TSTP Solution File: NUM510+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM510+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:31:02 EDT 2023
% Result : Theorem 29.19s 4.74s
% Output : CNFRefutation 29.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 34
% Syntax : Number of formulae : 353 ( 69 unt; 0 def)
% Number of atoms : 1317 ( 518 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1623 ( 659 ~; 771 |; 141 &)
% ( 15 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 355 ( 0 sgn; 242 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz00 != sz10
& 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(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f15,axiom,
! [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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(f25,axiom,
! [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) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f47,axiom,
( sz10 != xk
& sz00 != xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f53,conjecture,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& xn != sdtsldt0(xn,xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f54,negated_conjecture,
~ ( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& xn != sdtsldt0(xn,xr) ),
inference(negated_conjecture,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f60,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f59]) ).
fof(f65,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f66,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f67,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f66]) ).
fof(f70,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f71,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f75,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f79,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f83,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f85,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f84]) ).
fof(f89,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f90,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f92,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f94,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( 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) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( 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) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f95]) ).
fof(f99,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f100,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f99]) ).
fof(f103,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f104,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f117,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f118,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f117]) ).
fof(f124,plain,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| xn = sdtsldt0(xn,xr) ),
inference(ennf_transformation,[],[f54]) ).
fof(f125,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f83]) ).
fof(f126,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f126,f127]) ).
fof(f129,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f85]) ).
fof(f130,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f132,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f132,f133]) ).
fof(f135,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f106]) ).
fof(f136,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f135]) ).
fof(f137,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f138,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ( ( isPrime0(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
! [X0] :
( ( ( isPrime0(X0)
| ( sK2(X0) != X0
& sz10 != sK2(X0)
& doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f139,f140]) ).
fof(f144,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f145,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f146,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f147,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f148,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f151,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f153,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f155,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f156,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f157,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f158,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f161,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f163,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f165,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f167,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f168,plain,
! [X0,X1] :
( aNaturalNumber0(sK0(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f169,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f170,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f171,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f172,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f176,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f178,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f180,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f189,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f193,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f194,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f195,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f202,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f203,plain,
! [X0] :
( sz10 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f212,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f213,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f214,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f216,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f217,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f224,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f227,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f229,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f231,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f232,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f49]) ).
fof(f237,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f238,plain,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| xn = sdtsldt0(xn,xr) ),
inference(cnf_transformation,[],[f124]) ).
fof(f239,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f170]) ).
fof(f241,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f172]) ).
fof(f242,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f171]) ).
fof(f245,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f247,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f195]) ).
fof(f248,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f194]) ).
fof(f249,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(equality_resolution,[],[f203]) ).
fof(f250,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f202]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f144]) ).
cnf(c_50,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f146]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f145]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_58,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_60,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_61,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_62,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sz00 ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_67,plain,
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_69,plain,
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = sz00
| X1 = X2 ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_72,plain,
( sdtasdt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| X1 = sz00 ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f239]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_75,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_77,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f241]) ).
cnf(c_78,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(cnf_transformation,[],[f242]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_86,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1)) ),
inference(cnf_transformation,[],[f180]) ).
cnf(c_90,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_93,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_95,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f245]) ).
cnf(c_99,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| X0 = sz00 ),
inference(cnf_transformation,[],[f247]) ).
cnf(c_100,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(cnf_transformation,[],[f248]) ).
cnf(c_111,plain,
( ~ aNaturalNumber0(sz10)
| ~ isPrime0(sz10) ),
inference(cnf_transformation,[],[f249]) ).
cnf(c_112,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(cnf_transformation,[],[f250]) ).
cnf(c_116,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f214]) ).
cnf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f213]) ).
cnf(c_118,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f212]) ).
cnf(c_120,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f217]) ).
cnf(c_121,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f216]) ).
cnf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f224]) ).
cnf(c_132,plain,
sz00 != xk,
inference(cnf_transformation,[],[f227]) ).
cnf(c_133,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f231]) ).
cnf(c_135,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f229]) ).
cnf(c_137,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f232]) ).
cnf(c_141,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f237]) ).
cnf(c_142,negated_conjecture,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(cnf_transformation,[],[f238]) ).
cnf(c_147,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_165,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_188,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_112,c_49,c_112]) ).
cnf(c_190,plain,
~ isPrime0(sz10),
inference(global_subsumption_just,[status(thm)],[c_111,c_51,c_111]) ).
cnf(c_192,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
cnf(c_195,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_1669,plain,
sz10 != xr,
inference(resolution_lifted,[status(thm)],[c_190,c_133]) ).
cnf(c_1687,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_188,c_121]) ).
cnf(c_1691,plain,
sz00 != xr,
inference(resolution_lifted,[status(thm)],[c_188,c_133]) ).
cnf(c_3559,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_4893,plain,
sdtasdt0(sz10,xp) = xp,
inference(superposition,[status(thm)],[c_116,c_60]) ).
cnf(c_4896,plain,
sdtasdt0(sz10,xr) = xr,
inference(superposition,[status(thm)],[c_135,c_60]) ).
cnf(c_4905,plain,
sdtasdt0(xn,sz10) = xn,
inference(superposition,[status(thm)],[c_118,c_61]) ).
cnf(c_4914,plain,
sdtasdt0(sz00,xm) = sz00,
inference(superposition,[status(thm)],[c_117,c_62]) ).
cnf(c_4923,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_116,c_63]) ).
cnf(c_5106,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_82,c_142]) ).
cnf(c_5117,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5106,c_118]) ).
cnf(c_5173,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xp) = sdtasdt0(xp,X0) ),
inference(superposition,[status(thm)],[c_116,c_58]) ).
cnf(c_5174,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
cnf(c_5175,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xn) = sdtasdt0(xn,X0) ),
inference(superposition,[status(thm)],[c_118,c_58]) ).
cnf(c_5176,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xr) = sdtasdt0(xr,X0) ),
inference(superposition,[status(thm)],[c_135,c_58]) ).
cnf(c_5302,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_5117,c_74]) ).
cnf(c_5303,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_5302,c_118]) ).
cnf(c_5504,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sz00) ),
inference(superposition,[status(thm)],[c_4923,c_192]) ).
cnf(c_5506,plain,
doDivides0(xp,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_5504,c_116,c_49]) ).
cnf(c_5679,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| sz00 = xp
| sdtlseqdt0(sz10,xp) ),
inference(superposition,[status(thm)],[c_4893,c_93]) ).
cnf(c_5682,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr)
| sz00 = xr
| sdtlseqdt0(sz10,xr) ),
inference(superposition,[status(thm)],[c_4896,c_93]) ).
cnf(c_5696,plain,
( sz00 = xr
| sdtlseqdt0(sz10,xr) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5682,c_135,c_51]) ).
cnf(c_5705,plain,
( sz00 = xp
| sdtlseqdt0(sz10,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5679,c_116,c_51]) ).
cnf(c_5724,plain,
sdtlseqdt0(sz10,xr),
inference(global_subsumption_just,[status(thm)],[c_5696,c_1691,c_5696]) ).
cnf(c_5726,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xr)
| sdtpldt0(sz10,sK0(sz10,xr)) = xr ),
inference(superposition,[status(thm)],[c_5724,c_74]) ).
cnf(c_5727,plain,
sdtpldt0(sz10,sK0(sz10,xr)) = xr,
inference(forward_subsumption_resolution,[status(thm)],[c_5726,c_135,c_51]) ).
cnf(c_5768,plain,
sdtlseqdt0(sz10,xp),
inference(global_subsumption_just,[status(thm)],[c_5705,c_1687,c_5705]) ).
cnf(c_5770,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| sdtpldt0(sz10,sK0(sz10,xp)) = xp ),
inference(superposition,[status(thm)],[c_5768,c_74]) ).
cnf(c_5771,plain,
sdtpldt0(sz10,sK0(sz10,xp)) = xp,
inference(forward_subsumption_resolution,[status(thm)],[c_5770,c_116,c_51]) ).
cnf(c_5973,plain,
( sz00 != xr
| ~ aNaturalNumber0(sK0(sz10,xr))
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(superposition,[status(thm)],[c_5727,c_71]) ).
cnf(c_5974,plain,
( sz00 != xr
| ~ aNaturalNumber0(sK0(sz10,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5973,c_50,c_51]) ).
cnf(c_6027,plain,
( X0 != X1
| xr != X1
| X0 = xr ),
inference(instantiation,[status(thm)],[c_3559]) ).
cnf(c_6028,plain,
( sz00 != sz00
| xr != sz00
| sz00 = xr ),
inference(instantiation,[status(thm)],[c_6027]) ).
cnf(c_6254,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xr,sdtmndt0(xk,xr)) = xk ),
inference(superposition,[status(thm)],[c_137,c_77]) ).
cnf(c_6267,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_5117,c_77]) ).
cnf(c_6290,plain,
( ~ aNaturalNumber0(xk)
| sdtpldt0(xr,sdtmndt0(xk,xr)) = xk ),
inference(forward_subsumption_resolution,[status(thm)],[c_6254,c_135]) ).
cnf(c_6318,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_6267,c_118]) ).
cnf(c_6364,plain,
( X0 != X1
| xp != X1
| X0 = xp ),
inference(instantiation,[status(thm)],[c_3559]) ).
cnf(c_6365,plain,
( sz00 != sz00
| xp != sz00
| sz00 = xp ),
inference(instantiation,[status(thm)],[c_6364]) ).
cnf(c_6510,plain,
( sz00 != xp
| ~ aNaturalNumber0(sK0(sz10,xp))
| ~ aNaturalNumber0(sz10)
| sz00 = sz10 ),
inference(superposition,[status(thm)],[c_5771,c_71]) ).
cnf(c_6514,plain,
( sz00 != xp
| ~ aNaturalNumber0(sK0(sz10,xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6510,c_50,c_51]) ).
cnf(c_6695,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sz00 = xp
| aNaturalNumber0(xk) ),
inference(superposition,[status(thm)],[c_128,c_100]) ).
cnf(c_6705,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn
| sz00 = xr ),
inference(superposition,[status(thm)],[c_100,c_6318]) ).
cnf(c_6706,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn
| sz00 = xr ),
inference(superposition,[status(thm)],[c_100,c_5303]) ).
cnf(c_6707,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6695,c_116,c_120]) ).
cnf(c_6759,plain,
( sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn
| sz00 = xr ),
inference(forward_subsumption_resolution,[status(thm)],[c_6706,c_135,c_118,c_141]) ).
cnf(c_6763,plain,
( sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn
| sz00 = xr ),
inference(forward_subsumption_resolution,[status(thm)],[c_6705,c_135,c_118,c_141]) ).
cnf(c_6791,plain,
( ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sdtsldt0(X0,xp)) = X0
| xp = sz00 ),
inference(instantiation,[status(thm)],[c_99]) ).
cnf(c_6809,plain,
( ~ doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00
| xp = sz00 ),
inference(instantiation,[status(thm)],[c_6791]) ).
cnf(c_6967,plain,
( sdtsldt0(xn,xr) = xn
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr) ),
inference(global_subsumption_just,[status(thm)],[c_6759,c_1691,c_6759]) ).
cnf(c_6968,plain,
( sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(renaming,[status(thm)],[c_6967]) ).
cnf(c_7033,plain,
( sdtsldt0(xn,xr) = xn
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr) ),
inference(global_subsumption_just,[status(thm)],[c_6763,c_1691,c_6763]) ).
cnf(c_7034,plain,
( sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(renaming,[status(thm)],[c_7033]) ).
cnf(c_7041,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_7034,c_195]) ).
cnf(c_7042,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_7034,c_52]) ).
cnf(c_7043,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7042,c_118]) ).
cnf(c_7047,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7041,c_118]) ).
cnf(c_7152,plain,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),X0)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,X0) ),
inference(superposition,[status(thm)],[c_5117,c_81]) ).
cnf(c_7238,plain,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),X0)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7152,c_118]) ).
cnf(c_7611,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(X0,sdtsldt0(xn,xr))
| sdtlseqdt0(xn,X0) ),
inference(superposition,[status(thm)],[c_82,c_7238]) ).
cnf(c_7641,plain,
( ~ sdtlseqdt0(sdtsldt0(xn,xr),X0)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(xn,X1) ),
inference(superposition,[status(thm)],[c_7611,c_81]) ).
cnf(c_7863,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(X0,sdtsldt0(xn,xr))
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(xn,X1) ),
inference(superposition,[status(thm)],[c_82,c_7641]) ).
cnf(c_9399,plain,
( sdtpldt0(xn,X0) != sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_7034,c_67]) ).
cnf(c_9661,plain,
( sdtpldt0(xn,X0) != sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_9399,c_118]) ).
cnf(c_9778,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_82,c_142]) ).
cnf(c_9789,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9778,c_118]) ).
cnf(c_9849,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| sz00 = xr ),
inference(superposition,[status(thm)],[c_141,c_99]) ).
cnf(c_9851,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00
| sz00 = xp ),
inference(superposition,[status(thm)],[c_5506,c_99]) ).
cnf(c_9892,plain,
( sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00
| sz00 = xp ),
inference(forward_subsumption_resolution,[status(thm)],[c_9851,c_116,c_49]) ).
cnf(c_9895,plain,
( sdtasdt0(xr,sdtsldt0(xn,xr)) = xn
| sz00 = xr ),
inference(forward_subsumption_resolution,[status(thm)],[c_9849,c_135,c_118]) ).
cnf(c_10240,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xn,sdtpldt0(xn,X0)) ),
inference(instantiation,[status(thm)],[c_195]) ).
cnf(c_11248,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_9789,c_74]) ).
cnf(c_11249,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_11248,c_118]) ).
cnf(c_11388,plain,
( sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_11249,c_6968]) ).
cnf(c_12725,plain,
( ~ sdtlseqdt0(sdtmndt0(sdtsldt0(xn,xr),xn),X0)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(sdtsldt0(xn,xr),sdtpldt0(xn,X0)) ),
inference(superposition,[status(thm)],[c_7034,c_86]) ).
cnf(c_13342,plain,
( ~ sdtlseqdt0(sdtmndt0(sdtsldt0(xn,xr),xn),X0)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(sdtsldt0(xn,xr),sdtpldt0(xn,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12725,c_118]) ).
cnf(c_16554,plain,
( ~ aNaturalNumber0(sK0(xn,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_6968,c_9661]) ).
cnf(c_16671,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_75,c_16554]) ).
cnf(c_16672,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_16671,c_118]) ).
cnf(c_16816,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_9789,c_77]) ).
cnf(c_16867,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_16816,c_118]) ).
cnf(c_19211,plain,
( sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_16867,c_7034]) ).
cnf(c_20146,plain,
sz00 != xr,
inference(global_subsumption_just,[status(thm)],[c_5974,c_1691]) ).
cnf(c_20154,plain,
sz00 != xp,
inference(global_subsumption_just,[status(thm)],[c_6514,c_1687]) ).
cnf(c_22740,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(sdtsldt0(xn,xr),sdtpldt0(xn,X0))
| sdtlseqdt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn))
| sdtlseqdt0(X0,sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_7863,c_13342]) ).
cnf(c_26766,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtpldt0(xn,X0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_29765,plain,
sdtasdt0(xp,sdtsldt0(sz00,xp)) = sz00,
inference(global_subsumption_just,[status(thm)],[c_9892,c_116,c_49,c_147,c_165,c_1687,c_5506,c_6365,c_6809]) ).
cnf(c_30312,plain,
( ~ doDivides0(xr,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xr)
| xr = sz00
| aNaturalNumber0(sdtsldt0(X0,xr)) ),
inference(instantiation,[status(thm)],[c_100]) ).
cnf(c_31711,plain,
sdtasdt0(xr,sdtsldt0(xn,xr)) = xn,
inference(global_subsumption_just,[status(thm)],[c_9895,c_1691,c_9895]) ).
cnf(c_33422,plain,
( sdtpldt0(xn,X0) != sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_19211,c_67]) ).
cnf(c_33684,plain,
( sdtpldt0(xn,X0) != sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_33422,c_118]) ).
cnf(c_41463,plain,
( ~ aNaturalNumber0(sK0(xn,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_11388,c_33684]) ).
cnf(c_41546,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_41463,c_7043,c_7047,c_16672]) ).
cnf(c_41554,plain,
( ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_78,c_41546]) ).
cnf(c_41555,plain,
( ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_41554,c_118]) ).
cnf(c_41903,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_41555,c_5117,c_41555]) ).
cnf(c_41911,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| sz00 = xr ),
inference(superposition,[status(thm)],[c_100,c_41903]) ).
cnf(c_41912,plain,
( sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn
| sz00 = xr ),
inference(forward_subsumption_resolution,[status(thm)],[c_41911,c_135,c_118,c_141]) ).
cnf(c_45129,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(sdtsldt0(xn,xr),sdtpldt0(xn,X0))
| sdtlseqdt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn))
| sdtlseqdt0(X0,sdtsldt0(xn,xr)) ),
inference(global_subsumption_just,[status(thm)],[c_22740,c_7043,c_22740]) ).
cnf(c_45168,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn))
| sdtlseqdt0(X0,sdtsldt0(xn,xr))
| sdtlseqdt0(xn,sdtpldt0(xn,X0)) ),
inference(superposition,[status(thm)],[c_45129,c_7238]) ).
cnf(c_45857,plain,
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(xn,sdtpldt0(xn,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_45168,c_118,c_10240]) ).
cnf(c_45882,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,sdtpldt0(xn,X0))) = sdtpldt0(xn,X0) ),
inference(superposition,[status(thm)],[c_45857,c_74]) ).
cnf(c_45889,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(X0)
| sdtpldt0(xn,sK0(xn,sdtpldt0(xn,X0))) = sdtpldt0(xn,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_45882,c_118]) ).
cnf(c_46088,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xn,sK0(xn,sdtpldt0(xn,X0))) = sdtpldt0(xn,X0) ),
inference(global_subsumption_just,[status(thm)],[c_45889,c_118,c_26766,c_45889]) ).
cnf(c_46099,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(xn,sK0(xn,sdtpldt0(xn,sK0(X0,X1)))) = sdtpldt0(xn,sK0(X0,X1)) ),
inference(superposition,[status(thm)],[c_75,c_46088]) ).
cnf(c_53852,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_82,c_142]) ).
cnf(c_53855,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53852,c_118]) ).
cnf(c_55111,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_53855,c_74]) ).
cnf(c_55158,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_55111,c_118]) ).
cnf(c_55177,plain,
( sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_55158,c_6968]) ).
cnf(c_55279,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_53855,c_77]) ).
cnf(c_55330,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_55279,c_118]) ).
cnf(c_55676,plain,
( sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn)) = sdtsldt0(xn,xr)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_55330,c_7034]) ).
cnf(c_57320,plain,
( sdtpldt0(xn,X0) != sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_55676,c_67]) ).
cnf(c_57384,plain,
( sdtpldt0(xn,X0) != sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| ~ aNaturalNumber0(X0)
| sdtmndt0(sdtsldt0(xn,xr),xn) = X0
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_57320,c_118]) ).
cnf(c_57720,plain,
( ~ aNaturalNumber0(sK0(xn,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_55177,c_57384]) ).
cnf(c_57726,plain,
( sK0(xn,sdtsldt0(xn,xr)) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_57720,c_1691,c_41912]) ).
cnf(c_57732,plain,
( ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn)) ),
inference(superposition,[status(thm)],[c_57726,c_75]) ).
cnf(c_57737,plain,
( ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57732,c_118]) ).
cnf(c_69251,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| xr = sz00
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(instantiation,[status(thm)],[c_30312]) ).
cnf(c_80229,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_118,c_5174]) ).
cnf(c_80558,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_80229,c_53]) ).
cnf(c_80566,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_80558,c_118,c_117]) ).
cnf(c_83262,plain,
( sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn)) ),
inference(global_subsumption_just,[status(thm)],[c_57737,c_135,c_118,c_49,c_141,c_147,c_165,c_1691,c_5117,c_6028,c_57737,c_69251]) ).
cnf(c_84941,plain,
sdtasdt0(xn,xr) = sdtasdt0(xr,xn),
inference(superposition,[status(thm)],[c_135,c_5175]) ).
cnf(c_91055,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sdtpldt0(xn,sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))))) = sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_5117,c_46099]) ).
cnf(c_91471,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtpldt0(xn,sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))))) = sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_91055,c_118]) ).
cnf(c_92720,plain,
( sdtpldt0(xn,sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))))) = sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_91471,c_135,c_118,c_49,c_141,c_147,c_165,c_1691,c_6028,c_69251,c_91471]) ).
cnf(c_92731,plain,
( ~ aNaturalNumber0(sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))))
| ~ aNaturalNumber0(xn)
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) ),
inference(superposition,[status(thm)],[c_92720,c_52]) ).
cnf(c_92755,plain,
( sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) != sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))))
| ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_92720,c_9661]) ).
cnf(c_92762,plain,
( ~ aNaturalNumber0(sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))))
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_92731,c_118]) ).
cnf(c_94314,plain,
( ~ aNaturalNumber0(sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))))
| sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_92755,c_1691,c_6759,c_83262,c_92755]) ).
cnf(c_94322,plain,
( ~ sdtlseqdt0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))))
| ~ aNaturalNumber0(sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))))
| ~ aNaturalNumber0(xn)
| sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_75,c_94314]) ).
cnf(c_94323,plain,
( ~ aNaturalNumber0(sK0(xn,sdtsldt0(xn,xr)))
| sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_6968,c_94314]) ).
cnf(c_94327,plain,
( ~ sdtlseqdt0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))))
| ~ aNaturalNumber0(sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))))
| sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_94322,c_118]) ).
cnf(c_94875,plain,
sdtpldt0(xr,sdtmndt0(xk,xr)) = xk,
inference(global_subsumption_just,[status(thm)],[c_6290,c_1687,c_6290,c_6707,c_80566]) ).
cnf(c_94882,plain,
( ~ aNaturalNumber0(sdtmndt0(xk,xr))
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(xk) ),
inference(superposition,[status(thm)],[c_94875,c_52]) ).
cnf(c_94891,plain,
( ~ aNaturalNumber0(sdtmndt0(xk,xr))
| aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94882,c_135]) ).
cnf(c_95068,plain,
aNaturalNumber0(xk),
inference(global_subsumption_just,[status(thm)],[c_94891,c_1687,c_6707,c_80566]) ).
cnf(c_95110,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(superposition,[status(thm)],[c_95068,c_5173]) ).
cnf(c_95451,plain,
( ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_75,c_94323]) ).
cnf(c_95452,plain,
( ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_95451,c_118]) ).
cnf(c_104121,plain,
( sK0(xn,sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) = sdtmndt0(sdtsldt0(xn,xr),xn)
| sdtsldt0(xn,xr) = xn ),
inference(global_subsumption_just,[status(thm)],[c_94327,c_135,c_118,c_49,c_141,c_147,c_165,c_1691,c_5117,c_6028,c_69251,c_95452]) ).
cnf(c_104137,plain,
( ~ aNaturalNumber0(sdtmndt0(sdtsldt0(xn,xr),xn))
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) ),
inference(superposition,[status(thm)],[c_104121,c_92762]) ).
cnf(c_104148,plain,
( sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr))) = sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn))
| sdtsldt0(xn,xr) = xn ),
inference(superposition,[status(thm)],[c_104121,c_92720]) ).
cnf(c_104428,plain,
( ~ aNaturalNumber0(sK0(xn,sdtpldt0(xn,sdtmndt0(sdtsldt0(xn,xr),xn))))
| sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) ),
inference(superposition,[status(thm)],[c_104148,c_92762]) ).
cnf(c_107046,plain,
( sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtpldt0(xn,sK0(xn,sdtsldt0(xn,xr)))) ),
inference(global_subsumption_just,[status(thm)],[c_104428,c_83262,c_104137]) ).
cnf(c_107059,plain,
( sdtsldt0(xn,xr) = xn
| aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_6968,c_107046]) ).
cnf(c_110564,plain,
( sdtasdt0(xp,xk) != sz00
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sz00 = xp
| sz00 = xk ),
inference(superposition,[status(thm)],[c_95110,c_72]) ).
cnf(c_110577,plain,
sdtasdt0(xp,xk) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_110564,c_132,c_20154,c_95068,c_116]) ).
cnf(c_120150,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_107059,c_135,c_118,c_49,c_141,c_147,c_165,c_1691,c_6028,c_69251]) ).
cnf(c_120341,plain,
sdtasdt0(sdtsldt0(xn,xr),xr) = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(superposition,[status(thm)],[c_120150,c_5176]) ).
cnf(c_120364,plain,
sdtasdt0(sdtsldt0(xn,xr),xr) = xn,
inference(light_normalisation,[status(thm)],[c_120341,c_31711]) ).
cnf(c_122458,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xr)
| sz00 = xr
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(superposition,[status(thm)],[c_120364,c_93]) ).
cnf(c_122467,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(forward_subsumption_resolution,[status(thm)],[c_122458,c_20146,c_135,c_120150]) ).
cnf(c_122504,plain,
sdtsldt0(xn,xr) = xn,
inference(backward_subsumption_resolution,[status(thm)],[c_142,c_122467]) ).
cnf(c_122510,plain,
sdtasdt0(xr,xn) = xn,
inference(demodulation,[status(thm)],[c_31711,c_122504]) ).
cnf(c_122511,plain,
sdtasdt0(xn,xr) = xn,
inference(light_normalisation,[status(thm)],[c_122510,c_84941]) ).
cnf(c_122554,plain,
( sdtasdt0(xn,X0) != xn
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| X0 = xr
| sz00 = xn ),
inference(superposition,[status(thm)],[c_122511,c_69]) ).
cnf(c_122555,plain,
( ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| X0 = xr
| sz00 = xn
| sdtlseqdt0(sdtasdt0(xn,X0),xn) ),
inference(superposition,[status(thm)],[c_122511,c_90]) ).
cnf(c_122561,plain,
( sdtasdt0(xn,X0) != xn
| ~ aNaturalNumber0(X0)
| X0 = xr
| sz00 = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_122554,c_135,c_118]) ).
cnf(c_122568,plain,
( ~ sdtlseqdt0(X0,xr)
| ~ aNaturalNumber0(X0)
| X0 = xr
| sz00 = xn
| sdtlseqdt0(sdtasdt0(xn,X0),xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122555,c_135,c_118]) ).
cnf(c_122824,plain,
( ~ aNaturalNumber0(sz10)
| sz00 = xn
| sz10 = xr ),
inference(superposition,[status(thm)],[c_4905,c_122561]) ).
cnf(c_122831,plain,
( sz00 = xn
| sz10 = xr ),
inference(forward_subsumption_resolution,[status(thm)],[c_122824,c_51]) ).
cnf(c_122840,plain,
sz00 = xn,
inference(global_subsumption_just,[status(thm)],[c_122568,c_1669,c_122831]) ).
cnf(c_123271,plain,
sdtsldt0(sdtasdt0(sz00,xm),xp) = xk,
inference(demodulation,[status(thm)],[c_128,c_122840]) ).
cnf(c_123355,plain,
sdtsldt0(sz00,xp) = xk,
inference(light_normalisation,[status(thm)],[c_123271,c_4914]) ).
cnf(c_123761,plain,
sdtasdt0(xp,xk) = sz00,
inference(demodulation,[status(thm)],[c_29765,c_123355]) ).
cnf(c_123762,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_123761,c_110577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM510+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 10:26:06 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.19/4.74 % SZS status Started for theBenchmark.p
% 29.19/4.74 % SZS status Theorem for theBenchmark.p
% 29.19/4.74
% 29.19/4.74 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 29.19/4.74
% 29.19/4.74 ------ iProver source info
% 29.19/4.74
% 29.19/4.74 git: date: 2023-05-31 18:12:56 +0000
% 29.19/4.74 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 29.19/4.74 git: non_committed_changes: false
% 29.19/4.74 git: last_make_outside_of_git: false
% 29.19/4.74
% 29.19/4.74 ------ Parsing...
% 29.19/4.74 ------ Clausification by vclausify_rel & Parsing by iProver...
% 29.19/4.74
% 29.19/4.74 ------ 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
% 29.19/4.74
% 29.19/4.74 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 29.19/4.74
% 29.19/4.74 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 29.19/4.74 ------ Proving...
% 29.19/4.74 ------ Problem Properties
% 29.19/4.74
% 29.19/4.74
% 29.19/4.74 clauses 86
% 29.19/4.74 conjectures 1
% 29.19/4.74 EPR 33
% 29.19/4.74 Horn 61
% 29.19/4.74 unary 27
% 29.19/4.74 binary 8
% 29.19/4.74 lits 282
% 29.19/4.74 lits eq 78
% 29.19/4.74 fd_pure 0
% 29.19/4.74 fd_pseudo 0
% 29.19/4.74 fd_cond 15
% 29.19/4.74 fd_pseudo_cond 11
% 29.19/4.74 AC symbols 0
% 29.19/4.74
% 29.19/4.74 ------ Schedule dynamic 5 is on
% 29.19/4.74
% 29.19/4.74 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 29.19/4.74
% 29.19/4.74
% 29.19/4.74 ------
% 29.19/4.74 Current options:
% 29.19/4.74 ------
% 29.19/4.74
% 29.19/4.74
% 29.19/4.74
% 29.19/4.74
% 29.19/4.74 ------ Proving...
% 29.19/4.74
% 29.19/4.74
% 29.19/4.74 % SZS status Theorem for theBenchmark.p
% 29.19/4.74
% 29.19/4.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.19/4.74
% 29.19/4.74
%------------------------------------------------------------------------------