TSTP Solution File: NUM483+3 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM483+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 : Fri May 3 02:49:31 EDT 2024
% Result : Theorem 17.97s 3.22s
% Output : CNFRefutation 17.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 36
% Syntax : Number of formulae : 261 ( 43 unt; 0 def)
% Number of atoms : 1197 ( 418 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1512 ( 576 ~; 616 |; 267 &)
% ( 9 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 371 ( 0 sgn 230 !; 59 ?)
% 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(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
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(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(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(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(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(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(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sz00 != X1
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
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(f38,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(f39,axiom,
! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ( iLess0(X0,xk)
=> ? [X1] :
( isPrime0(X1)
& ! [X2] :
( ( ( doDivides0(X2,X1)
| ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X2) )
=> ( X1 = X2
| sz10 = X2 ) )
& sz10 != X1
& sz00 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1700) ).
fof(f40,axiom,
( sz10 != xk
& sz00 != xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716_04) ).
fof(f41,axiom,
~ ( isPrime0(xk)
| ! [X0] :
( ( doDivides0(X0,xk)
& ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) )
& aNaturalNumber0(X0) )
=> ( xk = X0
| sz10 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1725) ).
fof(f42,conjecture,
? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ),
inference(negated_conjecture,[],[f42]) ).
fof(f46,plain,
! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ( iLess0(X0,xk)
=> ? [X1] :
( isPrime0(X1)
& ! [X2] :
( ( ( doDivides0(X2,X1)
| ? [X3] :
( sdtasdt0(X2,X3) = X1
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X2) )
=> ( X1 = X2
| sz10 = X2 ) )
& sz10 != X1
& sz00 != X1
& doDivides0(X1,X0)
& ? [X4] :
( sdtasdt0(X1,X4) = X0
& aNaturalNumber0(X4) )
& aNaturalNumber0(X1) ) ) ),
inference(rectify,[],[f39]) ).
fof(f47,plain,
~ ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) )
& ( doDivides0(X0,xk)
| ? [X3] :
( xk = sdtasdt0(X0,X3)
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X0) ),
inference(rectify,[],[f43]) ).
fof(f48,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f65,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(f66,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,[],[f65]) ).
fof(f69,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f70,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f74,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f73]) ).
fof(f78,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f79,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f81,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f83,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f92,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f93,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f95,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f99,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f103,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f105,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f104]) ).
fof(f108,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(f109,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& ! [X2] :
( X1 = X2
| sz10 = X2
| ( ~ doDivides0(X2,X1)
& ! [X3] :
( sdtasdt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) )
& sz10 != X1
& sz00 != X1
& doDivides0(X1,X0)
& ? [X4] :
( sdtasdt0(X1,X4) = X0
& aNaturalNumber0(X4) )
& aNaturalNumber0(X1) )
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f111,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& ! [X2] :
( X1 = X2
| sz10 = X2
| ( ~ doDivides0(X2,X1)
& ! [X3] :
( sdtasdt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) )
& sz10 != X1
& sz00 != X1
& doDivides0(X1,X0)
& ? [X4] :
( sdtasdt0(X1,X4) = X0
& aNaturalNumber0(X4) )
& aNaturalNumber0(X1) )
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
( ~ isPrime0(xk)
& ? [X0] :
( xk != X0
& sz10 != X0
& doDivides0(X0,xk)
& ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) )
& aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f113,plain,
( ~ isPrime0(xk)
& ? [X0] :
( xk != X0
& sz10 != X0
& doDivides0(X0,xk)
& ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) )
& aNaturalNumber0(X0) ) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 ) )
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f115,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 ) )
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ? [X4] :
( sdtasdt0(X1,X4) = X0
& aNaturalNumber0(X4) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f117,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& ! [X2] :
( X1 = X2
| sz10 = X2
| ( ~ doDivides0(X2,X1)
& ! [X3] :
( sdtasdt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) )
& sz10 != X1
& sz00 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f111,f116]) ).
fof(f118,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 ) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f119,plain,
! [X0] :
( sP1(X0)
| ( ~ doDivides0(X0,xk)
& ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f115,f118]) ).
fof(f120,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,[],[f74]) ).
fof(f121,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,[],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK2(X0,X1)) = X1
& aNaturalNumber0(sK2(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f121,f122]) ).
fof(f126,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,[],[f95]) ).
fof(f127,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,[],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK3(X0,X1)) = X1
& aNaturalNumber0(sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK3(X0,X1)) = X1
& aNaturalNumber0(sK3(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f127,f128]) ).
fof(f132,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,[],[f109]) ).
fof(f133,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,[],[f132]) ).
fof(f134,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,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK4(X0) != X0
& sz10 != sK4(X0)
& doDivides0(sK4(X0),X0)
& aNaturalNumber0(sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
! [X0] :
( ( ( isPrime0(X0)
| ( sK4(X0) != X0
& sz10 != sK4(X0)
& doDivides0(sK4(X0),X0)
& aNaturalNumber0(sK4(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,[sK4])],[f134,f135]) ).
fof(f141,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& ! [X2] :
( X1 = X2
| sz10 = X2
| ( ~ doDivides0(X2,X1)
& ! [X3] :
( sdtasdt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) )
& sz10 != X1
& sz00 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK6(X0))
& ! [X2] :
( sK6(X0) = X2
| sz10 = X2
| ( ~ doDivides0(X2,sK6(X0))
& ! [X3] :
( sdtasdt0(X2,X3) != sK6(X0)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) )
& sz10 != sK6(X0)
& sz00 != sK6(X0)
& doDivides0(sK6(X0),X0)
& sP0(X0,sK6(X0))
& aNaturalNumber0(sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
! [X0] :
( ( isPrime0(sK6(X0))
& ! [X2] :
( sK6(X0) = X2
| sz10 = X2
| ( ~ doDivides0(X2,sK6(X0))
& ! [X3] :
( sdtasdt0(X2,X3) != sK6(X0)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) )
& sz10 != sK6(X0)
& sz00 != sK6(X0)
& doDivides0(sK6(X0),X0)
& sP0(X0,sK6(X0))
& aNaturalNumber0(sK6(X0)) )
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f117,f141]) ).
fof(f143,plain,
( ? [X0] :
( xk != X0
& sz10 != X0
& doDivides0(X0,xk)
& ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) )
& aNaturalNumber0(X0) )
=> ( xk != sK7
& sz10 != sK7
& doDivides0(sK7,xk)
& ? [X1] :
( xk = sdtasdt0(sK7,X1)
& aNaturalNumber0(X1) )
& aNaturalNumber0(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f144,plain,
( ? [X1] :
( xk = sdtasdt0(sK7,X1)
& aNaturalNumber0(X1) )
=> ( xk = sdtasdt0(sK7,sK8)
& aNaturalNumber0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f145,plain,
( ~ isPrime0(xk)
& xk != sK7
& sz10 != sK7
& doDivides0(sK7,xk)
& xk = sdtasdt0(sK7,sK8)
& aNaturalNumber0(sK8)
& aNaturalNumber0(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f113,f144,f143]) ).
fof(f146,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f147,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( sK9(X0) != X0
& sz10 != sK9(X0)
& doDivides0(sK9(X0),X0)
& ? [X2] :
( sdtasdt0(sK9(X0),X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f148,plain,
! [X0] :
( ? [X2] :
( sdtasdt0(sK9(X0),X2) = X0
& aNaturalNumber0(X2) )
=> ( sdtasdt0(sK9(X0),sK10(X0)) = X0
& aNaturalNumber0(sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( ( sK9(X0) != X0
& sz10 != sK9(X0)
& doDivides0(sK9(X0),X0)
& sdtasdt0(sK9(X0),sK10(X0)) = X0
& aNaturalNumber0(sK10(X0))
& aNaturalNumber0(sK9(X0)) )
| sz10 = X0
| sz00 = X0 ) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f146,f148,f147]) ).
fof(f150,plain,
! [X0] :
( sP1(X0)
| ( ~ doDivides0(X0,xk)
& ! [X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f119]) ).
fof(f151,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f152,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f153,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f154,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f155,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f156,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f158,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f159,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f164,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f169,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f172,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f182,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f183,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f185,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f197,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f200,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f204,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f206,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f207,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f212,plain,
! [X0] :
( isPrime0(X0)
| aNaturalNumber0(sK4(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f213,plain,
! [X0] :
( isPrime0(X0)
| doDivides0(sK4(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f214,plain,
! [X0] :
( isPrime0(X0)
| sz10 != sK4(X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f215,plain,
! [X0] :
( isPrime0(X0)
| sK4(X0) != X0
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f216,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f219,plain,
! [X0] :
( aNaturalNumber0(sK6(X0))
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f221,plain,
! [X0] :
( doDivides0(sK6(X0),X0)
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f226,plain,
! [X0] :
( isPrime0(sK6(X0))
| ~ iLess0(X0,xk)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f227,plain,
sz00 != xk,
inference(cnf_transformation,[],[f40]) ).
fof(f228,plain,
sz10 != xk,
inference(cnf_transformation,[],[f40]) ).
fof(f229,plain,
aNaturalNumber0(sK7),
inference(cnf_transformation,[],[f145]) ).
fof(f232,plain,
doDivides0(sK7,xk),
inference(cnf_transformation,[],[f145]) ).
fof(f235,plain,
~ isPrime0(xk),
inference(cnf_transformation,[],[f145]) ).
fof(f238,plain,
! [X0] :
( sdtasdt0(sK9(X0),sK10(X0)) = X0
| sz10 = X0
| sz00 = X0
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f242,plain,
! [X0] :
( ~ isPrime0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f243,plain,
! [X0,X1] :
( sP1(X0)
| sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f244,plain,
! [X0] :
( sP1(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f150]) ).
fof(f245,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f177]) ).
fof(f251,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f200]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f151]) ).
cnf(c_50,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f153]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f152]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_54,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_56,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_63,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_66,plain,
( sdtpldt0(X0,X1) != sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X2 ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f245]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f182]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f185]) ).
cnf(c_94,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_95,plain,
( ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f251]) ).
cnf(c_101,plain,
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f204]) ).
cnf(c_103,plain,
( ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_104,plain,
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_106,plain,
( sK4(X0) != X0
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(X0) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_107,plain,
( sK4(X0) != sz10
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(X0) ),
inference(cnf_transformation,[],[f214]) ).
cnf(c_108,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK4(X0),X0)
| isPrime0(X0) ),
inference(cnf_transformation,[],[f213]) ).
cnf(c_109,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK4(X0))
| isPrime0(X0) ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_113,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f216]) ).
cnf(c_116,plain,
( ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(sK6(X0)) ),
inference(cnf_transformation,[],[f226]) ).
cnf(c_121,plain,
( ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK6(X0),X0) ),
inference(cnf_transformation,[],[f221]) ).
cnf(c_123,plain,
( ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK6(X0)) ),
inference(cnf_transformation,[],[f219]) ).
cnf(c_124,plain,
sz10 != xk,
inference(cnf_transformation,[],[f228]) ).
cnf(c_125,plain,
sz00 != xk,
inference(cnf_transformation,[],[f227]) ).
cnf(c_126,plain,
~ isPrime0(xk),
inference(cnf_transformation,[],[f235]) ).
cnf(c_129,plain,
doDivides0(sK7,xk),
inference(cnf_transformation,[],[f232]) ).
cnf(c_132,plain,
aNaturalNumber0(sK7),
inference(cnf_transformation,[],[f229]) ).
cnf(c_133,plain,
( ~ isPrime0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f242]) ).
cnf(c_137,plain,
( ~ sP1(X0)
| sdtasdt0(sK9(X0),sK10(X0)) = X0
| X0 = sz00
| X0 = sz10 ),
inference(cnf_transformation,[],[f238]) ).
cnf(c_140,negated_conjecture,
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f244]) ).
cnf(c_141,negated_conjecture,
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(X0) ),
inference(cnf_transformation,[],[f243]) ).
cnf(c_149,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_171,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_205,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
cnf(c_208,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_2394,plain,
( X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| aNaturalNumber0(sK4(X0)) ),
inference(resolution_lifted,[status(thm)],[c_109,c_126]) ).
cnf(c_2395,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| aNaturalNumber0(sK4(xk)) ),
inference(unflattening,[status(thm)],[c_2394]) ).
cnf(c_2396,plain,
( xk = sz00
| xk = sz10
| aNaturalNumber0(sK4(xk)) ),
inference(global_subsumption_just,[status(thm)],[c_2395,c_113,c_2395]) ).
cnf(c_2407,plain,
( X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK4(X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_108,c_126]) ).
cnf(c_2408,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| doDivides0(sK4(xk),xk) ),
inference(unflattening,[status(thm)],[c_2407]) ).
cnf(c_2409,plain,
( xk = sz00
| xk = sz10
| doDivides0(sK4(xk),xk) ),
inference(global_subsumption_just,[status(thm)],[c_2408,c_113,c_2408]) ).
cnf(c_2420,plain,
( sK4(X0) != sz10
| X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10 ),
inference(resolution_lifted,[status(thm)],[c_107,c_126]) ).
cnf(c_2421,plain,
( sK4(xk) != sz10
| ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10 ),
inference(unflattening,[status(thm)],[c_2420]) ).
cnf(c_2422,plain,
( sK4(xk) != sz10
| xk = sz00
| xk = sz10 ),
inference(global_subsumption_just,[status(thm)],[c_2421,c_113,c_2421]) ).
cnf(c_2433,plain,
( sK4(X0) != X0
| X0 != xk
| ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10 ),
inference(resolution_lifted,[status(thm)],[c_106,c_126]) ).
cnf(c_2434,plain,
( sK4(xk) != xk
| ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10 ),
inference(unflattening,[status(thm)],[c_2433]) ).
cnf(c_4822,negated_conjecture,
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(X0) ),
inference(demodulation,[status(thm)],[c_141]) ).
cnf(c_4823,negated_conjecture,
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(demodulation,[status(thm)],[c_140]) ).
cnf(c_4824,plain,
X0 = X0,
theory(equality) ).
cnf(c_4826,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_6348,plain,
sdtpldt0(sz00,xk) = xk,
inference(superposition,[status(thm)],[c_113,c_56]) ).
cnf(c_6572,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_51,c_54]) ).
cnf(c_6801,plain,
( sz10 != X0
| xk != X0
| sz10 = xk ),
inference(instantiation,[status(thm)],[c_4826]) ).
cnf(c_6803,plain,
( sz00 != X0
| xk != X0
| sz00 = xk ),
inference(instantiation,[status(thm)],[c_4826]) ).
cnf(c_6804,plain,
( sz00 != sz00
| xk != sz00
| sz00 = xk ),
inference(instantiation,[status(thm)],[c_6803]) ).
cnf(c_6956,plain,
sdtpldt0(sz10,xk) = sdtpldt0(xk,sz10),
inference(superposition,[status(thm)],[c_113,c_6572]) ).
cnf(c_6991,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(xk,sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm)],[c_6956,c_208]) ).
cnf(c_6992,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| aNaturalNumber0(sdtpldt0(sz10,xk)) ),
inference(superposition,[status(thm)],[c_6956,c_52]) ).
cnf(c_6993,plain,
aNaturalNumber0(sdtpldt0(sz10,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_6992,c_113,c_51]) ).
cnf(c_6994,plain,
sdtlseqdt0(xk,sdtpldt0(sz10,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_6991,c_113,c_51]) ).
cnf(c_7005,plain,
sdtasdt0(sdtpldt0(sz10,xk),sz00) = sz00,
inference(superposition,[status(thm)],[c_6993,c_63]) ).
cnf(c_7106,plain,
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| doDivides0(X0,xk) ),
inference(instantiation,[status(thm)],[c_101]) ).
cnf(c_7401,plain,
( sz10 != sz10
| xk != sz10
| sz10 = xk ),
inference(instantiation,[status(thm)],[c_6801]) ).
cnf(c_7402,plain,
sz10 = sz10,
inference(instantiation,[status(thm)],[c_4824]) ).
cnf(c_7459,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(sz00)
| doDivides0(sdtpldt0(sz10,xk),sz00) ),
inference(superposition,[status(thm)],[c_7005,c_205]) ).
cnf(c_7462,plain,
doDivides0(sdtpldt0(sz10,xk),sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_7459,c_49,c_6993]) ).
cnf(c_7640,plain,
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| xk = sz00
| sdtlseqdt0(X0,xk) ),
inference(instantiation,[status(thm)],[c_104]) ).
cnf(c_7811,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sK7)
| sz00 = xk
| sdtlseqdt0(sK7,xk) ),
inference(superposition,[status(thm)],[c_129,c_104]) ).
cnf(c_7828,plain,
sdtlseqdt0(sK7,xk),
inference(forward_subsumption_resolution,[status(thm)],[c_7811,c_125,c_132,c_113]) ).
cnf(c_7851,plain,
( ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(xk)
| sz00 = xk
| sz10 = xk
| sP1(sK4(xk))
| isPrime0(xk) ),
inference(superposition,[status(thm)],[c_108,c_4823]) ).
cnf(c_7852,plain,
( ~ aNaturalNumber0(sK4(xk))
| sP1(sK4(xk)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7851,c_126,c_124,c_125,c_113]) ).
cnf(c_7871,plain,
sP1(sK4(xk)),
inference(global_subsumption_just,[status(thm)],[c_7852,c_49,c_125,c_124,c_149,c_171,c_2396,c_6804,c_7401,c_7402,c_7852]) ).
cnf(c_9136,plain,
( sdtasdt0(sK9(sK4(xk)),sK10(sK4(xk))) = sK4(xk)
| sK4(xk) = sz00
| sK4(xk) = sz10 ),
inference(superposition,[status(thm)],[c_7871,c_137]) ).
cnf(c_9214,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sK7)
| sdtlseqdt0(sK7,X0) ),
inference(superposition,[status(thm)],[c_7828,c_81]) ).
cnf(c_9223,plain,
( ~ sdtlseqdt0(xk,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sK7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9214,c_132,c_113]) ).
cnf(c_9524,plain,
( sK4(xk) = sz00
| sdtasdt0(sK9(sK4(xk)),sK10(sK4(xk))) = sK4(xk) ),
inference(global_subsumption_just,[status(thm)],[c_9136,c_49,c_125,c_124,c_149,c_171,c_2422,c_6804,c_7401,c_7402,c_9136]) ).
cnf(c_9525,plain,
( sdtasdt0(sK9(sK4(xk)),sK10(sK4(xk))) = sK4(xk)
| sK4(xk) = sz00 ),
inference(renaming,[status(thm)],[c_9524]) ).
cnf(c_9530,plain,
( ~ aNaturalNumber0(sK9(sK4(xk)))
| ~ aNaturalNumber0(sK10(sK4(xk)))
| sK4(xk) = sz00
| aNaturalNumber0(sK4(xk)) ),
inference(superposition,[status(thm)],[c_9525,c_53]) ).
cnf(c_9532,plain,
( sK4(xk) != xk
| ~ aNaturalNumber0(sK9(sK4(xk)))
| ~ aNaturalNumber0(sK10(sK4(xk)))
| sK4(xk) = sz00
| sP1(sK9(sK4(xk))) ),
inference(superposition,[status(thm)],[c_9525,c_4822]) ).
cnf(c_9552,plain,
sK4(xk) != xk,
inference(global_subsumption_just,[status(thm)],[c_9532,c_113,c_49,c_125,c_124,c_149,c_171,c_2434,c_6804,c_7401,c_7402]) ).
cnf(c_9598,plain,
aNaturalNumber0(sK4(xk)),
inference(global_subsumption_just,[status(thm)],[c_9530,c_49,c_125,c_124,c_149,c_171,c_2396,c_6804,c_7401,c_7402]) ).
cnf(c_9603,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sK4(xk),X0) = sdtpldt0(X0,sK4(xk)) ),
inference(superposition,[status(thm)],[c_9598,c_54]) ).
cnf(c_9604,plain,
sdtpldt0(sK4(xk),sz10) = sdtpldt0(sz10,sK4(xk)),
inference(superposition,[status(thm)],[c_9598,c_6572]) ).
cnf(c_10153,plain,
( ~ doDivides0(X0,sK4(xk))
| ~ doDivides0(sK4(xk),xk)
| ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| doDivides0(X0,xk) ),
inference(instantiation,[status(thm)],[c_7106]) ).
cnf(c_11368,plain,
( ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sK4(xk),sdtpldt0(sz10,sK4(xk))) ),
inference(superposition,[status(thm)],[c_9604,c_208]) ).
cnf(c_11369,plain,
( ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(sz10)
| aNaturalNumber0(sdtpldt0(sz10,sK4(xk))) ),
inference(superposition,[status(thm)],[c_9604,c_52]) ).
cnf(c_11372,plain,
aNaturalNumber0(sdtpldt0(sz10,sK4(xk))),
inference(forward_subsumption_resolution,[status(thm)],[c_11369,c_51,c_9598]) ).
cnf(c_11373,plain,
sdtlseqdt0(sK4(xk),sdtpldt0(sz10,sK4(xk))),
inference(forward_subsumption_resolution,[status(thm)],[c_11368,c_51,c_9598]) ).
cnf(c_11497,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sK4(xk)),X0)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK4(xk)))
| ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sK4(xk),X0) ),
inference(superposition,[status(thm)],[c_11373,c_81]) ).
cnf(c_11502,plain,
( ~ sdtlseqdt0(sdtpldt0(sz10,sK4(xk)),X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sK4(xk),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11497,c_9598,c_11372]) ).
cnf(c_21312,plain,
sdtpldt0(sK4(xk),xk) = sdtpldt0(xk,sK4(xk)),
inference(superposition,[status(thm)],[c_113,c_9603]) ).
cnf(c_25221,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(X0,xk)
| sdtlseqdt0(sK7,X0) ),
inference(superposition,[status(thm)],[c_82,c_9223]) ).
cnf(c_25227,plain,
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,xk)
| sdtlseqdt0(sK7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25221,c_113]) ).
cnf(c_26922,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,sK4(xk)))
| ~ aNaturalNumber0(xk)
| sdtlseqdt0(sK7,sdtpldt0(sz10,sK4(xk)))
| sdtlseqdt0(sK4(xk),xk) ),
inference(superposition,[status(thm)],[c_25227,c_11502]) ).
cnf(c_26959,plain,
( sdtlseqdt0(sK7,sdtpldt0(sz10,sK4(xk)))
| sdtlseqdt0(sK4(xk),xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26922,c_113,c_11372]) ).
cnf(c_27548,plain,
( ~ doDivides0(sK4(xk),xk)
| ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(xk)
| xk = sz00
| sdtlseqdt0(sK4(xk),xk) ),
inference(instantiation,[status(thm)],[c_7640]) ).
cnf(c_33238,plain,
( ~ doDivides0(X0,sdtpldt0(xk,sK4(xk)))
| ~ doDivides0(X0,sK4(xk))
| ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| doDivides0(X0,xk) ),
inference(superposition,[status(thm)],[c_21312,c_103]) ).
cnf(c_33268,plain,
( ~ doDivides0(X0,sdtpldt0(xk,sK4(xk)))
| ~ doDivides0(X0,sK4(xk))
| ~ aNaturalNumber0(X0)
| doDivides0(X0,xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33238,c_113,c_9598]) ).
cnf(c_35474,plain,
sdtlseqdt0(sK4(xk),xk),
inference(global_subsumption_just,[status(thm)],[c_26959,c_113,c_49,c_125,c_124,c_149,c_171,c_2395,c_2408,c_6804,c_7401,c_7402,c_27548]) ).
cnf(c_35480,plain,
( ~ aNaturalNumber0(sK4(xk))
| ~ aNaturalNumber0(xk)
| sK4(xk) = xk
| iLess0(sK4(xk),xk) ),
inference(superposition,[status(thm)],[c_35474,c_94]) ).
cnf(c_35483,plain,
iLess0(sK4(xk),xk),
inference(forward_subsumption_resolution,[status(thm)],[c_35480,c_9552,c_113,c_9598]) ).
cnf(c_35817,plain,
( ~ aNaturalNumber0(sK4(xk))
| sK4(xk) = sz00
| sK4(xk) = sz10
| aNaturalNumber0(sK6(sK4(xk))) ),
inference(superposition,[status(thm)],[c_35483,c_123]) ).
cnf(c_35818,plain,
( ~ aNaturalNumber0(sK4(xk))
| sK4(xk) = sz00
| sK4(xk) = sz10
| isPrime0(sK6(sK4(xk))) ),
inference(superposition,[status(thm)],[c_35483,c_116]) ).
cnf(c_35819,plain,
( sK4(xk) = sz00
| sK4(xk) = sz10
| isPrime0(sK6(sK4(xk))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35818,c_9598]) ).
cnf(c_35823,plain,
( sK4(xk) = sz00
| sK4(xk) = sz10
| aNaturalNumber0(sK6(sK4(xk))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35817,c_9598]) ).
cnf(c_35831,plain,
( sK4(xk) = sz00
| isPrime0(sK6(sK4(xk))) ),
inference(global_subsumption_just,[status(thm)],[c_35819,c_49,c_125,c_124,c_149,c_171,c_2422,c_6804,c_7401,c_7402,c_35819]) ).
cnf(c_35837,plain,
( ~ sP1(sK6(sK4(xk)))
| sK4(xk) = sz00 ),
inference(superposition,[status(thm)],[c_35831,c_133]) ).
cnf(c_57000,plain,
( ~ doDivides0(X0,sK4(xk))
| ~ aNaturalNumber0(X0)
| doDivides0(X0,xk) ),
inference(global_subsumption_just,[status(thm)],[c_33268,c_113,c_49,c_125,c_124,c_149,c_171,c_2396,c_2409,c_6804,c_7401,c_7402,c_10153]) ).
cnf(c_57010,plain,
( ~ aNaturalNumber0(sK6(sK4(xk)))
| ~ iLess0(sK4(xk),xk)
| ~ aNaturalNumber0(sK4(xk))
| sK4(xk) = sz00
| sK4(xk) = sz10
| doDivides0(sK6(sK4(xk)),xk) ),
inference(superposition,[status(thm)],[c_121,c_57000]) ).
cnf(c_57038,plain,
( ~ aNaturalNumber0(sK6(sK4(xk)))
| sK4(xk) = sz00
| sK4(xk) = sz10
| doDivides0(sK6(sK4(xk)),xk) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57010,c_9598,c_35483]) ).
cnf(c_57159,plain,
( sK4(xk) = sz00
| doDivides0(sK6(sK4(xk)),xk) ),
inference(global_subsumption_just,[status(thm)],[c_57038,c_49,c_125,c_124,c_149,c_171,c_2422,c_6804,c_7401,c_7402,c_35823,c_57038]) ).
cnf(c_57173,plain,
( ~ aNaturalNumber0(sK6(sK4(xk)))
| sK4(xk) = sz00
| sP1(sK6(sK4(xk))) ),
inference(superposition,[status(thm)],[c_57159,c_4823]) ).
cnf(c_57599,plain,
sK4(xk) = sz00,
inference(global_subsumption_just,[status(thm)],[c_57173,c_49,c_125,c_124,c_149,c_171,c_2422,c_6804,c_7401,c_7402,c_35823,c_35837,c_57173]) ).
cnf(c_57603,plain,
( ~ doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,xk) ),
inference(demodulation,[status(thm)],[c_57000,c_57599]) ).
cnf(c_58244,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| doDivides0(sdtpldt0(sz10,xk),xk) ),
inference(superposition,[status(thm)],[c_7462,c_57603]) ).
cnf(c_58261,plain,
doDivides0(sdtpldt0(sz10,xk),xk),
inference(forward_subsumption_resolution,[status(thm)],[c_58244,c_6993]) ).
cnf(c_60292,plain,
( ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(xk)
| sz00 = xk
| sdtlseqdt0(sdtpldt0(sz10,xk),xk) ),
inference(superposition,[status(thm)],[c_58261,c_104]) ).
cnf(c_60296,plain,
sdtlseqdt0(sdtpldt0(sz10,xk),xk),
inference(forward_subsumption_resolution,[status(thm)],[c_60292,c_125,c_113,c_6993]) ).
cnf(c_60948,plain,
( ~ sdtlseqdt0(xk,sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(sdtpldt0(sz10,xk))
| ~ aNaturalNumber0(xk)
| sdtpldt0(sz10,xk) = xk ),
inference(superposition,[status(thm)],[c_60296,c_80]) ).
cnf(c_60957,plain,
sdtpldt0(sz10,xk) = xk,
inference(forward_subsumption_resolution,[status(thm)],[c_60948,c_113,c_6993,c_6994]) ).
cnf(c_61042,plain,
( sdtpldt0(X0,xk) != xk
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| X0 = sz10 ),
inference(superposition,[status(thm)],[c_60957,c_66]) ).
cnf(c_61049,plain,
( sdtpldt0(X0,xk) != xk
| ~ aNaturalNumber0(X0)
| X0 = sz10 ),
inference(forward_subsumption_resolution,[status(thm)],[c_61042,c_113,c_51]) ).
cnf(c_61075,plain,
( sdtpldt0(sz00,xk) != xk
| ~ aNaturalNumber0(sz00)
| sz00 = sz10 ),
inference(instantiation,[status(thm)],[c_61049]) ).
cnf(c_61076,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_61075,c_6348,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM483+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 20:05:01 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.97/3.22 % SZS status Started for theBenchmark.p
% 17.97/3.22 % SZS status Theorem for theBenchmark.p
% 17.97/3.22
% 17.97/3.22 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.97/3.22
% 17.97/3.22 ------ iProver source info
% 17.97/3.22
% 17.97/3.22 git: date: 2024-05-02 19:28:25 +0000
% 17.97/3.22 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.97/3.22 git: non_committed_changes: false
% 17.97/3.22
% 17.97/3.22 ------ Parsing...
% 17.97/3.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.97/3.22
% 17.97/3.22 ------ 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
% 17.97/3.22
% 17.97/3.22 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.97/3.22
% 17.97/3.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.97/3.22 ------ Proving...
% 17.97/3.22 ------ Problem Properties
% 17.97/3.22
% 17.97/3.22
% 17.97/3.22 clauses 88
% 17.97/3.22 conjectures 2
% 17.97/3.22 EPR 25
% 17.97/3.22 Horn 53
% 17.97/3.22 unary 15
% 17.97/3.22 binary 10
% 17.97/3.22 lits 332
% 17.97/3.22 lits eq 110
% 17.97/3.22 fd_pure 0
% 17.97/3.22 fd_pseudo 0
% 17.97/3.22 fd_cond 23
% 17.97/3.22 fd_pseudo_cond 13
% 17.97/3.22 AC symbols 0
% 17.97/3.22
% 17.97/3.22 ------ Schedule dynamic 5 is on
% 17.97/3.22
% 17.97/3.22 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.97/3.22
% 17.97/3.22
% 17.97/3.22 ------
% 17.97/3.22 Current options:
% 17.97/3.22 ------
% 17.97/3.22
% 17.97/3.22
% 17.97/3.22
% 17.97/3.22
% 17.97/3.22 ------ Proving...
% 17.97/3.22
% 17.97/3.22
% 17.97/3.22 % SZS status Theorem for theBenchmark.p
% 17.97/3.22
% 17.97/3.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.97/3.22
% 17.97/3.22
%------------------------------------------------------------------------------