/18.43 %
% 54.69/18.43 % clauses 148
% 54.69/18.43 % conjectures 4
% 54.69/18.43 % EPR 57
% 54.69/18.43 % Horn 106
% 54.69/18.43 % unary 62
% 54.69/18.43 % binary 20
% 54.69/18.43 % lits 426
% 54.69/18.43 % lits eq 132
% 54.69/18.43 % fd_pure 0
% 54.69/18.43 % fd_pseudo 0
% 54.69/18.43 % fd_cond 24
% 54.69/18.43 % fd_pseudo_cond 11
% 54.69/18.43 % AC symbols 0
% 54.69/18.43
% 54.69/18.43 % ------ Input Options Time Limit: Unbounded
% 54.69/18.43
% 54.69/18.43
% 54.69/18.43 % ------
% 54.69/18.43 % Current options:
% 54.69/18.43 % ------
% 54.69/18.43
% 54.69/18.43
% 54.69/18.43 %
% 54.69/18.43
% 54.69/18.43 % ------ Proving...
% 54.69/18.43 %
% 54.69/18.43
% 54.69/18.43 % SZS status Theorem for theBenchmark.p
% 54.69/18.43
% 54.69/18.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 54.69/18.44
% 54.69/18.44
%------------------------------------------------------------------------------