%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM510+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 : n017.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 02:25:33 PM UTC 2026
% Result : Theorem 205.29s 43.53s
% Output : CNFRefutation 205.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 24
% Syntax : Number of formulae : 195 ( 50 unt; 1 def)
% Number of atoms : 768 ( 272 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 921 ( 348 ~; 357 |; 179 &)
% ( 9 <=>; 28 =>; 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 : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 231 ( 0 sgn 206 !; 25 ?; 42 :)
% 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(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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(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(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(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
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/sandbox/benchmark/theBenchmark.p',mMonMul) ).
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(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
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(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f47,axiom,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
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,conjecture,
( ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) ) ) )
& ~ ( sdtsldt0(xn,xr) = xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f54,negated_conjecture,
~ ( ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) ) ) )
& ~ ( sdtsldt0(xn,xr) = xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f56,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(f58,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(f65,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,[],[f56]) ).
fof(f66,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,[],[f65]) ).
fof(f70,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,[],[f58]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ! [X0] :
( xn != sdtpldt0(sdtsldt0(xn,xr),X0)
| ~ aNaturalNumber0(X0) ) )
| ( sdtsldt0(xn,xr) = xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f73,plain,
( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ! [X0] :
( xn != sdtpldt0(sdtsldt0(xn,xr),X0)
| ~ aNaturalNumber0(X0) ) )
| ( sdtsldt0(xn,xr) = xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(flattening,[],[f76]) ).
fof(f78,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(f79,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,[],[f78]) ).
fof(f84,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(f85,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f87,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f90,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f97]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f111]) ).
fof(f117,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f118,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f117]) ).
fof(f125,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f126,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f125]) ).
fof(f129,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f130,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f129]) ).
fof(f134,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(f135,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,[],[f134]) ).
fof(f151,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK8)
& aNaturalNumber0(sK8)
& 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,[sK8]),skolemize(X2,sK8)],[f66]) ).
fof(f153,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,sK11)
& aNaturalNumber0(sK11)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f71]) ).
fof(f160,plain,
( doDivides0(xr,xn)
& xn = sdtasdt0(xr,sK17)
& aNaturalNumber0(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f52]) ).
fof(f162,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,[],[f98]) ).
fof(f163,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,[],[f162]) ).
fof(f164,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK18(X0,X1)) = X1
& aNaturalNumber0(sK18(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X3,sK18(X0,X1))],[f163]) ).
fof(f165,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,[],[f112]) ).
fof(f166,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,[],[f165]) ).
fof(f167,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK19(X0,X1)) = X1
& aNaturalNumber0(sK19(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X3,sK19(X0,X1))],[f166]) ).
fof(f173,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,[],[f135]) ).
fof(f174,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,[],[f173]) ).
fof(f175,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f176,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f177,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f201,plain,
sz00 != xp,
inference(cnf_transformation,[],[f151]) ).
fof(f215,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f216,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f220,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f224,plain,
sz10 != xr,
inference(cnf_transformation,[],[f153]) ).
fof(f225,plain,
sz00 != xr,
inference(cnf_transformation,[],[f153]) ).
fof(f229,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f153]) ).
fof(f246,plain,
xn = sdtasdt0(xr,sK17),
inference(cnf_transformation,[],[f160]) ).
fof(f247,plain,
aNaturalNumber0(sK17),
inference(cnf_transformation,[],[f160]) ).
fof(f252,plain,
( sP3
| xn = sdtsldt0(xn,xr) ),
inference(cnf_transformation,[],[f142]) ).
fof(f254,plain,
( sP3
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f256,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f257,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f264,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f85]) ).
fof(f266,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f267,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f86]) ).
fof(f268,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f87]) ).
fof(f270,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f273,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f276,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f283,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK18(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f164]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
fof(f292,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f293,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f296,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f167]) ).
fof(f299,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f311,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f314,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f130]) ).
fof(f319,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtsldt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f174]) ).
fof(f321,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f285]) ).
fof(f322,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f296]) ).
fof(f326,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(X2)
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2 ),
inference(equality_resolution,[],[f319]) ).
tcf(c_49,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f177]) ).
tcf(c_50,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f176]) ).
tcf(c_51,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f175]) ).
tcf(c_68,plain,
xp != sz00,
inference(cnf_transformation,[],[f201]) ).
tcf(c_88,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f216]) ).
tcf(c_89,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f215]) ).
tcf(c_93,plain,
sz00 != xk,
inference(cnf_transformation,[],[f220]) ).
tcf(c_95,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f229]) ).
tcf(c_99,plain,
sz00 != xr,
inference(cnf_transformation,[],[f225]) ).
tcf(c_100,plain,
sz10 != xr,
inference(cnf_transformation,[],[f224]) ).
tcf(c_119,plain,
aNaturalNumber0(sK17),
inference(cnf_transformation,[],[f247]) ).
tcf(c_120,plain,
sdtasdt0(xr,sK17) = xn,
inference(cnf_transformation,[],[f246]) ).
tcf(c_126,negated_conjecture,
( sP3
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_128,negated_conjecture,
( sP3
| ( sdtsldt0(xn,xr) = xn ) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f257]) ).
tcf(c_139,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,[],[f264]) ).
tcf(c_140,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_141,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f266]) ).
tcf(c_143,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_144,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f270]) ).
tcf(c_147,plain,
! [X0: $i] :
( ( sdtasdt0(sz10,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_148,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f276]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f321]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK18(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f293]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f322]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtsldt0(sdtasdt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f326]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_167,c_172,c_167]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_156,c_165,c_156]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtsldt0(sdtasdt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_190,c_172,c_190,c_270]) ).
tcf(c_11069,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(xr,X0),xr) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_95,c_280]) ).
tcf(c_11098,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(xr,X0),xr) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11069,c_99]) ).
tcf(c_50724,plain,
sdtsldt0(sdtasdt0(xr,sK17),xr) = sK17,
inference(superposition,[status(thm)],[c_119,c_11098]) ).
tcf(c_50738,plain,
sdtsldt0(xn,xr) = sK17,
inference(light_normalisation,[status(thm)],[c_50724,c_120]) ).
tcf(c_50805,plain,
( sP3
| ( xn = sK17 ) ),
inference(demodulation,[status(thm)],[c_128,c_50738]) ).
tcf(c_393227,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ( sz00 = xk )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_89,c_130]) ).
tcf(c_393237,plain,
sdtlseqdt0(xp,sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_393227,c_93,c_88,c_51]) ).
tcf(c_393335,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,sK17),xn)
| ( sz00 = sK17 )
| ( X0 = xr )
| ~ aNaturalNumber0(sK17)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xr) ),
inference(superposition,[status(thm)],[c_120,c_134]) ).
tcf(c_393336,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,sK17),xn)
| ( sz00 = sK17 )
| ( X0 = xr )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xr) ),
inference(forward_subsumption_resolution,[status(thm)],[c_393335,c_119,c_95]) ).
tcf(c_393512,plain,
! [X0: $i] :
( ( sz00 = sK17 )
| ( X0 = xr )
| ~ aNaturalNumber0(sK17)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,sK17) != xn ) ),
inference(superposition,[status(thm)],[c_120,c_139]) ).
tcf(c_393514,plain,
! [X0: $i] :
( ( sz00 = sK17 )
| ( X0 = xr )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,sK17) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_393512,c_119,c_95]) ).
tcf(c_393634,plain,
sdtasdt0(xr,sz00) = sz00,
inference(superposition,[status(thm)],[c_95,c_140]) ).
tcf(c_393664,plain,
sdtasdt0(sz00,xm) = sz00,
inference(superposition,[status(thm)],[c_50,c_141]) ).
tcf(c_393944,plain,
sdtpldt0(sz00,xp) = xp,
inference(superposition,[status(thm)],[c_51,c_143]) ).
tcf(c_393959,plain,
sdtpldt0(sz00,sK17) = sK17,
inference(superposition,[status(thm)],[c_119,c_143]) ).
tcf(c_394264,plain,
sdtasdt0(sz10,xr) = xr,
inference(superposition,[status(thm)],[c_95,c_147]) ).
tcf(c_394271,plain,
sdtasdt0(sz10,sK17) = sK17,
inference(superposition,[status(thm)],[c_119,c_147]) ).
tcf(c_408284,plain,
( sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_393944,c_273]) ).
tcf(c_408301,plain,
sdtlseqdt0(sz00,xp),
inference(forward_subsumption_resolution,[status(thm)],[c_408284,c_144,c_51]) ).
tcf(c_408445,plain,
( ( xp = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,sz00) ),
inference(superposition,[status(thm)],[c_408301,c_187]) ).
tcf(c_408451,plain,
~ sdtlseqdt0(xp,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_408445,c_68,c_144,c_51]) ).
tcf(c_410984,plain,
( sdtlseqdt0(sz00,sK17)
| ~ aNaturalNumber0(sK17)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_393959,c_273]) ).
tcf(c_411001,plain,
sdtlseqdt0(sz00,sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_410984,c_119,c_144]) ).
tcf(c_411683,plain,
( iLess0(sz00,sK17)
| ( sz00 = sK17 )
| ~ aNaturalNumber0(sK17)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_411001,c_166]) ).
tcf(c_411686,plain,
( iLess0(sz00,sK17)
| ( sz00 = sK17 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_411683,c_119,c_144]) ).
tcf(c_421756,plain,
( sdtlseqdt0(sz10,xr)
| ( sz00 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm)],[c_394264,c_130]) ).
tcf(c_421763,plain,
sdtlseqdt0(sz10,xr),
inference(forward_subsumption_resolution,[status(thm)],[c_421756,c_99,c_95,c_148]) ).
tcf(c_423985,plain,
( ( sz10 = xr )
| ( sz00 = sK17 )
| ~ aNaturalNumber0(sz10)
| ( xn != sK17 ) ),
inference(superposition,[status(thm)],[c_394271,c_393514]) ).
tcf(c_423987,plain,
( sdtlseqdt0(sK17,xn)
| ( sz10 = xr )
| ( sz00 = sK17 )
| ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz10,xr) ),
inference(superposition,[status(thm)],[c_394271,c_393336]) ).
tcf(c_423992,plain,
( ( sz00 = sK17 )
| ( xn != sK17 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_423985,c_100,c_148]) ).
tcf(c_423995,plain,
( sdtlseqdt0(sK17,xn)
| ( sz00 = sK17 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_423987,c_100,c_148,c_421763]) ).
fof(f141,definition,
( ~ sP3
| ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ! [X0] :
( xn != sdtpldt0(sdtsldt0(xn,xr),X0)
| ~ aNaturalNumber0(X0) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f142,plain,
( sP3
| ( sdtsldt0(xn,xr) = xn
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(definition_folding,[],[f73,f141]) ).
fof(f161,plain,
( ~ sP3
| ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ! [X0] :
( xn != sdtpldt0(sdtsldt0(xn,xr),X0)
| ~ aNaturalNumber0(X0) ) ) ),
inference(nnf_transformation,[],[f141]) ).
fof(f249,plain,
( ~ sP3
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f161]) ).
fof(f250,plain,
( ~ sP3
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_123,plain,
( ~ sP3
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_124,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sP3 ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_258,negated_conjecture,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_126,c_126,c_124]) ).
tcf(c_264,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_124,c_258]) ).
tcf(c_11773,plain,
( sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ sP3
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_185,c_123]) ).
tcf(c_11776,plain,
( sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ sP3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_11773,c_49,c_264]) ).
tcf(c_50799,plain,
( sdtlseqdt0(xn,sK17)
| ~ sP3 ),
inference(demodulation,[status(thm)],[c_11776,c_50738]) ).
tcf(c_50838,plain,
( ( sdtpldt0(xn,sK18(xn,sK17)) = sK17 )
| ~ sP3
| ~ aNaturalNumber0(sK17)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_50799,c_158]) ).
tcf(c_50845,plain,
( ( sdtpldt0(xn,sK18(xn,sK17)) = sK17 )
| ~ sP3 ),
inference(forward_subsumption_resolution,[status(thm)],[c_50838,c_119,c_49]) ).
tcf(c_51136,plain,
( ( xn = sK17 )
| ( sdtpldt0(xn,sK18(xn,sK17)) = sK17 ) ),
inference(superposition,[status(thm)],[c_50805,c_50845]) ).
tcf(c_51406,plain,
( sdtlseqdt0(xn,sK17)
| ( xn = sK17 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK18(xn,sK17)) ),
inference(superposition,[status(thm)],[c_51136,c_273]) ).
tcf(c_51416,plain,
( sdtlseqdt0(xn,sK17)
| ( xn = sK17 )
| ~ aNaturalNumber0(sK18(xn,sK17)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51406,c_49]) ).
tcf(c_51533,plain,
( sdtlseqdt0(xn,sK17)
| ( xn = sK17 ) ),
inference(global_subsumption_just,[status(thm)],[c_51416,c_50805,c_50799]) ).
tcf(c_51539,plain,
( ( xn = sK17 )
| ~ aNaturalNumber0(sK17)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(sK17,xn) ),
inference(superposition,[status(thm)],[c_51533,c_187]) ).
tcf(c_51543,plain,
( ( xn = sK17 )
| ~ sdtlseqdt0(sK17,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51539,c_119,c_49]) ).
tcf(c_431971,plain,
sz00 = sK17,
inference(global_subsumption_just,[status(thm)],[c_411686,c_51543,c_423995,c_423992]) ).
tcf(c_431998,plain,
sdtasdt0(xr,sz00) = xn,
inference(demodulation,[status(thm)],[c_120,c_431971]) ).
tcf(c_432004,plain,
xn = sz00,
inference(light_normalisation,[status(thm)],[c_431998,c_393634]) ).
tcf(c_432146,plain,
sdtlseqdt0(xp,sdtasdt0(sz00,xm)),
inference(demodulation,[status(thm)],[c_393237,c_432004]) ).
tcf(c_432248,plain,
sdtlseqdt0(xp,sz00),
inference(light_normalisation,[status(thm)],[c_432146,c_393664]) ).
tcf(c_432249,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_432248,c_408451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM510+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/15.39 % Computer : n017.cluster.edu
% 0.12/15.39 % Model : x86_64 x86_64
% 0.12/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.39 % Memory : 8046.5625MB
% 0.12/15.39 % OS : Linux 6.8.0-71-generic
% 0.12/15.39 % CPULimit : 300
% 0.12/15.39 % WCLimit : 300
% 0.12/15.39 % DateTime : Thu Sep 24 04:17:01 UTC 2026
% 0.12/15.39 % CPUTime :
% 0.12/15.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/15.43 Running first-order theorem proving
% 0.15/15.43 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
% 0.15/15.44
% 0.15/15.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.44
% 0.15/15.44 % Detected problem language: tptp
% 0.15/15.45 % Proving...
% 205.29/43.53 % SZS status Started for theBenchmark.p
% 205.29/43.53 % SZS status Theorem for theBenchmark.p
% 205.29/43.53
% 205.29/43.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 205.29/43.53
% 205.29/43.53 % ------ iProver source info
% 205.29/43.53
% 205.29/43.53 % git: date: 2026-07-19 20:42:38 +0200
% 205.29/43.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 205.29/43.53 % git: non_committed_changes: false
% 205.29/43.53
% 205.29/43.53 % ------ Parsing...
% 205.29/43.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 205.29/43.53
% 205.29/43.53 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 205.29/43.53
% 205.29/43.53 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 205.29/43.53
% 205.29/43.53 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 205.29/43.53 % ------ Proving...
% 205.29/43.53 % ------ Problem Properties
% 205.29/43.53
% 205.29/43.53 %
% 205.29/43.53 % clauses 134
% 205.29/43.53 % conjectures 1
% 205.29/43.53 % EPR 52
% 205.29/43.53 % Horn 91
% 205.29/43.53 % unary 50
% 205.29/43.53 % binary 20
% 205.29/43.53 % lits 406
% 205.29/43.53 % lits eq 126
% 205.29/43.53 % fd_pure 0
% 205.29/43.53 % fd_pseudo 0
% 205.29/43.53 % fd_cond 24
% 205.29/43.53 % fd_pseudo_cond 11
% 205.29/43.53 % AC symbols 0
% 205.29/43.53
% 205.29/43.53 % ------ Schedule dynamic 5 is on
% 205.29/43.53
% 205.29/43.53 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 205.29/43.53
% 205.29/43.53
% 205.29/43.53 % ------
% 205.29/43.53 % Current options:
% 205.29/43.53 % ------
% 205.29/43.53
% 205.29/43.53
% 205.29/43.53 %
% 205.29/43.53
% 205.29/43.53 % ------ Proving...
% 205.29/43.53 % Proof_search_loop: time out after: 3689 full_loop iterations
% 205.29/43.53
% 205.29/43.53 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 205.29/43.53
% 205.29/43.53
% 205.29/43.53 % ------
% 205.29/43.53 % Current options:
% 205.29/43.53 % ------
% 205.29/43.53
% 205.29/43.53
% 205.29/43.53 %
% 205.29/43.53
% 205.29/43.53 % ------ Proving...
% 205.29/43.53 % Proof_search_loop: time out after: 5078 full_loop iterations
% 205.29/43.53
% 205.29/43.53 % ------ Option_1: Negative Selections Time Limit: 35.
% 205.29/43.53
% 205.29/43.53
% 205.29/43.53 % ------
% 205.29/43.53 % Current options:
% 205.29/43.53 % ------
% 205.29/43.53
% 205.29/43.53
% 205.29/43.53 %
% 205.29/43.53
% 205.29/43.53 % ------ Proving...
% 205.29/43.53 %
% 205.29/43.53
% 205.29/43.53 % SZS status Theorem for theBenchmark.p
% 205.29/43.53
% 205.29/43.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 205.29/43.53
% 205.29/43.53
%------------------------------------------------------------------------------